JP2018071963A - Hvac system with multivariable optimization using plural single-variable extremum-seeking controllers - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an HVAC system with multivariable optimization using a plurality of single-variable extremum-seeking controllers.SOLUTION: An HVAC system 20 for a building includes a plant and a plurality of single-variable extremum-seeking controllers (ESCs). Each of the single-variable ESCs is configured to perturb a different manipulated variable with a different excitation signal and provide the manipulated variables as perturbed inputs to the plant. The plant uses multiple perturbed inputs to concurrently affect a performance variable. The single-variable ESCs are configured to estimate a gradient of the performance variable with respect to each of the manipulated variables and independently drive the gradients toward zero by independently modulating the manipulated variables.SELECTED DRAWING: Figure 2

Description

CROSS REFERENCE TO RELATED APPLICATIONS This application was filed on March 24, 2016, which claims the benefit and priority of US Provisional Patent Application No. 62 / 296,713, filed February 18, 2016. Claims the benefit and priority of US patent application Ser. No. 15 / 284,468, filed Oct. 3, 2016, which is a continuation-in-part of US patent application Ser. No. 15 / 080,435. The entire disclosure of each of these patent applications is incorporated herein by reference.

  The present disclosure relates generally to extreme value search control (ESC) systems. ESC is a class of self-optimizing control strategies that can dynamically search for unknown and / or time-varying inputs of a system to optimize a particular figure of merit. ESC can be viewed as a mechanical realization of gradient search through the use of dither signals. The slope of the system output y with respect to the system input u can be obtained by slightly perturbing the system operation and applying demodulation means. Optimization of system performance can be obtained by bringing the slope to zero by using a negative feedback loop in a closed loop system. ESC is a non-model based control strategy, which means that ESC does not need a model of the control system to optimize the system.

US Pat. No. 8,473,080 US Pat. No. 7,827,813 US Pat. No. 8,027,742 US Pat. No. 8,200,345 US Pat. No. 8,200,344 US patent application Ser. No. 14 / 495,773 US patent application Ser. No. 14 / 538,700 US Patent Application No. 14 / 975,527 US patent application Ser. No. 14 / 961,747 US patent application Ser. No. 15 / 232,800

  Multi-variable optimization with inseparable variables can be a difficult problem to solve using ESC, because the adjustment of the gain of each ESC feedback loop can depend on knowledge of all channels. Previous solutions to this problem ideally use a centralized multivariable extremum search controller with information about the performance map Hessian. However, a centralized multivariable controller is difficult to implement, configure and troubleshoot, which makes it difficult to implement these solutions in practice.

  One implementation of the present disclosure is a building heating, ventilation or air conditioning (HVAC) system. The HVAC system includes a plant having an HVAC facility operable to affect a building's environmental conditions, a first single variable extreme value search controller (ESC), and a second single variable ESC. The first single variable ESC is configured to perturb the first manipulated variable using the first excitation signal and to provide the first manipulated variable as a first perturbation input to the plant. The second single variable ESC is configured to perturb the second manipulated variable using the second excitation signal and to provide the second manipulated variable as a second perturbation input to the plant. The plant uses both perturbation inputs to affect performance variables simultaneously. Both single variable ESCs are configured to receive the same performance variable as feedback from the plant. The first single variable ESC is configured to estimate a first slope of the performance variable relative to the first manipulated variable. The second single variable ESC is configured to estimate a second slope of the performance variable relative to the second manipulated variable. The single variable ESC is configured to independently bring the first and second slopes to zero by independently adjusting the first and second manipulated variables.

  Another implementation of the present disclosure is another HVAC system in a building. The HVAC system provides a plant with HVAC equipment operable to affect the environmental conditions of the building and a first set of manipulated variables as input to the plant while operating in a first mode of operation. A single set of configured single variable extremum search controllers (ESCs) and a single unit configured to provide a second set of manipulated variables as input to the plant while operating in a second mode of operation. And a second set of univariate ESCs. The multivariable ESC switches from the first set of single variable ESCs to the second set of single variable ESCs in response to detecting a transition from the first mode of operation to the second mode of operation. Configured.

  Another implementation of the present disclosure is a method for operating a building heating and ventilation or air conditioning (HVAC) system. The method includes perturbing a first manipulated variable using a first excitation signal, perturbing a second manipulated variable using a second excitation signal, and a first perturbation input to the plant. Providing a second operational variable and a second operational variable. The plant includes HVAC equipment and uses both perturbation inputs to simultaneously affect performance variables. The method receives the performance variable as feedback from the plant, estimates a first slope of the performance variable for the first manipulated variable, and estimates a second slope of the performance variable for the second manipulated variable; And independently adjusting the second manipulated variable to independently bring the first and second slopes to zero. The method includes operating the plant HVAC facility to influence the environmental conditions of the building using the first and second operating variables.

  Those skilled in the art will appreciate that the summary is merely exemplary and is not intended to be limiting in any way. Other aspects of the devices and / or processes described herein, features and advantages of the invention, as defined solely by the claims, are described in detail in conjunction with the accompanying drawings. It will become clear in the explanation.

1 is a drawing of a building in which an extreme value search control system can be implemented, according to some embodiments. 1 is a block diagram of a building HVAC system that can implement an extreme value search control system, according to some embodiments. FIG. FIG. 2 is a block diagram of an extreme value search control system that uses a periodic dither signal to perturb the control input provided to the plant, according to some embodiments. FIG. 4 is a block diagram of another extreme search control system that uses a periodic dither signal to perturb the control input provided to the plant, according to some embodiments. In some embodiments, a recursive estimation technique is used to estimate a slope or coefficient that uses a stochastic dither signal to perturb the control input provided to the plant and associates the plant output with the control input. It is a block diagram of the used extreme value search control system. FIG. 6A is a graph of a control input provided to a plant showing periodic oscillations caused by perturbing the control input with a periodic dither signal, according to some embodiments. FIG. 6B is a graph of performance variables received from a plant resulting from the perturbation control input shown in FIG. 6A, according to some embodiments. FIG. 7A is a graph of a control input provided to a plant when a stochastic excitation signal is used to perturb the control input, according to some embodiments. FIG. 7B is a graph of performance variables received from a plant resulting from the perturbation control input shown in FIG. 7A, according to some embodiments. FIG. 3 is a flow diagram illustrating an extreme value search control technique in which a stochastic excitation signal is used to perturb a control input to a plant, according to some embodiments. FIG. 4 is a flow diagram illustrating an extreme value search control technique in which normalized correlation coefficients are used to associate performance variables received from a plant with control inputs provided to the plant, according to some embodiments. FIG. 2 is a block diagram of a cooling water plant that may implement the systems and methods of the present disclosure, according to some embodiments. FIG. 10B is a flow diagram illustrating an extreme search control technique in which a stochastic excitation signal is used to perturb the condenser water temperature setpoint of the cooling water plant of FIG. 10A, according to some embodiments. FIG. 10B is a flow diagram illustrating an extreme search control technique in which a normalized correlation coefficient is used to correlate total system power consumption with the condenser water temperature setpoint of the cooling water plant of FIG. 10A, according to some embodiments. . 2 is a block diagram of another cooling water plant that may implement the systems and methods of the present disclosure according to some embodiments. FIG. FIG. 11B is a flow diagram illustrating an extreme search control technique in which stochastic excitation signals are used to perturb the condenser water pump speed and cooling tower fan speed of the cooling water plant of FIG. 11A, according to some embodiments. . FIG. 10 illustrates an extreme search control technique in which normalized correlation coefficients are used to correlate total system power consumption with the condenser water pump speed and cooling tower fan speed of the cooling water plant of FIG. 11A, according to some embodiments. FIG. 1 is a block diagram of a variable refrigerant flow system that can implement the systems and methods of the present disclosure in accordance with some embodiments. FIG. 12B is a flow diagram illustrating an extreme value search control technique in which a stochastic excitation signal is used to perturb the refrigerant pressure setpoint of the variable refrigerant flow system of FIG. 12A, according to some embodiments. 12B is a flow diagram illustrating an extreme value search control technique in which a normalized correlation coefficient is used to correlate total system power consumption with the refrigerant pressure setpoint of the variable refrigerant flow system of FIG. 12A, according to some embodiments. 2 is a block diagram of another variable refrigerant flow system that can implement the systems and methods of the present disclosure, according to some embodiments. FIG. FIG. 13B is a flow diagram illustrating an extreme value search control technique in which stochastic excitation signals are used to perturb the refrigerant pressure setpoint and refrigerant superheat setpoint of the variable refrigerant flow system of FIG. 13A, according to some embodiments. . FIG. 14 illustrates an extreme value search control technique in which normalized correlation coefficients are used to correlate total system power consumption with the refrigerant pressure setpoint and refrigerant superheat setpoint of the variable refrigerant flow system of FIG. 13A, according to some embodiments. FIG. FIG. 2 is a block diagram of a vapor compression system that can implement the systems and methods of the present disclosure, according to some embodiments. FIG. 14B is a flow diagram illustrating an extreme value search control technique in which a stochastic excitation signal is used to perturb the charge temperature setpoint of the vapor compression system of FIG. 14A, according to some embodiments. FIG. 14B is a flow diagram illustrating an extreme value search control technique in which a normalized correlation coefficient is used to correlate total system power consumption with the charge air temperature setpoint of the vapor compression system of FIG. 14A, according to some embodiments. FIG. 6 is a block diagram of another vapor compression system that can implement the systems and methods of the present disclosure, according to some embodiments. FIG. 15B is a flow diagram illustrating an extreme search control technique in which a stochastic excitation signal is used to perturb the evaporator fan speed of the vapor compression system of FIG. 15A, according to some embodiments. FIG. 15B is a flow diagram illustrating an extreme search control technique in which a normalized correlation coefficient is used to correlate total system power consumption with the evaporator fan speed of the vapor compression system of FIG. 15A, according to some embodiments. FIG. 6 is a block diagram of another vapor compression system that can implement the systems and methods of the present disclosure, according to some embodiments. FIG. 16B is a flow diagram illustrating an extreme search control technique in which a stochastic excitation signal is used to perturb the charge temperature setpoint and condenser fan speed of the vapor compression system of FIG. 16A, according to some embodiments. . 16 illustrates an extreme search control technique in which a normalized correlation coefficient is used to correlate total system power consumption with the charge temperature setpoint and condenser fan speed of the vapor compression system of FIG. 16A, according to some embodiments. FIG. 2 is a block diagram of another extreme value search control system that uses a multivariable extreme value search controller to provide multiple manipulated variables to a multiple input single output (MISO) system, according to some embodiments. FIG. 2 is a block diagram of another extreme value search control system that uses multiple single variable extreme value search controllers to provide multiple manipulated variables to a MISO system, according to some embodiments. FIG. 2 is a block diagram of another extreme value search control system using a multivariable controller having multiple single variable extreme value search controllers to provide multiple manipulated variables to the MISO system, according to some embodiments. FIG. 2 is a block diagram of an example extreme value search control system that uses two single variable extreme value search controllers to provide two manipulated variables to a MISO system, according to some embodiments. FIG. FIG. 21 is a graph illustrating performance variables that converge to an optimal value when controlled by the extreme value search control system of FIG. 20 according to some embodiments. FIG. 21 is a graph illustrating a first manipulated variable that converges to an optimal value when controlled by the extreme value search control system of FIG. 20 according to some embodiments. FIG. 21 is a graph illustrating a second manipulated variable that converges to an optimal value when controlled by the extreme value search control system of FIG. 20 according to some embodiments. FIG. 3 is a flow diagram illustrating an extreme value search control technique in which multiple single variable extreme value search controllers are used to provide multiple manipulated variables to a MISO system, according to some embodiments. FIG. 3 is a flow diagram illustrating an extreme value search control technique in which a multivariable controller switches between different sets of single variable extreme value search controllers as soon as there is a transition between operating modes, according to some embodiments. 2 is a block diagram of another cooling water plant that may implement the systems and methods of the present disclosure according to some embodiments. FIG. 2 is a block diagram of another variable refrigerant flow system that can implement the systems and methods of the present disclosure, according to some embodiments. FIG. FIG. 6 is a block diagram of another vapor compression system that can implement the systems and methods of the present disclosure, according to some embodiments.

Overview Referring generally to the drawings, various extreme value search control (ESC) systems and methods according to some embodiments are illustrated. In general, ESC is a class of self-optimizing control strategies that can dynamically search for unknown and / or time-varying inputs of a system to optimize a particular figure of merit. ESC can be viewed as a mechanical realization of gradient search through the use of dither signals. The slope of the system output y with respect to the system input u can be obtained by slightly perturbing the system operation and applying demodulation means.

  Optimization of system performance can be obtained by bringing the slope to zero by using a feedback loop of a closed loop system. ESC is a non-model based control strategy, which means that ESC does not need a model of the control system to optimize the system. Regarding various mounting forms of ESC, (Patent Document 1), (Patent Document 2), (Patent Document 3), (Patent Document 4), (Patent Document 5), (Patent Document 6), (Patent Document 7) , (Patent Document 8) and (Patent Document 9). Each of these patents and patent applications is incorporated herein by reference.

  In some embodiments, the extreme value search controller uses the stochastic excitation signal q to perturb the control input u provided to the plant. The controller may include a stochastic signal generator configured to generate a stochastic signal. A stochastic signal can be a random signal (eg, random walk signal, white noise signal, etc.), aperiodic signal, unpredictable signal, disturbance signal, or any other type of non-deterministic or non-repetitive signal. It can be. In some embodiments, the stochastic signal has a non-zero average. The stochastic signal can be integrated to generate the excitation signal q.

The stochastic excitation signal q can provide a variation of the control input u sufficient to estimate the slope of the plant output (ie, the performance variable y) relative to the control input u. The stochastic excitation signal q has several advantages over the conventional periodic dither signal v. For example, the stochastic excitation signal q is not as perceptible as the conventional periodic dither signal v. Therefore, the effect of the stochastic excitation signal q on the control input u is not as pronounced as the periodic oscillation caused by the conventional periodic dither signal v. Another advantage of the stochastic excitation signal q is that the controller is easier to tune because the dither frequency ω _v is no longer a required parameter. Accordingly, the controller does not need to know or estimate the natural frequency of the plant in generating the stochastic excitation signal q.

の推定を生成するために、再帰的最小二乗（ＲＬＳ）推定技法を使用することができる。いくつかの実施形態では、コントローラは、ＲＬＳ推定技法の一部として指数忘却を使用する。例えば、コントローラは、再帰的推定技法で使用される性能変数ｙ、制御入力ｕおよび／または他の変数の指数加重移動平均（ＥＷＭＡ）を計算するように構成することができる。指数忘却は、データ格納に必要な量を低減し（バッチ処理と比べて）、コントローラが最近のデータに対してより感度が高い状態ひいては最適点のシフトに対してより感応度が高い状態のままでいられるようにする。 In some embodiments, the extreme value search controller uses a recursive estimation technique to estimate the slope of the performance variable y with respect to the control input u. For example, the controller has a gradient

A recursive least square (RLS) estimation technique can be used to generate an estimate of. In some embodiments, the controller uses exponential forgetting as part of the RLS estimation technique. For example, the controller can be configured to calculate an exponential weighted moving average (EWMA) of the performance variable y, control input u, and / or other variables used in the recursive estimation technique. Exponential forgetting reduces the amount required to store data (compared to batch processing), and keeps the controller more sensitive to recent data and thus more sensitive to optimal point shifts. To be able to go.

と関連付ける（例えば、

に比例する）ことができるが、性能変数ｙの範囲に基づいてスケーリングすることができる。例えば、相関係数ρは、範囲−１≦ρ≦１にスケーリングされた性能勾配

の正規化尺度であり得る。正規化相関係数ρは、性能変数ｙと制御入力ｕとの間の共分散、性能変数ｙの分散および制御入力ｕの分散に基づいて推定することができる。いくつかの実施形態では、正規化相関係数ρは、再帰的推定プロセスを使用して推定することができる。 In some embodiments, the extreme value search controller estimates a normalized correlation coefficient ρ that associates the performance variable y with the control input u. The correlation coefficient ρ is the performance gradient

Associated with (for example,

Can be scaled based on the range of the performance variable y. For example, the correlation coefficient ρ is a performance gradient scaled to the range −1 ≦ ρ ≦ 1.

Can be a normalization measure. The normalized correlation coefficient ρ can be estimated based on the covariance between the performance variable y and the control input u, the variance of the performance variable y, and the variance of the control input u. In some embodiments, the normalized correlation coefficient ρ can be estimated using a recursive estimation process.

の代わりに、フィードバックコントローラによって使用することができる。例えば、フィードバックコントローラは、相関係数ρをゼロに至らせるために、制御入力ｕのＤＣ値ｗを調整することができる。性能勾配

の代わりに相関係数ρを使用する利点の１つは、フィードバックコントローラによって使用される調整パラメータが、性能変数ｙのスケールに基づいてカスタマイズまたは調整する必要のない調整パラメータの一般集合であり得ることである。この利点により、フィードバックコントローラに対する制御ループ特有の調整を実行する必要性が排除され、フィードバックコントローラは、多くの異なる制御ループおよび／またはプラントにわたって適用可能な調整パラメータの一般集合を使用できるようになる。 The correlation coefficient ρ is the performance gradient

Can be used by a feedback controller instead. For example, the feedback controller can adjust the DC value w of the control input u to bring the correlation coefficient ρ to zero. Performance gradient

One advantage of using the correlation coefficient ρ instead of is that the tuning parameters used by the feedback controller can be a general set of tuning parameters that do not need to be customized or adjusted based on the scale of the performance variable y. It is. This advantage eliminates the need to perform control loop specific adjustments to the feedback controller, allowing the feedback controller to use a general set of adjustment parameters applicable across many different control loops and / or plants.

  Additional features and advantages of the extreme value search controller are described in further detail below.

Building and HVAC System Referring now to FIGS. 1 and 2, a building 10 and an HVAC system 20 are shown that may implement an extreme value search control system, according to some embodiments. Although the ESC system and method of the present disclosure is described primarily in the context of a building HVAC system, it should be understood that ESC is generally applicable to any type of control system that optimizes or regulates variables of interest. . For example, the ESC systems and methods of the present disclosure optimize the amount of energy produced by various types of energy production systems or devices (eg, power plants, steam or wind turbines, solar panels, combustion systems, etc.) And / or optimizing the amount of energy consumed by various types of energy consuming systems or devices (eg, electronic circuits, mechanical equipment, aerospace and land vehicles, building equipment, HVAC devices, refrigeration systems, etc.) Can be used to

  In various implementations, the ESC optimizes the variable of interest to achieve a setpoint for the variable of interest (eg, by minimizing the difference between the measured or calculated input and the setpoint). Can be used in any type of controller that functions to optimize (eg, maximize or minimize an output variable). Various types of controllers (eg, motor controllers, power controllers, fluid controllers, HVAC controllers, lighting controllers, chemical controllers, process controllers, etc.) and various types of control systems (eg, closed loop control systems, open loop control systems, It is contemplated that ESCs can be easily implemented in feedback control systems, feedforward control systems, etc.). All such implementations should be considered within the scope of this disclosure.

  With particular reference to FIG. 1, a perspective view of a building 10 is shown. The building 10 is supplied by an HVAC system 20. The HVAC system 20 is shown to include a refrigerator 22, a boiler 24, a rooftop cooling unit 26 and a plurality of air treatment units (AHU) 36. The HVAC system 20 provides heating and / or cooling to the building 10 using a fluid circulation system. The circulating fluid can be cooled by the refrigerator 22 or heated by the boiler 24 depending on whether cooling or heating is required. The boiler 24 can add heat to the circulating fluid by burning a combustible material (eg, natural gas). The refrigerator 22 can place the circulating fluid and another fluid (for example, a refrigerant) in the heat exchanger (for example, an evaporator) in a heat exchange relationship. The refrigerant removes heat from the circulating fluid during the evaporation process, thereby cooling the circulating fluid.

  Circulating fluid from the refrigerator 22 or the boiler 24 can be transported to the AHU 36 via the pipe 32. The AHU 36 can place the circulating fluid and the airflow flowing through the AHU 36 in a heat exchange relationship. For example, the airflow can flow over the piping of a fan coil unit or other air conditioning terminal unit through which the circulating fluid flows. The AHU 36 can transfer heat between the air stream and the circulating fluid to provide heating or cooling to the air stream. Heated or cooled air can be delivered to the building 10 via an air distribution system that includes an air supply duct 38 and can return to the AHU 36 via a return air duct 40. In FIG. 1, the HVAC system 20 is shown to include a separate AHU 36 on each floor of the building 10. In other embodiments, a single AHU (eg, a rooftop AHU) can supply air to multiple floors or zones. The circulating fluid from the AHU 36 can return to the refrigerator 22 or the boiler 24 via the pipe 34.

  In some embodiments, the refrigerant of the refrigerator 22 evaporates as soon as the heat is absorbed from the circulating fluid. The vapor refrigerant can be provided to a compressor in the refrigerator 22 where the temperature and pressure of the refrigerant increase (eg, rotary impeller, screw compressor, scroll compressor, reciprocating compressor, centrifugal Using a compressor etc.). The compressed refrigerant can be discharged to a condenser in the refrigerator 22. In some embodiments, water (or another cooling fluid) flows through the condenser tube of the refrigerator 22 to absorb heat from the refrigerant vapor, thereby condensing the refrigerant. The water flowing in the condenser tube can be sent out from the refrigerator 22 to the rooftop cooling unit 26 via the pipe 28. The cooling unit 26 can remove heat from the water using fan driven cooling or fan driven evaporation. The cooling water in the roof unit 26 can be returned to the refrigerator 22 via the pipe 30, and the cycle is repeated.

  Referring now to FIG. 2, a block diagram illustrating a portion of the HVAC system 20 is shown in further detail according to some embodiments. In FIG. 2, the AHU 36 is shown as an economizer type air treatment unit. Economizer type air treatment units vary the amount of outside and return air used by the air treatment unit for heating or cooling. For example, AHU 36 may receive return air 82 from building 10 via return air duct 40 and deliver supply air 86 to building 10 via supply air duct 38. The AHU 36 can be configured to operate the exhaust damper 60, the mixing damper 62, and the outside air damper 64 to control the amount of outside air 80 and return air 82 that are combined to form the supply air 86. The return air 82 that does not pass through the mixing damper 62 can be discharged from the AHU 36 through the exhaust damper 60 as exhaust 84.

  Each of the dampers 60 to 64 can be operated by an actuator. As shown in FIG. 2, the exhaust damper 60 is operated by the actuator 54, the mixing damper 62 is operated by the actuator 56, and the outside air damper 64 is operated by the actuator 58. Actuators 54-58 can communicate with AHU controller 44 via communication link 52. AHU controller 44 is an economizer controller configured to control actuators 54-58 using one or more control algorithms (e.g., state-based algorithms, ESC algorithms, PID control algorithms, model predictive control algorithms, etc.). It can be. An example of an ESC method that can be used by the AHU controller 44 will be described in more detail with reference to FIGS.

  Actuators 54-58 can receive control signals from AHU controller 44 and provide feedback signals to AHU controller 44. The feedback signal includes, for example, an indication of the current actuator or damper position, the amount of torque or force applied by the actuator, diagnostic information (eg, results of a diagnostic test performed by the actuators 54-58), status information, and test run information , Configuration settings, calibration data, and / or other types of information or data that can be collected, stored, or used by the actuators 54-58.

  Still referring to FIG. 2, the AHU 36 is shown to include a cooling coil 68, a heating coil 70 and a fan 66. In some embodiments, the cooling coil 68, the heating coil 70, and the fan 66 are disposed in the air supply duct 38. The fan 66 can be configured to force the air supply 86 to flow through the cooling coil 68 and / or the heating coil 70. AHU controller 44 can communicate with fan 66 via communication link 78 to control the flow rate of supply air 86. The cooling coil 68 can receive the cooling fluid from the refrigerator 22 via the pipe 32 and return the cooling fluid to the refrigerator 22 via the pipe 34. Valve 92 can be positioned along line 32 or line 34 to control the amount of cooling fluid provided to cooling coil 68. The heating coil 70 can receive the heating fluid from the boiler 24 via the pipe 32 and can return the heating fluid to the boiler 24 via the pipe 34. Valve 94 can be positioned along line 32 or line 34 to control the amount of heating fluid provided to heating coil 70.

  Each of the valves 92, 94 can be controlled by an actuator. As shown in FIG. 2, the valve 92 is controlled by an actuator 88 and the valve 94 is controlled by an actuator 90. Actuators 88, 90 can communicate with AHU controller 44 via communication links 96, 98. Actuators 88, 90 can receive control signals from AHU controller 44 and provide feedback signals to controller 44. In some embodiments, the AHU controller 44 receives a supply air temperature measurement from a temperature sensor 72 located in the supply air duct 38 (eg, downstream of the cooling coil 68 and the heating coil 70). However, the temperature sensor 72 is not essential and may not be included in some embodiments.

  The AHU controller 44 adjusts the amount of heating or cooling provided to the supply air 86 (eg, to achieve a set point temperature for the supply air 86 or to maintain the temperature of the supply air 86 within a set point temperature range. The valves 92 and 94 can be operated via actuators 88 and 90. The position of the valves 92, 94 affects the amount of cooling or heating provided to the supply air 86 by the cooling coil 68 or heating coil 70, and the amount of energy consumed to achieve the desired supply air temperature. Can be correlated. In various embodiments, the valves 92, 94 can be operated by the AHU controller 44 or a separate controller for the HVAC system 20.

  AHU controller 44 can monitor the position of valves 92, 94 via communication links 96, 98. The AHU controller 44 can use the position of the valves 92, 94 as a variable that is optimized using ESC control techniques. The AHU controller 44 can determine and / or set the position of the dampers 60-64 to achieve the optimal or target position of the valves 92,94. The optimal or target position of the valves 92, 94 is the minimum amount of mechanical heating or cooling used by the HVAC system 20 to achieve the set point charge temperature (eg, the minimum fluid flow rate through the valves 92, 94). ).

  Still referring to FIG. 2, the HVAC system 20 is shown to include a monitoring controller 42 and a client device 46. The monitoring controller 42 may include one or more computer systems (eg, servers, BAS controllers, etc.) that function as enterprise level controllers, application or data servers, head nodes, master controllers or field controllers for the HVAC system 20. . The supervisory controller 42 communicates with a plurality of downstream building systems or subsystems (eg, HVAC systems, security systems, etc.) via the communication link 50 according to similar or dissimilar protocols (eg, LON, BACnet, etc.). be able to.

  In some embodiments, AHU controller 44 receives information (eg, commands, setpoints, operating boundaries, etc.) from supervisory controller 42. For example, the monitoring controller 42 can provide a high fan speed limit and a low fan speed limit to the AHU controller 44. Low limits can avoid starting up frequent components and high power load fans, while high limits can avoid operating near fan system mechanical or thermal limits. In various embodiments, the AHU controller 44 and the monitoring controller 42 can be separated (as shown in FIG. 2) or integrated. In an integrated implementation, the AHU controller 44 may be a software module configured to be executed by the processor of the supervisory controller 42.

  The client device 46 may include one or more human machine interfaces or client interfaces (eg, graphical user interfaces, reporting) for controlling, viewing, or otherwise interacting with the HVAC system 20, its subsystems and / or devices. Interface, text-based computer interface, web services directly addressing customers, web servers providing pages to web clients, etc.). Client device 46 may be a computer workstation, client terminal, remote or local interface, or any other type of user interface device. The client device 46 may be a stationary terminal or a mobile device. For example, the client device 46 can be a desktop computer, a computer server with a user interface, a laptop computer, a tablet, a smartphone, a PDA, or any other type of mobile or non-mobile device.

Extreme Value Search Control System with Periodic Dither Signal Referring now to FIG. 3, a block diagram of an extreme value search control (ESC) system 300 with periodic dither signal is shown, according to some embodiments. The ESC system 300 is shown to include an extreme value search controller 302 and a plant 304. A control theoretical plant is a combination of a process and one or more machine control outputs. For example, the plant 304 can be an air treatment unit configured to control the temperature in a building space via one or more machine controlled actuators and / or dampers. In various embodiments, the plant 304 may have a chiller operating process, a damper conditioning process, a mechanical cooling process, a ventilation process, a refrigeration process, or an input variable to the plant 304 (ie, an operating variable u) from the plant 304. It may include any other process that is adjusted to affect the output (ie, performance variable y).

  The extreme value search controller 302 adjusts the manipulated variable u using the extreme value search control logic. For example, the controller 302 can perturb the value of the manipulated variable u using a periodic (eg, sinusoidal) perturbation signal or a dither signal to extract the performance gradient p. The manipulated variable u can be perturbed by adding periodic oscillations to the DC value of the performance variable u that can be determined by a feedback control loop. The performance gradient p represents the gradient or slope of the performance variable y with respect to the manipulated variable u. The controller 302 uses extreme value search control logic to determine the value of the manipulated variable u that brings the performance gradient p to zero.

  The controller 302 can determine the DC value of the manipulated variable u based on the measured value or other indication of the performance variable y received as feedback from the plant 304 via the input interface 310. Measurements from the plant 304 may include, but are not limited to, information received from sensors about the state of the plant 304 or control signals sent to other devices in the system. In some embodiments, the performance variable y is the measured or observed position of one of the valves 92,94. In other embodiments, the performance variable y is a measured or calculated power consumption, fan speed, damper position, temperature, or any other variable that can be measured or calculated by the plant 304. The performance variable y may be a variable that the extremum search controller 302 seeks to optimize via an extremum search control technique. The performance variable y can be output by the plant 304 or observed at the plant 304 (eg, via a sensor) and provided to the extreme value search controller at the input interface 310.

  Input interface 310 provides performance variable y to performance gradient probe 312 to detect performance gradient 314. The performance gradient 314 can indicate the slope of the function y = f (u), where y represents a performance variable received from the plant 304 and u represents an operational variable provided to the plant 304. . If the performance gradient 314 is zero, the performance variable y has an extreme value (eg, maximum or minimum). Accordingly, the extreme value search controller 302 can optimize the value of the performance variable y by bringing the performance gradient 314 to zero.

  The operation variable updater 316 generates an updated operation variable u based on the performance gradient 314. In some embodiments, the manipulated variable updater 316 includes an integrator for bringing the performance gradient 314 to zero. The manipulated variable updater 316 then provides the updated manipulated variable u to the plant 304 via the output interface 318. In some embodiments, the manipulated variable u is provided as a control signal to one of the dampers 60-64 (FIG. 2) or an actuator that affects the dampers 60-64 via the output interface 318. The plant 304 can adjust the position of the dampers 60-64 using the manipulated variable u as a set point, thereby the relative ratio of the outside air 80 and the recirculated air 83 provided to the temperature control space. Can be controlled.

  Referring now to FIG. 4, a block diagram of another ESC system 400 with a periodic dither signal is shown according to some embodiments. The ESC system 400 is shown to include a plant 404 and an extreme value search controller 402. The controller 402 optimizes the performance variable y received as output from the plant 404 using an extreme value search control strategy. Optimizing the performance variable y is to minimize y, maximize y, control y to achieve the setpoint, or otherwise regulate the value of the performance variable y Can be included.

  The plant 404 may be the same as the plant 304 as described with reference to FIG. For example, the plant 404 can be a combination of a process and one or more machine control outputs. In some embodiments, the plant 404 is an air treatment unit configured to control the temperature in the building space via one or more machine controlled actuators and / or dampers. In other embodiments, the plant 404 includes a chiller operating process, a damper conditioning process, a mechanical cooling process, a ventilation process, or any other process that generates output based on one or more control inputs. obtain.

  The plant 404 can be mathematically represented as a combination of the input dynamics 422, the performance map 424, the output dynamics 426, and the disturbance d. In some embodiments, input dynamics 422 is linear time invariant (LTI) input dynamics and output dynamics 426 is LTI output dynamics. The performance map 424 may be a static non-linear performance map. The disturbance d may include process noise, measurement noise, or a combination of both. It should be noted that although the components of plant 404 are shown in FIG. 4, it is not necessary to know the actual mathematical model of plant 404 in order to apply ESC.

  The plant 404 receives a control input u (for example, a control signal, an operation variable, etc.) from the extreme value search controller 402 via the output interface 430. The input dynamics 422 can use the control input u to generate a function signal x based on the control input (eg, x = f (u)). The function signal x can be sent to the performance map 424, which generates an output signal z as a function of the function signal (ie, z = f (x)). The output signal z can pass through the output dynamics 426 to produce a signal z ', which is modified by the disturbance d to produce a performance variable y (eg, y = z' + d). The performance variable y is provided as an output from the plant 404 and received by the extreme value search controller 402. The extreme value search controller 402 may strive to find values for x and / or u that optimize the output z and / or performance variable y of the performance map 424.

  Still referring to FIG. 4, the extreme value search controller 402 is shown to receive the performance variable y via the input interface 432 and provide the performance variable y to the control loop 405 in the controller 402. The control loop 405 is shown to include a high pass filter 406, a demodulation element 408, a low pass filter 410, an integrator feedback controller 412 and a dither signal element 414. The control loop 405 can be configured to extract the performance gradient p from the performance variable y using a dither demodulation technique. The integrator feedback controller 412 analyzes the performance gradient p and adjusts the DC value (ie, variable w) of the plant input to bring the performance gradient p to zero.

  The first step of the dither demodulation technique is performed by dither signal generator 416 and dither signal element 414. Dither signal generator 416 generates a periodic dither signal v, which is typically a sine wave signal. The dither signal element 414 receives the dither signal v from the dither signal generator 416 and receives the DC value of the plant input w from the controller 412. The dither signal element 414 combines the dither signal v with the DC value of the plant input w to generate a perturbation control input u that is provided to the plant 404 (eg, u = w + v). The perturbation control input u is provided to the plant 404 and used by the plant 404 to generate the performance variable y as previously described.

  The second step of the dither demodulation technique is performed by high pass filter 406, demodulation element 408 and low pass filter 410. High pass filter 406 filters performance variable y and provides a filtered output to demodulation element 408. Demodulation element 408 demodulates the output of high pass filter 406 by applying phase shift 418 and multiplying the filtered output by dither signal v. The DC value of this multiplication is proportional to the performance gradient p of the performance variable y with respect to the control input u. The output of the demodulating element 408 is provided to a low-pass filter 410 that extracts the performance gradient p (ie, the DC value of the demodulated output). An estimate of the performance gradient p is then provided to the integrator feedback controller 412, which brings the performance gradient estimate p to zero by adjusting the DC value w of the plant input u.

  Still referring to FIG. 4, the extreme value search controller 402 is shown to include an amplifier 420. It may be desirable to amplify the dither signal v so that the amplitude of the dither signal v is sufficiently large relative to the effect of the dither signal v, as is evident at the plant output y. A large amplitude of the dither signal v can cause a large fluctuation of the control input u even if the DC value w of the control input u remains constant. Graphs showing the control input u and performance variable y due to periodic vibrations caused by the periodic dither signal v are shown in FIGS. 6A and 6B (discussed in more detail below). Due to the periodic nature of the dither signal v, large fluctuations in the plant input u (ie vibrations caused by the dither signal v) are often noticeable to the plant operator.

In addition, it may be desirable to carefully select the frequency of the dither signal v to ensure that the ESC strategy is effective. For example, it may be desirable to select the dither signal frequency ω _v based on the natural frequency ω _n of the plant 304 to enhance the effect of the dither signal v on the performance variable y. Proper selection of the dither frequency ω _v without knowledge of the plant 404 dynamics can be difficult and laborious. For these reasons, the use of the periodic dither signal v is one of the disadvantages of conventional ESCs.

In the ESC system 400, the output of the high pass filter 406 can be expressed as the difference between the value of the performance variable y and the expected value of the performance variable y, as shown in the following equation.
High-pass filter output: y-E [y]
In the equation, the variable E [y] is an expected value of the performance variable y. The result of the cross-correlation performed by demodulation element 408 (ie, the output of demodulation element 408) can be expressed as the product of the high pass filter output and the phase shifted dither signal, as shown in the following equation: .
Cross-correlation result: (y-E [y]) (v-E [v])
In the equation, the variable E [v] is an expected value of the dither signal v. The output of the low-pass filter 410 can be expressed as the covariance of the dither signal v and the performance variable y, as shown in the following equation.
Low-pass filter output: E [(y−E [y]) (v−E [u])] ≡Cov (v, y)
In the equation, the variable E [u] is an expected value of the control input u.

  The preceding equation indicates that the ESC system 400 generates an estimate of the covariance Cov (v, y) between the dither signal v and the plant output (ie performance variable y). The covariance Cov (v, y) can be used as a proxy for the performance gradient p in the ESC system 400. For example, the covariance Cov (v, y) can be calculated by the high pass filter 406, the demodulation element 408, and the low pass filter 410 and provided to the integrator feedback controller 412 as a feedback input. The integrator feedback controller 412 can adjust the DC value w of the plant input u to minimize the covariance Cov (v, y) as part of the feedback control loop.

Extreme Value Search Control System with Probabilistic Excitation Signal Referring now to FIG. 5, a block diagram of an ESC system 500 with a stochastic excitation signal is shown, according to some embodiments. The ESC system 500 is shown to include a plant 504 and an extreme value search controller 502. Controller 502 is shown to receive performance variable y as feedback from plant 504 via input interface 526 and to provide control input u to plant 504 via output interface 524. Controller 502 can operate similarly to controllers 302 and 402 as described with reference to FIGS. For example, the controller 502 can optimize the performance variable y received as output from the plant 504 using an extreme value search control (ESC) strategy. However, rather than perturbing the control input u using a periodic dither signal, the controller 502 can perturb the control input u using a stochastic excitation signal q. The controller 502 can adjust the control input u to bring the slope of the performance variable y to zero. In this way, the controller 502 identifies the value of the control input u that achieves the optimal value (eg, maximum or minimum) of the performance variable y.

  In some embodiments, ESC logic implemented by controller 502 generates a value for control input u based on received control signals (eg, setpoints, operating mode signals, etc.). The control signal may be user control (eg, thermostat, local user interface, etc.), client device 536 (eg, computer terminal, mobile user device, mobile phone, laptop, tablet, desktop computer, etc.), supervisory controller 532, or other From any external system or device. In various embodiments, the controller 502 uses direct communication with external systems and devices (eg, using NFC, Bluetooth, WiFi Direct, cables, etc.) or using wired or wireless electronic data communications. Communication via a communication network 534 (for example, BACnet network, LonWorks network, LAN, WAN, Internet, cellular network, etc.).

  The plant 504 may be similar to the plant 404 as described with reference to FIG. For example, the plant 504 can be a combination of a process and one or more machine control outputs. In some embodiments, the plant 504 is an air treatment unit configured to control the temperature in the building space via one or more machine control actuators and / or dampers. In other embodiments, the plant 504 includes a chiller operating process, a damper conditioning process, a mechanical cooling process, a ventilation process, or any other process that generates output based on one or more control inputs. obtain.

  The plant 504 can be expressed mathematically as static non-linearity connected in series with dynamic components. For example, the plant 504 is shown to include a static nonlinear function block 516 connected in series with a constant gain block 518 and a transfer function block 520. It should be noted that although the components of plant 504 are shown in FIG. 5, it is not necessary to know the actual mathematical model of plant 504 in order to apply ESC. The plant 504 receives a control input u (for example, a control signal, an operation variable, etc.) from the extreme value search controller 502 via the output interface 524. The non-linear function block 516 can use the control input u to generate a function signal x based on the control input (eg, x = f (u)). The function signal x can be sent to a constant gain block 518, which multiplies the function signal x by a constant gain K to produce an output signal z (ie, z = Kx). Output signal z can pass through transfer function block 520 to produce signal z ′, which is modified by disturbance d to produce a performance variable y (eg, y = z ′ + d). . The disturbance d may include process noise, measurement noise, or a combination of both. The performance variable y is provided as an output from the plant 504 and received by the extreme value search controller 502.

  Still referring to FIG. 5, the controller 502 is shown to include a communication interface 530, an input interface 526, and an output interface 524. Interfaces 530 and 524, 526 may include any number of jacks, wire terminals, wire ports, wireless antennas, or other communication interfaces for communicating information and / or control signals. Interfaces 530 and 524, 526 may be the same type of device or different types of devices. For example, the input interface 526 can be configured to receive analog feedback signals (eg, output variables, measurement signals, sensor outputs, control variables) from the plant 504, and the communication interface 530 can be monitored via the network 534. A digital setpoint signal may be configured to be received from controller 532. The output interface 524 may be a digital output (eg, an optical digital interface) configured to provide digital control signals (eg, manipulated variables, control inputs) to the plant 504. In other embodiments, the output interface 524 is configured to provide an analog output signal.

  In some embodiments, interfaces 530 and 524, 526 can be joined as one or two interfaces rather than as three separate interfaces. For example, the communication interface 530 and the input interface 526 can be combined as one Ethernet interface configured to receive network communications from the supervisory controller 532. In some embodiments, the monitoring controller 532 provides both setpoints and feedback over an Ethernet network (eg, network 534). In such embodiments, output interface 524 may be dedicated to the control component of plant 504. In other embodiments, output interface 524 may be another standardized communication interface for communicating data or control signals. Interfaces 530 and 524, 526 are communication electronics (eg, receivers, transmitters, transceivers, modulators, demodulators, filters, filters, etc.) configured to provide or facilitate communication of the signals described herein. Communication processor, communication logic module, buffer, decoder, encoder, encryptor, amplifier, etc.).

  Still referring to FIG. 5, the controller 502 is shown to include a processing circuit 538 having a processor 540 and a memory 542. The processor 540 may be a general purpose or special purpose processor, application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable processing components. The processor 540 is configured to execute computer code or instructions stored in the memory 542 or received from other computer readable media (eg, CDROM, network storage, remote server, etc.).

  Memory 542 may include one or more devices (eg, memory units, memory devices, storage devices) for storing data and / or computer code for completing and / or facilitating various processes described in this disclosure. Etc.). Memory 542 may be random access memory (RAM), read only memory (ROM), hard drive storage, temporary storage, non-volatile memory, flash memory, optical memory, or other for storing software objects and / or computer instructions. Any suitable memory may be included. Memory 542 may include database components, object code components, script components, or information structures to support any other type of various activities and the information structures described in this disclosure. Memory 542 can be communicatively coupled to processor 540 via processing circuitry 538 and stores computer code for executing (eg, by processor 540) one or more processes described herein. May be included.

を決定し、制御入力ｕのＤＣ値（すなわち、変数ｗ）を調整して勾配

をゼロに至らせるように構成することができる。 Still referring to FIG. 5, the extreme value search controller 502 is shown to receive the performance variable y via the input interface 526 and provide the performance variable y to the control loop 505 in the controller 502. The control loop 505 is shown to include a recursive gradient estimator 506, a feedback controller 508, and an excitation signal element 510. The control loop 505 is the slope of the performance variable y with respect to the control input u

And adjust the DC value of the control input u (ie, the variable w) to adjust the slope

Can be configured to reach zero.

を推定するように構成することができる。勾配

は、ＥＳＣシステム４００において決定される性能勾配ｐと同様のものであり得る。しかし、ＥＳＣシステム５００とＥＳＣシステム４００の根本的な違いは、勾配

が得られる方法である。ＥＳＣシステム４００では、性能勾配ｐは、共分散推定に類似した図４を参照して説明されるディザ復調技法を介して得られる。反対に、ＥＳＣシステム５００における勾配

は、制御入力ｕに対する性能変数ｙの傾きを推定するための再帰的回帰技法を実行することによって得られる。再帰的推定技法は、再帰的勾配推定器５０６によって実行することができる。 Recursive gradient estimation Recursive gradient estimator 506 is the gradient of performance variable y with respect to control input u.

Can be configured to estimate. Slope

May be similar to the performance gradient p determined in the ESC system 400. However, the fundamental difference between ESC system 500 and ESC system 400 is the gradient

Is a method that can be obtained. In the ESC system 400, the performance gradient p is obtained via a dither demodulation technique described with reference to FIG. 4 similar to covariance estimation. Conversely, the gradient in the ESC system 500

Is obtained by performing a recursive regression technique to estimate the slope of the performance variable y with respect to the control input u. The recursive estimation technique can be performed by a recursive gradient estimator 506.

を推定するために、様々な再帰的推定技法のいずれも使用することができる。例えば、再帰的勾配推定器５０６は、再帰的最小二乗（ＲＬＳ）推定技法を使用して、勾配

の推定を生成することができる。いくつかの実施形態では、再帰的勾配推定器５０６は、ＲＬＳ推定技法の一部として指数忘却を使用する。指数忘却は、バッチ処理と比べてデータ格納に必要な量を低減する。また、指数忘却は、ＲＬＳ推定技法が最近のデータに対してより感度が高い状態ひいては最適点のシフトに対してより感応度が高い状態のままでいられるようにすることもできる。再帰的勾配推定器５０６によって実行することができるＲＬＳ推定技法の例は、以下で詳細に説明する。 The recursive gradient estimator 506

Any of a variety of recursive estimation techniques can be used to estimate. For example, the recursive gradient estimator 506 uses a recursive least square (RLS) estimation technique to determine the gradient.

Can be generated. In some embodiments, the recursive gradient estimator 506 uses exponential forgetting as part of the RLS estimation technique. Exponential forgetting reduces the amount required to store data compared to batch processing. Exponential forgetting can also allow the RLS estimation technique to remain more sensitive to recent data and thus more sensitive to optimal point shifts. Examples of RLS estimation techniques that can be performed by the recursive gradient estimator 506 are described in detail below.

式中、ｕ_ｋは、時間ｋにおける制御入力ｕの値である。同様に、再帰的勾配推定器５０６は、以下の方程式に示されるように、パラメータベクトル

を構築することができる。

式中、パラメータ

は、時間ｋにおける勾配

の推定である。 Recursive gradient estimator 506 is shown to receive performance variable y from plant 504 and control input u from excitation signal element 510. In some embodiments, recursive slope estimator 506 receives multiple samples or measurements of performance variable y and control input u over time. The recursive gradient estimator 506 can construct an input vector x _k using a sample of the control input u at time k, as shown in the following equation:

Wherein, u _k is the value of the control input u at time k. Similarly, the recursive gradient estimator 506 is a parameter vector as shown in the following equation:

Can be built.

Where the parameter

Is the gradient at time k

Is an estimate.

を推定することができる。

このモデルの予測誤差は、以下の方程式に示されるように、時間ｋにおける性能変数の実際の値ｙ_ｋと時間ｋにおける性能変数の推定値

との差である。

The recursive gradient estimator 506 uses the following linear model to perform the performance variable at time k:

Can be estimated.

Predictive error of the model, as shown in the following equation, the estimated value of the performance variables in the actual values y _k and time k performance variable at time k

Is the difference.

を決定することができる。様々なＲＬＳ技法のいずれも、様々な実装形態において使用することができる。再帰的勾配推定器５０６によって実行することができるＲＬＳ技法の例は、以下の通りである。

式中、ｇ_ｋは、利得ベクトルであり、Ｐ_ｋは、共分散行列であり、λは、忘却因子である（λ＜１）。いくつかの実施形態では、忘却因子λは、以下の通り定義される。

式中、Δｔは、サンプリング周期であり、τは、忘却時定数である。 Recursive gradient estimator 506 uses the estimated error _{e k} in RLS technique, the parameter values

Can be determined. Any of various RLS techniques can be used in various implementations. An example of an RLS technique that can be performed by the recursive gradient estimator 506 is as follows.

Where g _k is a gain vector, P _k is a covariance matrix, and λ is a forgetting factor (λ <1). In some embodiments, the forgetting factor λ is defined as follows:

In the equation, Δt is a sampling period, and τ is a forgetting time constant.

の値および忘却因子に基づいて、時間ｋにおける利得ベクトルｇ_ｋを計算することができる。再帰的勾配推定器５０６は、Ｐ_ｋの方程式を使用して、忘却因子λ、時間ｋにおける利得ベクトルｇ_ｋの値および時間ｋにおける入力ベクトル

の値に基づいて、時間ｋにおける共分散行列Ｐ_ｋを計算することができる。再帰的勾配推定器５０６は、

の方程式を使用して、時間ｋにおける誤差ｅ_ｋおよび時間ｋにおける利得ベクトルｇ_ｋに基づいて、時間ｋにおけるパラメータベクトル

を計算することができる。パラメータベクトル

が計算された時点で、再帰的勾配推定器５０６は、以下の方程式に示されるように、

からパラメータ

の値を抽出することによって勾配

の値を決定することができる。

The recursive gradient estimator 506 uses the equation for g _k to use the previous value P _k−1 of the covariance matrix at time k ₋₁ and the input vector at time k.

Based on the value of and the forgetting factor, the gain vector g _k at time k can be calculated. The recursive gradient estimator 506 uses the equation for P _k to calculate the forgetting factor λ, the value of the gain vector g _k at time k, and the input vector at time k.

The covariance matrix P _k at time k can be calculated based on the value of. The recursive gradient estimator 506

Parameter vector at time k based on error e _{k at} time k and gain vector g _k at time k

Can be calculated. Parameter vector

When is calculated, the recursive gradient estimator 506, as shown in the following equation:

To parameters

Gradient by extracting the value of

The value of can be determined.

を推定することができる。例えば、再帰的勾配推定器５０６は、カルマンフィルタ、正規化勾配技法、非正規化勾配適応技法、再帰的ベイジアン推定技法、または、様々な線形もしくは非線形フィルタのいずれかを使用して、

を推定することができる。他の実施形態では、再帰的勾配推定器５０６は、再帰的推定技法というよりむしろ、バッチ推定技法を使用することができる。従って、勾配推定器５０６は、再帰的勾配推定器というよりむしろ、バッチ勾配推定器であり得る。バッチ推定技法では、勾配推定器５０６は、バッチ回帰アルゴリズムへの入力として制御入力ｕおよび性能変数ｙの前値のバッチ（例えば、前値または履歴値のベクトルまたは集合）を使用することができる。適切な回帰アルゴリズムは、例えば、最小二乗回帰、多項式回帰、部分最小二乗回帰、リッジ回帰、主成分回帰、または、様々な線形もしくは非線形回帰技法のいずれかを含み得る。 In various embodiments, the recursive gradient estimator 506 uses any of a variety of other recursive estimation techniques to:

Can be estimated. For example, the recursive gradient estimator 506 uses either a Kalman filter, a normalized gradient technique, a denormalized gradient adaptation technique, a recursive Bayesian estimation technique, or various linear or non-linear filters,

Can be estimated. In other embodiments, the recursive gradient estimator 506 may use a batch estimation technique rather than a recursive estimation technique. Thus, the gradient estimator 506 can be a batch gradient estimator rather than a recursive gradient estimator. In the batch estimation technique, the slope estimator 506 can use a batch of previous values of the control input u and the performance variable y (eg, a vector or set of previous values or history values) as input to the batch regression algorithm. Suitable regression algorithms may include, for example, least square regression, polynomial regression, partial least square regression, ridge regression, principal component regression, or any of a variety of linear or non-linear regression techniques.

  In some embodiments, it is desirable for the recursive gradient estimator 506 to use a recursive estimation technique rather than a batch estimation technique due to several advantages provided by the recursive estimation technique. For example, the recursive estimation technique described above (ie, RLS with exponential forgetting) has been shown to greatly improve the performance of the gradient estimation technique compared to batch least squares. In addition to requiring less data storage than batch processing, RLS estimation techniques with exponential forgetting are more sensitive to recent data and thus more sensitive to optimal point shifts. You can stay in the state.

を推定する。例えば、最小二乗手法における傾き

の推定は、

と定義することができ、式中、Ｃｏｖ（ｕ，ｙ）は、制御入力ｕと性能変数ｙとの間の共分散であり、Ｖａｒ（ｕ）は、制御入力ｕの分散である。再帰的勾配推定器５０６は、以前の方程式を使用して、推定傾き

を計算し、勾配

のプロキシとして推定傾き

を使用することができる。とりわけ、推定傾き

は、制御入力ｕおよび性能変数ｙのみの関数である。これは、推定性能勾配ｐがディザ信号ｖと性能変数ｙとの間の共分散の関数である、図４を参照して説明される共分散微分技法とは異なる。ディザ信号ｖを制御入力ｕに置換することにより、コントローラ５０２は、ディザ信号ｖ（図４に示される）または励起信号ｑ（図５に示される）の知識なしで、傾き

の推定を生成することができる。 In some embodiments, the recursive gradient estimator 506 uses the covariance between the control input u and the performance variable y to gradient.

Is estimated. For example, the slope in the least squares method

Is an estimate of

Where Cov (u, y) is the covariance between the control input u and the performance variable y, and Var (u) is the variance of the control input u. The recursive gradient estimator 506 uses the previous equation to calculate the estimated slope

Calculate the slope

The estimated slope as a proxy for

Can be used. Above all, the estimated slope

Is a function of only the control input u and the performance variable y. This is different from the covariance derivative technique described with reference to FIG. 4, where the estimated performance gradient p is a function of the covariance between the dither signal v and the performance variable y. By substituting the dither signal v with the control input u, the controller 502 can tilt without knowledge of the dither signal v (shown in FIG. 4) or the excitation signal q (shown in FIG. 5).

Can be generated.

を推定する。例えば、再帰的勾配推定器５０６は、以下の二次曲線モデルを使用して、時間ｋにおける性能変数

を推定することができる。

二次曲線モデルは、以下の通り、入力ベクトルｘ_ｋおよびパラメータベクトル

を更新することによって

の形態で記載することができる。

In some embodiments, the recursive slope estimator 506 uses a higher order model (eg, a quadratic curve model, a cubic curve model, etc.) rather than a linear model to perform the performance variable.

Is estimated. For example, the recursive slope estimator 506 uses the following quadratic curve model to perform a performance variable at time k:

Can be estimated.

The quadratic curve model is as follows: input vector x _k and parameter vector

By updating

It can be described in the form of

を計算し、フィードバック信号として勾配

を提供することができる。

を推定するために線形モデルを使用した実施形態の場合、勾配

（すなわち、ｕについての線形モデルの導関数）は、スカラ値である。コントローラ５０８がフィードバック信号として勾配

のスカラ値を受信すると、コントローラ５０８は、制御入力ｕの最適値（すなわち、勾配

をもたらす制御入力ｕの値）に達するまで、勾配

をゼロに至らせる方向に制御入力ｕの値を漸増調整することができる。 Recursive slope estimator 506 uses a quadratic curve model to fit a quadratic curve (rather than a straight line) to the data points defined by the combination of control input u and performance variable y at various times k. be able to. The quadratic curve model provides quadratic information not provided by the linear model and can be used to improve the convergence of the feedback controller 508. For example, in a linear model, the recursive slope estimator 506 is the slope at a particular location along the curve (ie, for a particular value of the control input u).

Calculate the gradient as a feedback signal

Can be provided.

For embodiments that use a linear model to estimate

(Ie, the derivative of the linear model with respect to u) is a scalar value. Controller 508 provides gradient as feedback signal

Controller 508 receives the optimal value of control input u (ie, the slope).

Until the value of the control input u) is reached

The value of the control input u can be gradually increased and adjusted so as to bring the value to zero.

の関数をフィードバックコントローラ５０８に提供することができる。

を推定するために二次曲線モデルを使用した実施形態の場合、勾配

（すなわち、ｕについての二次曲線モデルの導関数）は、制御入力ｕの線形関数であり、例えば、

である。コントローラ５０８がフィードバック信号として勾配

の線形関数を受信すると、コントローラ５０８は、勾配

をもたらす制御入力ｕの最適値、例えば、

を解析的に計算することができる。それに従って、コントローラ５０８は、勾配

がゼロに近づいているかどうかを判断するための漸増調整および実験に頼ることなく、最適値に急速に近づくスマートステップを使用して、制御入力ｕを調整することができる。 In a quadratic curve model, the recursive slope estimator 506 uses a slope rather than a simple scalar value.

Can be provided to the feedback controller 508.

For embodiments that use a quadratic curve model to estimate

(Ie, the derivative of the quadratic curve model with respect to u) is a linear function of the control input u, eg

It is. Controller 508 provides gradient as feedback signal

Controller 508 receives the linear function of

The optimal value of the control input u that yields

Can be calculated analytically. Accordingly, the controller 508 determines the slope

The control input u can be adjusted using a smart step that rapidly approaches the optimal value without resorting to incremental adjustments and experiments to determine if is approaching zero.

を確実に推定するため、性能変数ｙを成し遂げる制御入力ｕの十分な変動を提供することが望ましい場合がある。コントローラ５０２は、確率論的信号ジェネレータ５１２および積分器５１４を使用して、持続的な励起信号ｑを生成することができる。励起信号ｑは、制御入力ｕを形成するために、励起信号要素５１０において制御入力ｕのＤＣ値ｗに加えることができる（例えば、ｕ＝ｗ＋ｑ）。 Probabilistic Excitation Signal Still referring to FIG. 5, the extreme value search controller 502 is shown to include a stochastic signal generator 512 and an integrator 514. Slope

It may be desirable to provide sufficient variation of the control input u to achieve the performance variable y in order to reliably estimate. The controller 502 can use the stochastic signal generator 512 and the integrator 514 to generate a continuous excitation signal q. The excitation signal q can be added to the DC value w of the control input u at the excitation signal element 510 to form the control input u (eg, u = w + q).

  Probabilistic signal generator 512 may be configured to generate a stochastic signal. In various embodiments, the stochastic signal is a random signal (eg, random walk signal, white noise signal, etc.), aperiodic signal, unpredictable signal, disturbance signal, or any other type of non-deterministic. It can be a logical or non-repetitive signal. In some embodiments, the stochastic signal has a non-zero average. The stochastic signal can be integrated by integrator 514 to generate excitation signal q.

  Excitation signal q may provide sufficient variation of control input u for the gradient estimation technique performed by recursive gradient estimator 506. In some instances, the addition of the excitation signal q causes the control input u to move away from its optimal value. However, the feedback controller 508 can compensate for such drift by adjusting the DC value w so that the control input u is constantly pulled back to its optimal value. As with conventional ESCs, the magnitude of the excitation signal q can be selected (eg, manually by the user, eg, to overcome the additive noise (eg, process noise, measurement noise, etc.) found in the performance variable y. Or automatically by controller 502).

  The stochastic excitation signal q generated by the extreme value search controller 502 has several advantages over the periodic dither signal v generated by the controller 402. For example, the stochastic excitation signal q is not as perceptible as the conventional periodic dither signal v. Therefore, the effect of the stochastic excitation signal q on the control input u is not as pronounced as the periodic oscillation caused by the conventional periodic dither signal v. Graphs showing the control input u excited by the stochastic excitation signal q and the resulting performance variable y are shown in FIGS. 7A and 7B (discussed in more detail below).

を計算することができる。 Another advantage of the stochastic excitation signal q is that the controller 502 is easier to tune because the dither frequency ω _v is no longer a required parameter. Accordingly, the controller 502 need not know or estimate the natural frequency of the plant 504 in generating the stochastic excitation signal q. In some embodiments, the extreme value search controller 502 provides a plurality of control inputs u to the plant 504. Each of the control inputs can be excited by a separate stochastic excitation signal q. Since each of the stochastic excitation signals q is random, there is no need to ensure that the stochastic excitation signals q do not correlate with each other. Controller 502 performs the gradient of performance variable y for each of control inputs u without performing frequency-specific dither demodulation techniques.

Can be calculated.

が性能変数ｙの範囲またはスケールの関数であることである。性能変数ｙの範囲またはスケールは、プラント５０４の静的および動的コンポーネントに依存し得る。例えば、プラント５０４は、定利得Ｋ（すなわち、定利得ブロック５１８）と直列接続された非線形関数ｆ（ｕ）（すなわち、関数ブロック５１６）を含むように示されている。この表現から、性能変数ｙの範囲またはスケールは定利得Ｋの関数であることが明白である。 Correlation coefficient One of the problems in conventional ESC is the performance gradient

Is a function of the range or scale of the performance variable y. The range or scale of the performance variable y may depend on the static and dynamic components of the plant 504. For example, plant 504 is shown to include a non-linear function f (u) (ie, function block 516) connected in series with a constant gain K (ie, constant gain block 518). From this representation it is clear that the range or scale of the performance variable y is a function of the constant gain K.

の値は、非線形関数ｆ（ｕ）によって提供される非線形性により、制御入力ｕの値に基づいて異なり得る。しかし、性能勾配

のスケールは、定利得Ｋの値にも依存する。例えば、性能勾配

は、以下の方程式を使用して決定することができる。

式中、Ｋは、定利得であり、ｆ’（ｕ）は、関数ｆ（ｕ）の導関数である。一貫したフィードバック制御ループ性能を提供するために、性能勾配

をスケーリングまたは正規化することが望ましい場合がある（例えば、スケーリングパラメータκを乗じることによって）。しかし、性能変数ｙのスケールの知識なしでは（例えば、プラント５０４によって適用される定利得Ｋを知らなければ）、スケーリングパラメータκの適切な値を決定することは苦労を伴うものであり得る。 Performance gradient

The value of may vary based on the value of the control input u due to the non-linearity provided by the non-linear function f (u). But performance gradient

This scale also depends on the value of the constant gain K. For example, performance gradient

Can be determined using the following equation:

In the equation, K is a constant gain, and f ′ (u) is a derivative of the function f (u). Performance gradients to provide consistent feedback control loop performance

It may be desirable to scale or normalize (eg, by multiplying by the scaling parameter κ). However, without knowledge of the scale of the performance variable y (eg, without knowing the constant gain K applied by the plant 504), determining an appropriate value for the scaling parameter κ can be laborious.

と関連付ける（例えば、

に比例する）ことができるが、性能変数ｙの範囲に基づいてスケーリングされる。例えば、相関係数ρは、性能勾配

の正規化尺度であり得る（例えば、範囲０≦ρ≦１にスケーリングされる）。 Still referring to FIG. 5, the extreme value search controller 502 is shown to include a correlation coefficient estimator 528. Correlation coefficient estimator 528 may be configured to generate correlation coefficient ρ and provide correlation coefficient ρ to feedback controller 508. The correlation coefficient ρ is the performance gradient

Associated with (for example,

Scaled based on the range of performance variable y. For example, the correlation coefficient ρ is the performance gradient

(For example, scaled to the range 0 ≦ ρ ≦ 1).

式中、Ｃｏｖ（ｕ，ｙ）は、制御入力ｕと性能変数ｙとの間の共分散であり、Ｖａｒ（ｕ）は、制御入力ｕの分散であり、Ｖａｒ（ｙ）は、性能変数ｙの分散である。以前の方程式は、制御入力ｕの標準偏差σ_ｕおよび性能変数ｙの標準偏差σ_ｙの観点から以下の通り記載しなおすことができる。

式中、

である。 Correlation coefficient estimator 528 is shown to receive control input u and performance variable y as inputs. Correlation coefficient estimator 528 can generate correlation coefficient ρ based on the variance and covariance of control input u and performance variable y, as shown in the following equation:

Where Cov (u, y) is the covariance between the control input u and the performance variable y, Var (u) is the variance of the control input u, and Var (y) is the performance variable y Is the dispersion of. Previous equation can be re-described as follows in terms of the standard deviation sigma _y of the standard deviation sigma _u and performance variable y of the control input u.

Where

It is.

式中、

は、時間ｋにおける制御入力ｕおよび性能変数ｙのＥＷＭＡであり、

は、時間ｋ−１における制御入力ｕおよび性能変数ｙの以前のＥＷＭＡであり、ｕ_ｋおよびｙ_ｋは、時間ｋにおける制御入力ｕおよび性能変数ｙの現行値であり、ｋは、各変数の収集されたサンプルの総数であり、Ｗは、忘却窓の持続時間である。 In some embodiments, correlation coefficient estimator 528 estimates correlation coefficient ρ using a recursive estimation technique. For example, correlation coefficient estimator 528 may calculate an exponential weighted moving average (EWMA) of control input u and performance variable y using the following equation:

Where

Is the EWMA of control input u and performance variable y at time k,

Is the previous EWMA of the control input u and performance variable y at time k−1, u _k and y _k are the current values of the control input u and performance variable y at time k, and k is for each variable The total number of samples collected, W is the duration of the forgetting window.

式中、Ｖ_ｕ，ｋ、Ｖ_ｙ，ｋおよびｃ_ｋはそれぞれ、時間ｋにおける制御入力分散Ｖａｒ（ｕ）、性能変数分散Ｖａｒ（ｙ）および共分散Ｃｏｖ（ｕ，ｙ）のＥＷＭＡである。Ｖ_{ｕ，ｋ−１}、Ｖ_{ｙ，ｋ−１}およびｃ_ｋ−１はそれぞれ、時間ｋ−１における制御入力分散Ｖａｒ（ｕ）、性能変数分散Ｖａｒ（ｙ）および共分散Ｃｏｖ（ｕ，ｙ）のＥＷＭＡである。相関係数推定器５２８は、以下の方程式を使用して、これらの再帰的推定に基づいて相関係数ρの推定を生成することができる。

Similarly, correlation coefficient estimator 528 may calculate EWMA for control input variance Var (u), performance variable variance Var (y) and covariance Cov (u, y) using the following equations: it can.

_Where V _{u, k} , V _{y, k} and c _k are the EWMA of control input variance Var (u), performance variable variance Var (y) and covariance Cov (u, y) at time k, respectively. V _{u, k−1} , V _{y, k−1} and c _k−1 are the control input variance Var (u), performance variable variance Var (y) and covariance Cov (u, y) at time k−1, respectively. EWMA. Correlation coefficient estimator 528 can generate an estimate of correlation coefficient ρ based on these recursive estimates using the following equation:

に基づいて相関係数ρを生成する。以前に説明されるように、推定傾き

は、以下の方程式を使用して計算することができる。

式中、Ｃｏｖ（ｕ，ｙ）は、制御入力ｕと性能変数ｙとの間の共分散であり、Ｖａｒ（ｕ）は、制御入力ｕの分散であり、すなわち、

である。相関係数推定器５２８は、以下の方程式を使用して、傾き

から相関係数ρを計算することができる。

以前の方程式から、標準偏差σ_ｕとσ_ｙが等しい際（すなわち、σ_ｕ＝σ_ｙの際）は、相関係数ρと推定傾き

は等しいことが分かる。 In some embodiments, the correlation coefficient estimator 528 includes an estimated slope.

Based on the above, a correlation coefficient ρ is generated. Estimated slope, as previously explained

Can be calculated using the following equation:

Where Cov (u, y) is the covariance between the control input u and the performance variable y, and Var (u) is the variance of the control input u, ie

It is. Correlation coefficient estimator 528 uses the following equation to calculate the slope

The correlation coefficient ρ can be calculated from

From the previous equation, when the standard deviations σ _u and σ _y are equal (that is, when σ _u = σ _y ), the correlation coefficient ρ and the estimated slope

Are equal.

を受信するか、または、制御入力ｕおよび性能変数ｙの値の集合を使用して推定傾き

を計算することができる。例えば、ｕおよびｙの有限分散を想定すると、相関係数推定器５２８は、以下の最小二乗推定を使用して、傾き

を推定することができる。

Correlation coefficient estimator 528 calculates the estimated slope from recursive gradient estimator 506.

Or estimated slope using a set of values of control input u and performance variable y

Can be calculated. For example, assuming a finite variance of u and y, the correlation coefficient estimator 528 uses the following least squares estimation to

Can be estimated.

は、以下の方程式に示されるように、性能勾配のプロキシとして使用することができる。

以前の方程式に示されるように、推定傾き

は定利得Ｋを含み、定利得Ｋは未知数であり得る。しかし、標準偏差σ_ｕおよびσ_ｙによって提供される正規化は、定利得Ｋの効果を無効にする。例えば、性能変数ｙの標準偏差σ_ｙは、以下の方程式に示されるように、制御入力ｕの標準偏差σ_ｕと関連付けられる。

In case of small range of control input u, estimated slope

Can be used as a proxy for performance gradient, as shown in the equation below.

Estimated slope, as shown in the previous equation

Includes a constant gain K, which may be an unknown. However, the normalization provided by the standard deviations σ _u and σ _y negates the effect of the constant gain K. For example, a standard deviation sigma _y of the performance variables y, as shown in the following equation, is associated with the standard deviation sigma _u of the control input u.

に比率

を乗じることは、定利得Ｋで除することに等しい。相関係数ρおよび推定傾き

は両方とも、制御入力ｕと性能変数ｙとの関係の強さを示す。しかし、相関係数ρは、正規化されているという利点を有し、それにより、フィードバック制御ループの調整がはるかに簡単になる。 Estimated slope to calculate correlation coefficient ρ

To ratio

Multiplication is equivalent to dividing by a constant gain K. Correlation coefficient ρ and estimated slope

Both indicate the strength of the relationship between the control input u and the performance variable y. However, the correlation coefficient ρ has the advantage of being normalized, which makes the adjustment of the feedback control loop much easier.

の代わりに、フィードバックコントローラ５０８によって使用される。例えば、フィードバックコントローラ５０８は、相関係数ρをゼロに至らせるために、制御入力ｕのＤＣ値ｗを調整することができる。性能勾配

の代わりに相関係数ρを使用する利点の１つは、フィードバックコントローラ５０８によって使用される調整パラメータが、性能変数ｙのスケールに基づいてカスタマイズまたは調整する必要のない調整パラメータの一般集合であり得ることである。この利点により、フィードバックコントローラ５０８に対する制御ループ特有の調整を実行する必要性が排除され、フィードバックコントローラ５０８は、多くの異なる制御ループおよび／またはプラントにわたって適用可能な調整パラメータの一般集合を使用できるようになる。 In some embodiments, the correlation coefficient ρ is a performance gradient.

Is used by the feedback controller 508 instead. For example, the feedback controller 508 can adjust the DC value w of the control input u to bring the correlation coefficient ρ to zero. Performance gradient

One advantage of using the correlation coefficient ρ instead of is that the tuning parameters used by the feedback controller 508 may be a general set of tuning parameters that do not need to be customized or adjusted based on the scale of the performance variable y. That is. This advantage eliminates the need to perform control loop specific adjustments to the feedback controller 508 so that the feedback controller 508 can use a general set of adjustment parameters applicable across many different control loops and / or plants. Become.

Example Graphs Referring now to FIGS. 6A-7B, there are shown several graphs 600-750 comparing the performance of extreme search controller 402 and extreme search controller 502, according to some embodiments. Controllers 402 and 502 were used to control a dynamic system with optimal control input value u = 2 and optimal performance variable y = −10. Both controllers 402 and 502 started with a value of u = 4 and were able to adjust the value of the control input u using the extreme value search control technique described with reference to FIGS. Controller 402 uses periodic dither signal v, and controller 502 uses stochastic excitation signal q.

  With particular reference to FIGS. 6A and 6B, graphs 600 and 650 illustrate the performance of the extreme value search controller 402, as described with reference to FIG. The controller 402 uses the periodic dither signal v to perturb the control input u. Graph 600 shows the value of control input u at various sample times, and graph 650 shows the value of the corresponding performance variable y. The control input u starts with a value of u = 4 and is perturbed using a periodic (ie sine wave) dither signal v. The vibrational perturbations caused by the periodic dither signal v are seen both at the control input u and the performance variable y.

  With particular reference to FIGS. 7A and 7B, graphs 700 and 750 illustrate the performance of the extreme value search controller 502, as described with reference to FIG. The controller 502 perturbs the control input u using the stochastic excitation signal q. Graph 700 shows the value of control input u at various sample times, and graph 750 shows the value of the corresponding performance variable y. The control input u starts with a value of u = 4 and is perturbed using the stochastic excitation signal q. The stochastic excitation signal q applies a random walk to the control input u. However, since the stochastic excitation signal q has a non-periodic effective small amplitude, the perturbations caused by the stochastic excitation signal q can be barely recognized in the graphs 700 and 750. In addition, the control input u of the graph 700 reaches the optimum value faster than the control input of the graph 600.

Extreme Value Search Control Technique Referring now to FIG. 8, a flow diagram 800 illustrating an extreme value search control (ESC) technique is shown, according to some embodiments. The ESC technique shown in flow diagram 800 may be performed by one or more components of a feedback controller (eg, controller 502) to monitor and control a plant (eg, plant 504). For example, the controller 502 can use ESC techniques to determine the optimal value of the control input u provided to the plant 504 by perturbing the control input u with the stochastic excitation signal q. .

  Flow diagram 800 is shown to include providing control input u to the plant (block 802) and receiving performance variable y as feedback from the plant (block 804). The control input u can be provided to the plant by an extreme value search controller and / or a feedback controller. The controller may be any of the previously described controllers (eg, controller 302, controller 402, controller 502, etc.) or any other type of controller that provides a control input u to the plant. In some embodiments, the controller is an extreme value search controller configured to achieve the optimum value of the performance variable y by adjusting the control input u. The optimal value may be the extreme value (eg, maximum or minimum) of the performance variable y.

  A control theoretical plant is a combination of a process and one or more machine control outputs. The plant can be any of the previously described plants (eg, plant 304, plant 404, plant 504, etc.) or any other controllable system or process. For example, the plant may be an air treatment unit configured to control the temperature in a building space via one or more machine controlled actuators and / or dampers. In various embodiments, the plant is tuned such that the refrigerator operating process, damper adjustment process, mechanical cooling process, ventilation process, refrigeration process, or control input u to the plant affects the performance variable y. Any other process may be included. The performance variable y is a measured variable (eg, measured temperature, measured power consumption, measured flow rate, etc.) observed by one or more sensors in the plant, a calculated variable based on a measured or observed value (eg, calculated efficiency, calculated Power consumption, computational cost, etc.) or any other type of variable that indicates the performance of the plant in response to the control input u.

または推定傾き

であり得る。例えば、勾配は、曲線に沿った特定の場所における（例えば、ｕの特定の値における）関数ｙ＝ｆ（ｕ）によって定義された曲線の傾きまたは微分係数であり得る。勾配は、制御入力ｕおよび性能変数ｙの１対または複数対の値を使用して推定することができる。 The flow diagram 800 is shown to include estimating the slope of the performance variable y with respect to the control input u (block 806). In some embodiments, the gradient is the performance gradient p described with reference to FIG. In other embodiments, the gradient is a performance gradient described with reference to FIG.

Or estimated slope

It can be. For example, the slope can be the slope or derivative of the curve defined by the function y = f (u) at a particular location along the curve (eg, at a particular value of u). The slope can be estimated using one or more pairs of values for the control input u and the performance variable y.

式中、ｘ_ｋは、入力ベクトルであり、

は、パラメータベクトルである。入力ベクトルｘ_ｋおよびパラメータベクトル

は、以下の通り定義することができる。

式中、ｕ_ｋは、時間ｋにおける制御入力ｕの値であり、パラメータ

は、時間ｋにおける勾配

の推定である。 In some embodiments, the gradient can be estimated by performing a recursive gradient estimation technique. The recursive gradient estimation technique may include obtaining a model of the performance variable y as a function of the control input u. For example, the slope can be estimated using the following linear model.

Where x _k is the input vector,

Is a parameter vector. Input vector x _k and parameter vector

Can be defined as follows:

Where u _k is the value of the control input u at time k and the parameter

Is the gradient at time k

Is an estimate.

との差である。

推定誤差ｅ_ｋは、パラメータ値

を決定するために、再帰的勾配推定技法において使用することができる。様々な回帰技法のいずれも、パラメータベクトル

の値を推定するために使用することができる。 Predictive error of the model, as shown in the following equation, the estimated value of the performance variables in the actual values y _k and time k performance variable at time k

Is the difference.

The estimation error _ek is the parameter value

Can be used in a recursive gradient estimation technique. All of the various regression techniques use parameter vectors

Can be used to estimate the value of.

を推定することができる。

In some embodiments, rather than a linear model, a higher order model (eg, a quadratic curve model, a cubic curve model, etc.) can be used to estimate the slope. For example, using the following quadratic curve model, the slope at a particular location along the curve defined by the model:

Can be estimated.

の値を決定することができる。

式中、ｇ_ｋは、利得ベクトルであり、Ｐ_ｋは、共分散行列であり、λは、忘却因子である（λ＜１）。いくつかの実施形態では、忘却因子λは、以下の通り定義される。

式中、Δｔは、サンプリング周期であり、τは、忘却時定数である。パラメータベクトル

を計算した時点で、

からパラメータ

の値を抽出することによって、勾配を推定することができる。 In some embodiments, the slope is estimated using a recursive least square (RLS) estimation technique with exponential forgetting. Any of various RLS techniques can be used in various implementations. An example of an RLS technique that can be performed to estimate the gradient is shown in the following equation, and the parameter vector is solved by solving the equation:

The value of can be determined.

Where g _k is a gain vector, P _k is a covariance matrix, and λ is a forgetting factor (λ <1). In some embodiments, the forgetting factor λ is defined as follows:

In the equation, Δt is a sampling period, and τ is a forgetting time constant. Parameter vector

When calculating

To parameters

The gradient can be estimated by extracting the value of.

  In various embodiments, the gradient can be estimated using any of a variety of other recursive estimation techniques. For example, the gradient can be estimated using a Kalman filter, a normalized gradient technique, a denormalized gradient adaptation technique, a recursive Bayesian estimation technique, or any of a variety of linear or non-linear filters. In some embodiments, the gradient can be estimated using a batch estimation technique rather than a recursive estimation technique. Batch estimation techniques can use a batch of previous values of control input u and performance variable y (eg, a vector or set of previous or historical values) as input to a batch regression algorithm. Suitable regression algorithms may include, for example, least square regression, polynomial regression, partial least square regression, ridge regression, principal component regression, or any of a variety of linear or non-linear regression techniques.

の推定は、

と定義することができ、式中、Ｃｏｖ（ｕ，ｙ）は、制御入力ｕと性能変数ｙとの間の共分散であり、Ｖａｒ（ｕ）は、制御入力ｕの分散である。推定傾き

は、以前の方程式を使用して計算し、勾配

のプロキシとして使用することができる。 In some embodiments, the slope can be estimated using the covariance between the control input u and the performance variable y. For example, the slope in the least squares method

Is an estimate of

Where Cov (u, y) is the covariance between the control input u and the performance variable y, and Var (u) is the variance of the control input u. Estimated slope

Calculate using the previous equation and the gradient

Can be used as a proxy.

  Still referring to FIG. 8, the flow diagram 800 is shown to include bringing the estimated slope to zero by adjusting the output of the feedback controller (block 808). In some embodiments, the feedback controller is the feedback controller 508 shown in FIG. The feedback controller can receive the estimated gradient as input and adjust its output (eg, DC output w) to bring the estimated gradient to zero. The feedback controller can increase or decrease the value of the DC output w until the optimum value of the DC output w is reached. The optimal value of DC output w can be defined as the value that yields the optimal value (eg, maximum or minimum value) of performance variable y. The optimum value of the performance variable y occurs when the slope becomes zero. Accordingly, the feedback controller can achieve the optimum value of the performance variable y by adjusting its output w to bring the slope to zero.

  Flow diagram 800 generates a new control input u by generating a stochastic excitation signal q (block 810) and perturbing the output w of the feedback controller using the stochastic excitation signal q. (Block 812). The stochastic excitation signal q can be generated by a stochastic signal generator 512 and / or an integrator 514 as described with reference to FIG. In various embodiments, the stochastic signal is a random signal (eg, random walk signal, white noise signal, etc.), aperiodic signal, unpredictable signal, disturbance signal, or any other type of non-deterministic. It can be a logical or non-repetitive signal. In some embodiments, the stochastic signal has a non-zero average. The stochastic signal can be integrated to generate the excitation signal q.

  The stochastic excitation signal q can be added to the DC value w generated by the feedback controller to form a new control input u (eg u = w + q). After the new control input u is generated, the new control input u can be provided to the plant (block 802) and the ESC control technique can be repeated. The stochastic excitation signal q may provide a variation of the control input u sufficient to estimate the performance gradient at block 806. In some instances, the addition of the excitation signal q causes the control input u to move away from its optimal value. However, the feedback controller can compensate for such drift by adjusting the DC value w so that the control input u is constantly pulled back to its optimal value. As with conventional ESCs, the magnitude of the excitation signal q can be selected (eg, manually by the user, eg, to overcome the additive noise (eg, process noise, measurement noise, etc.) found in the performance variable y. Or automatically by the controller).

The stochastic excitation signal q has several advantages over the periodic dither signal v. For example, the stochastic excitation signal q is not as perceptible as the conventional periodic dither signal v. Therefore, the effect of the stochastic excitation signal q on the control input u is not as pronounced as the periodic oscillation caused by the conventional periodic dither signal v. Another advantage of the stochastic excitation signal q is that the controller is easier to tune because the dither frequency ω _v is no longer a required parameter. Accordingly, the controller does not need to know or estimate the natural frequency of the plant in generating the stochastic excitation signal q.

  Referring now to FIG. 9, a flow diagram 900 illustrating another extreme value search control (ESC) technique is shown according to some embodiments. The ESC technique shown in flow diagram 900 may be performed by one or more components of a feedback controller (eg, controller 502) to monitor and control a plant (eg, plant 504). For example, the controller 502 can use ESC techniques to estimate a normalized correlation coefficient ρ that associates a plant output (eg, performance variable y) with a control input u provided to the plant. The controller 502 can determine the optimum value of the control input u by bringing the normalized correlation coefficient ρ to zero.

  Flow diagram 900 is shown to include providing control input u to the plant (block 902) and receiving performance variable y as feedback from the plant (block 904). The control input u can be provided to the plant by an extreme value search controller and / or a feedback controller. The controller may be any of the previously described controllers (eg, controller 302, controller 402, controller 502, etc.) or any other type of controller that provides a control input u to the plant. In some embodiments, the controller is an extreme value search controller configured to achieve the optimum value of the performance variable y by adjusting the control input u. The optimal value may be the extreme value (eg, maximum or minimum) of the performance variable y.

  A control theoretical plant is a combination of a process and one or more machine control outputs. The plant can be any of the previously described plants (eg, plant 304, plant 404, plant 504, etc.) or any other controllable system or process. For example, the plant may be an air treatment unit configured to control the temperature in a building space via one or more machine controlled actuators and / or dampers. In various embodiments, the plant is tuned such that the refrigerator operating process, damper adjustment process, mechanical cooling process, ventilation process, refrigeration process, or control input u to the plant affects the performance variable y. Any other process may be included. The performance variable y is a measured variable (eg, measured temperature, measured power consumption, measured flow rate, etc.) observed by one or more sensors in the plant, a calculated variable based on a measured or observed value (eg, calculated efficiency, calculated Power consumption, computational cost, etc.) or any other type of variable that indicates the performance of the plant in response to the control input u.

と関連付ける（例えば、

に比例する）ことができるが、性能変数ｙの範囲に基づいてスケーリングされる。例えば、相関係数ρは、性能勾配

の正規化尺度であり得る（例えば、範囲０≦ρ≦１にスケーリングされる）。 The flow diagram 900 is shown to include estimating a normalized correlation coefficient ρ that associates the performance variable y with the control input u. The correlation coefficient ρ is the performance gradient

Associated with (for example,

Scaled based on the range of performance variable y. For example, the correlation coefficient ρ is the performance gradient

(For example, scaled to the range 0 ≦ ρ ≦ 1).

式中、Ｃｏｖ（ｕ，ｙ）は、制御入力ｕと性能変数ｙとの間の共分散であり、Ｖａｒ（ｕ）は、制御入力ｕの分散であり、Ｖａｒ（ｙ）は、性能変数ｙの分散である。以前の方程式は、制御入力ｕの標準偏差σ_ｕおよび性能変数ｙの標準偏差σ_ｙの観点から以下の通り記載しなおすことができる。

式中、

である。 In some embodiments, the correlation coefficient ρ can be estimated based on the variance and covariance of the control input u and the performance variable y, as shown in the following equation:

Where Cov (u, y) is the covariance between the control input u and the performance variable y, Var (u) is the variance of the control input u, and Var (y) is the performance variable y Is the dispersion of. Previous equation can be re-described as follows in terms of the standard deviation sigma _y of the standard deviation sigma _u and performance variable y of the control input u.

Where

It is.

式中、

は、時間ｋにおける制御入力ｕおよび性能変数ｙのＥＷＭＡであり、

は、時間ｋ−１における制御入力ｕおよび性能変数ｙの以前のＥＷＭＡであり、ｕ_ｋおよびｙ_ｋは、時間ｋにおける制御入力ｕおよび性能変数ｙの現行値であり、ｋは、各変数の収集されたサンプルの総数であり、Ｗは、忘却窓の持続時間である。 In some embodiments, the correlation coefficient ρ is estimated using a recursive estimation technique. The recursive estimation technique may include calculating an exponential weighted moving average (EWMA) of the control input u and the performance variable y. For example, the EWMA of the control input u and the performance variable y can be calculated using the following equation:

Where

Is the EWMA of control input u and performance variable y at time k,

Is the previous EWMA of the control input u and performance variable y at time k−1, u _k and y _k are the current values of the control input u and performance variable y at time k, and k is for each variable The total number of samples collected, W is the duration of the forgetting window.

式中、Ｖ_ｕ，ｋ、Ｖ_ｙ，ｋおよびｃ_ｋはそれぞれ、時間ｋにおける制御入力分散Ｖａｒ（ｕ）、性能変数分散Ｖａｒ（ｙ）および共分散Ｃｏｖ（ｕ，ｙ）のＥＷＭＡである。Ｖ_{ｕ，ｋ−１}、Ｖ_{ｙ，ｋ−１}およびｃ_ｋ−１はそれぞれ、時間ｋ−１における制御入力分散Ｖａｒ（ｕ）、性能変数分散Ｖａｒ（ｙ）および共分散Ｃｏｖ（ｕ，ｙ）のＥＷＭＡである。相関係数ρは、以下の方程式を使用して、これらの再帰的推定に基づいて推定することができる。

EWMA can also be calculated for control input variance Var (u), performance variable variance Var (y) and covariance Cov (u, y) using the following equations:

_Where V _{u, k} , V _{y, k} and c _k are the EWMA of control input variance Var (u), performance variable variance Var (y) and covariance Cov (u, y) at time k, respectively. V _{u, k−1} , V _{y, k−1} and c _k−1 are the control input variance Var (u), performance variable variance Var (y) and covariance Cov (u, y) at time k−1, respectively. EWMA. The correlation coefficient ρ can be estimated based on these recursive estimates using the following equation:

に基づいて推定される。以前に説明されるように、推定傾き

は、以下の方程式を使用して計算することができる。

式中、Ｃｏｖ（ｕ，ｙ）は、制御入力ｕと性能変数ｙとの間の共分散であり、Ｖａｒ（ｕ）は、制御入力ｕの分散であり、すなわち、

である。相関係数ρは、以下の方程式を使用して、傾き

から計算することができる。

以前の方程式から、標準偏差σ_ｕとσ_ｙが等しい際（すなわち、σ_ｕ＝σ_ｙの際）は、相関係数ρと推定傾き

は等しいことが分かる。 In some embodiments, the correlation coefficient ρ is an estimated slope

Is estimated based on Estimated slope, as previously explained

Can be calculated using the following equation:

Where Cov (u, y) is the covariance between the control input u and the performance variable y, and Var (u) is the variance of the control input u, ie

It is. The correlation coefficient ρ is sloped using the following equation:

Can be calculated from

From the previous equation, when the standard deviations σ _u and σ _y are equal (that is, when σ _u = σ _y ), the correlation coefficient ρ and the estimated slope

Are equal.

は、制御入力ｕおよび性能変数ｙの値の集合を使用して計算することができる。例えば、ｕおよびｙの有限分散を想定すると、傾き

は、以下の最小二乗推定を使用して推定することができる。

In some embodiments, the estimated slope

Can be calculated using a set of values for the control input u and the performance variable y. For example, assuming a finite variance of u and y, the slope

Can be estimated using the following least squares estimation:

は、以下の方程式に示されるように、性能勾配のプロキシとして使用することができる。

以前の方程式に示されるように、推定傾き

は定利得Ｋを含み、定利得Ｋは未知数であり得る。しかし、標準偏差σ_ｕおよびσ_ｙによって提供される正規化は、定利得Ｋの効果を無効にする。例えば、性能変数ｙの標準偏差σ_ｙは、以下の方程式に示されるように、制御入力ｕの標準偏差σ_ｕと関連付けられる。

In case of small range of control input u, estimated slope

Can be used as a proxy for performance gradient, as shown in the equation below.

Estimated slope, as shown in the previous equation

Includes a constant gain K, which may be an unknown. However, the normalization provided by the standard deviations σ _u and σ _y negates the effect of the constant gain K. For example, a standard deviation sigma _y of the performance variables y, as shown in the following equation, is associated with the standard deviation sigma _u of the control input u.

に比率

を乗じることは、定利得Ｋで除することに等しい。相関係数ρおよび推定傾き

は両方とも、制御入力ｕと性能変数ｙとの関係の強さを示す。しかし、相関係数ρは、正規化されているという利点を有し、それにより、フィードバック制御ループの調整がはるかに簡単になる。 Estimated slope to calculate correlation coefficient ρ

To ratio

Multiplication is equivalent to dividing by a constant gain K. Correlation coefficient ρ and estimated slope

Both indicate the strength of the relationship between the control input u and the performance variable y. However, the correlation coefficient ρ has the advantage of being normalized, which makes the adjustment of the feedback control loop much easier.

  Still referring to FIG. 9, the flow diagram 900 is shown to include bringing the estimated correlation coefficient ρ to zero (block 908) by adjusting the output of the feedback controller. In some embodiments, the feedback controller is the feedback controller 508 shown in FIG. The feedback controller can receive the estimated correlation coefficient ρ as an input and adjust its output (eg, DC output w) to bring the estimated correlation coefficient ρ to zero. The feedback controller can increase or decrease the value of the DC output w until the optimum value of the DC output w is reached. The optimal value of the DC output w can be defined as the value that yields the optimal value (eg, the maximum or minimum value) of the performance variable y. The optimum value of the performance variable y occurs when the slope becomes zero. Accordingly, the feedback controller can achieve the optimum value of the performance variable y by adjusting its output w to bring the estimated correlation coefficient ρ to zero.

  Flow diagram 900 includes generating an excitation signal (block 910) and generating a new control input u (block 912) by perturbing the output w of the feedback controller using the excitation signal. Is shown in In various embodiments, the excitation signal is a periodic dither signal v as described with reference to FIGS. 3 and 4, or a stochastic excitation signal q as described with reference to FIG. obtain. The excitation signal can be added to the DC value w generated by the feedback controller to form a new control input u (eg u = w + q or u = w + v). After the new control input u is generated, the new control input u can be provided to the plant (block 902) and the ESC control technique can be repeated.

  The excitation signal may provide a variation of the control input u sufficient to estimate the correlation coefficient ρ at block 906. In some instances, the addition of the excitation signal causes the control input u to move away from its optimal value. However, the feedback controller can compensate for such drift by adjusting the DC value w so that the control input u is constantly pulled back to its optimal value. The magnitude of the excitation signal can be selected (eg, manually by the user or automatically by the controller) to overcome the additional noise (eg, process noise, measurement noise, etc.) found in the performance variable y.

Example Implementations Referring now to FIGS. 10A-16C, some example implementations of the extreme search control system and method of the present disclosure are shown. The implementation shown in FIGS. 10A-16C includes a plant 504 that can be controlled by an extreme value search controller 502, a control input u that can be provided to the plant 504 by the extreme value search controller 502, and an extreme value search controller 502. Shows various embodiments of the performance variable y that can be received as feedback from the plant 504.

Cooling water plant 1000
With particular reference to FIG. 10A, a cooling water plant 1000 according to some embodiments is shown. The cooling water plant 1000 is shown to include a refrigerator 1002, a cooling tower 1004, and an air treatment unit (AHU) 1006. The refrigerator 1002 includes a condenser 1018, an evaporator 1020, and a compressor 1034. The compressor 1034 is configured to circulate refrigerant between the condenser 1018 and the evaporator 1020 via the refrigerant loop 1026. The refrigerator 1002 also includes at least one expansion valve between the condenser 1018 and the evaporator 1020 on the refrigerant loop 1026. The refrigerator 1002 operates using a vapor compression refrigeration cycle. In the vapor compression refrigeration cycle, the refrigerant in the refrigerant loop 1026 absorbs heat in the evaporator 1020 and exhausts heat in the condenser 1018. The refrigerator 1002 can include any number of sensors, control valves, and / or other components that assist the refrigerator 1002 in refrigeration cycle operation.

  The refrigerator 1002 is connected to the cooling tower 1004 by a condenser water supply loop 1022. A condenser water pump 1014 located along the condenser water loop 1022 circulates the condenser water via the condenser water loop 1022 between the cooling tower 1004 and the refrigerator 1002. The condenser water pump 1014 can be a fixed speed pump or a variable speed pump. The condenser water supply loop 1022 circulates the condenser water through the condenser 1018, and the condenser water absorbs heat from the refrigerant in the refrigeration loop 1026. The heated condenser water is then delivered to the cooling tower 1004 where it is exhausted to the surrounding environment. The cooling tower fan system 1036 provides an airflow that flows through the cooling tower 1004 to facilitate cooling of the condenser water within the cooling tower 1004. The cooled condenser water is then sent back to the refrigerator 1002 by the condenser water pump 1014.

  The refrigerator 1002 is connected to the AHU 1006 via the cooling fluid loop 1024. A cooling fluid pump 1016 located along the cooling fluid loop 1024 circulates cooling fluid between the refrigerator 1002 and the AHU 1006. The pump 1016 can be a fixed speed pump or a variable speed pump. The cooling fluid loop 1024 circulates the cooling fluid through the evaporator 1020, and the cooling fluid exhausts heat to the refrigerant in the refrigeration loop 1026 in the evaporator 1020. The cooling fluid is then delivered to the AHU 1006, where the cooling fluid absorbs heat from the supply air flowing through the AHU 1006, thereby providing cooling to the supply air. The heated fluid is then sent back to the refrigerator 1002 by the pump 1016.

  In the embodiment shown in FIG. 10A, AHU 1006 is shown as an economizer type air treatment unit. Economizer type AHUs vary the amount of outside and return air used by the AHU for cooling. AHU 1006 is shown to include an economizer controller 1032 that utilizes one or more algorithms (eg, state-based algorithms, extreme value search control algorithms, etc.) to affect the actuators and dampers or fans of AHU 1006. Has been. The flow rate of the cooling fluid supplied to the AHU 1006 can be variably controlled. For example, PI control 1008 is shown to control a valve 1038 that regulates the flow rate of cooling fluid to AHU 1006. The PI control 1008 can control the flow rate of cooling fluid to the AHU 1006 to achieve the setpoint supply air temperature. The economizer controller 1032, the controller for the refrigerator 1002 and the PI control 1008 can be monitored by one or more building management system (BMS) controllers 1010.

  A BMS controller is generally a computer-based system configured to control, monitor and manage equipment in or around a building or building area. BMS controllers are available from Johnson Controls, Inc. May include a METASYS® brand building controller or other device sold by The BMS controller 1010 may include one or more human machine interfaces or client interfaces (eg, graphical user interface, reporting interface, text, etc.) for controlling, viewing or otherwise interacting with the BMS, its subsystems and devices. Base computer interfaces, web services directly addressing customers, web servers that serve pages to web clients, etc.). For example, the BMS controller 1010 can provide a web-based graphical user interface that allows a user to set a desired setpoint temperature for a building space. The BMS controller 1010 may use a BMS sensor 1012 (connected to the BMS controller 1010 via a wired or wireless BMS or IT network) to determine whether a setpoint temperature for the building space has been achieved. it can. The BMS controller 1010 may use such a determination to provide commands to the PI control 1008, the refrigerator 1002, the economizer controller 1032, or other components of the building HVAC system.

  In some embodiments, the extremum search controller 502 does not receive control commands from the BMS controller 1010 or perform its output calculation based on input from the BMS controller 1010. In other embodiments, the extreme value search controller 502 receives information (eg, commands, setpoints, operating boundaries, etc.) from the BMS controller 1010. For example, the BMS controller 1010 can provide a high fan speed limit and a low fan speed limit to the extreme value search controller 502. Low limits can avoid starting up frequent components and high power load fans, while high limits can avoid operating near fan system mechanical or thermal limits.

The extreme value search controller 502 is a power input P _total representing the total power consumed by the cooling tower fan system 1036 P _tower , the condenser water pump 1014 P _pump and the compressor 1034 P _chiller of the refrigerator 1002 (ie, P _total = It is shown to receive the _{P tower + P pump + P chiller} ). As shown in FIG. 10A, the power input _{P tower, P pump} and _{P chiller} is to provide a combined signal representative of the total power _{P total,} be sum outside the summation block 1040 extremum search controller 502 it can. In another embodiment, the extremum search controller 502, individual power input _{P tower,} receives the _{P pump} and _{P chiller,} to implement the sum of the total block 1040. In either case, extreme value search controller 502, even if the single sum or power input as a combination signal _{P total} representing the total system power is provided, the power input _{P tower,} the _{P pump} and _{P chiller} It can be said that it receives.

In some embodiments, the total system power P _total is a performance variable that the extremum search controller 502 seeks to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the cooling water plant 1000. In the embodiment shown in FIG. 10A, the total system power _{P total includes P tower, P pump} and _{P chiller.} However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total may include power consumption of fans in the AHU 1006, power consumption of the cooling fluid pump 1016, and / or any other power consumption that occurs in the cooling water plant 1000.

The extreme value search controller 502 is shown to provide a temperature setpoint T _sp to the feedback controller 1028. In some embodiments, the temperature setpoint _Tsp is an manipulated variable that the extreme value search controller 502 adjusts to affect the _total system power _Ptotal . The temperature set point T _sp is a set point for the temperature T _cw of the condenser water provided from the cooling tower 1004 to the refrigerator 1002. The condenser water temperature T _cw may be measured by a temperature sensor 1030 located along the condenser water loop 1022 between the cooling tower 1004 and the refrigerator 1002 (eg, upstream or downstream of the condenser water pump 1014). it can. The feedback controller 1028 is shown to receive the condenser water temperature T _cw as a feedback signal.

The feedback controller 1028 can operate the cooling tower fan system 1036 and / or the condenser water pump 1014 to achieve the temperature setpoint T _sp provided by the extreme value search controller 502. For example, the feedback controller 1028 may increase the speed of the condenser water pump 1014 to increase the amount of heat removed from the refrigerant in the condenser 1018, or the amount of heat removed from the refrigerant in the condenser 1018. The speed of the condenser water pump 1014 can also be reduced to reduce. Similarly, the feedback controller 1028 increases the speed of the cooling tower fan system 1036 to increase the amount of heat removed from the condenser water by the cooling tower 1004 and is also removed from the condenser water by the cooling tower 1004. The cooling tower fan system 1036 can also be slowed to reduce the amount of heat.

The extreme value search controller 502 dynamically uses unknown inputs (eg, optimal condenser water temperature setpoint T _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement an extreme value search control strategy to search for. Although feedback controller 1028 and extreme value search controller 502 are shown as separate devices, in some embodiments, feedback controller 1028 and extreme value search controller 502 are combined into a single device (eg, extreme value search controller). It is contemplated that it can be a single controller that performs the functions of both 502 and feedback controller 1028. For example, the extreme value search controller 502 can be configured to directly control the cooling tower fan system 1036 and the condenser water pump 1014 without the need for an intermediate feedback controller 1028.

Referring now to FIGS. 10B and 10C, a pair of flow diagrams 1050 and 1070 illustrating the operation of the extreme value search controller 502 of the cooling water plant 1000 are shown, according to some embodiments. In both flow diagrams 1050 and 1070, the extreme value search controller 502 provides a temperature setpoint T _sp to a feedback controller 1028 that operates to control the condenser water temperature T _cw of the cooling water plant 1000 (block 1052 and 1072). The extreme value search controller 502 may receive the total power consumption P _total of the cooling water plant 1000 as a feedback signal (blocks 1054 and 1074).

In the flow diagram 1050, the extreme value search controller 502 estimates the slope of the _total power consumption _Ptotal relative to the condenser water temperature set point Tsp (block 1056). Extremum search controller 502, by bringing the slope obtained by adjusting the temperature set point T _sp to zero, it is possible to provide a control on the cooling water plant 1000 (block 1058). In some embodiments, the extreme value search controller 502 generates a stochastic excitation signal (block 1060) and uses the stochastic excitation signal to generate a new condenser water temperature setpoint _Tsp . For example, the extremum search controller 502, by perturbing the condenser water temperature setpoint T _sp using stochastic excitation signal, can generate a new temperature setpoint T _sp (block 1062).

In flow diagram 1070, extremum search controller 502 estimates the normalized correlation coefficient relating the total power consumption _{P total} and the condenser water temperature setpoint _{T sp} (block 1076). Extremum search controller 502, by bringing the estimated correlation coefficient to zero by adjusting the temperature set point T _sp, it is possible to provide a control on the cooling water plant 1000 (block 1078). In some embodiments, the extreme search controller 502 generates an excitation signal (block 1080) and uses the excitation signal to generate a new condenser water temperature setpoint _Tsp . For example, the extremum search controller 502, by perturbing the condenser water temperature setpoint T _sp using an excitation signal, it is possible to generate a new temperature setpoint T _sp (block 1082).

Cooling water plant 1100
Referring now to FIG. 11A, another cooling water plant 1100 is shown according to some embodiments. The cooling water plant 1100 may include some or all of the components of the cooling water plant 1000 as described with reference to FIG. 10A. For example, the cooling water plant 1100 is shown to include a refrigerator 1102, a cooling tower 1104, and an air treatment unit (AHU) 1106. The refrigerator 1102 is connected to the cooling tower 1104 by a condenser water supply loop 1122. A condenser water pump 1114 located along the condenser water loop 1122 circulates the condenser water between the cooling tower 1104 and the refrigerator 1102. The cooling tower fan system 1136 provides an airflow that flows through the cooling tower 1104 to facilitate cooling of the condenser water in the cooling tower 1104. The refrigerator 1102 is also connected to the AHU 1106 via a cooling fluid loop 1124. A cooling fluid pump 1116 located along the cooling fluid loop 1124 circulates cooling fluid between the refrigerator 1102 and the AHU 1106.

Extremum search controller 502, the cooling tower fan system 1136 P _tower, condenser water pump 1114 P _pump and power representing the total power consumed by the compressor 1134 P _chiller refrigerator 1102 input _{P total (i.e., P total} = It is shown to receive the _{P tower + P pump + P chiller} ). In some embodiments, the total system power P _total is a performance variable that the extremum search controller 502 seeks to optimize (eg, minimize). In the embodiment shown in FIG. 11A, the total system power _{P total includes P tower, P pump} and _{P chiller.} However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total may include power consumption of fans in the AHU 1106, power consumption of the cooling fluid pump 1116, and / or any other power consumption that occurs in the cooling water plant 1100.

The extreme value search controller 502 provides a first control signal that regulates the fan speed Fan _sp of the cooling tower fan system 1136 and a second control signal that regulates the pump speed Pump _sp of the condenser water pump 1114. Is shown in In some embodiments, the fan speed Fan _sp and pump speed Pump _sp are manipulated variables that the extremum search controller 502 adjusts to affect the _total system power P _total . For example, the extreme value search controller 502 can increase the pump speed Pump _sp to increase the amount of heat removed from the refrigerant in the condenser 1118, or can reduce the amount of heat removed from the refrigerant in the condenser 1118. The pump speed Pump _sp can also be reduced to reduce it. Similarly, the extremum search controller 502 can increase the fan speed Fan _sp to increase the amount of heat removed from the condenser water by the cooling tower 1104, or the heat removed from the condenser water by the cooling tower 1104. The fan speed Fan _sp can also be reduced to reduce the amount of.

Referring now to FIGS. 11B and 11C, a pair of flow diagrams 1150 and 1170 are shown that illustrate the operation of the extreme value search controller 502 of the cooling water plant 1100, according to some embodiments. In both flow diagrams 1150 and 1170, the extreme search controller 502 provides a fan speed control signal Fan _sp to the cooling tower fan system and a pump speed control signal Pump _sp to the condenser water pump (blocks 1152 and 1172). ). The extreme value search controller 502 may receive the total power consumption P _total of the cooling water plant 1100 as a feedback signal (blocks 1154 and 1174).

In the flow diagram 1150, the extremum search controller 502 has a first slope of the total power consumption P _total with respect to the fan speed Fan _sp and a second slope of the total power consumption P _total with respect to the condenser water pump speed Pump _sp . Is estimated (block 1156). The extreme value search controller 502 can provide control on the cooling water plant 1100 by bringing the slope obtained by adjusting the fan speed Fan _sp and the condenser water pump speed Pump _sp to zero ( Block 1158). In some embodiments, the extreme value search controller 502 generates a stochastic excitation signal for each of the rate control signals (block 1160) and uses the stochastic excitation signal to generate a new rate control signal ( Block 1162). For example, the extreme value search controller 502 can generate a new fan speed control signal Fan _sp by perturbing the fan speed control signal Fan _sp using the first stochastic excitation signal. The extreme value search controller 502 can generate a new pump speed control signal Pump _sp by perturbing the pump speed control signal Pump _sp with the second stochastic excitation signal.

In the flow diagram 1170, the extremum search controller 502 uses a first normalized correlation coefficient that relates the total power consumption P _total to the fan speed Fan _sp , and the total power consumption P _total to the condenser water pump speed Pump _sp. Is estimated (block 1176). Extreme search controller 502 may provide control on cooling water plant 1100 by bringing the estimated correlation coefficient to zero by adjusting fan speed Fan _sp and pump speed Pump _sp (block 1178). . In some embodiments, the extreme search controller 502 generates an excitation signal for each of the speed control signals (block 1180) and uses the excitation signal to generate new fan and pump speeds (block 1182). For example, the extreme value search controller 502 can generate a new fan speed control signal Fan _sp by perturbing the fan speed control signal Fan _sp using the first excitation signal. The extreme value search controller 502 can generate a new pump speed control signal Pump _sp by perturbing the pump speed control signal Pump _sp using the second excitation signal.

Variable refrigerant flow system 1200
Referring now to FIG. 12A, a variable refrigerant flow (VRF) system 1200 according to some embodiments is shown. VRF system 1200 is shown to include an outdoor unit 1202, several heat recovery units 1204, and several indoor units 1206. In some embodiments, the outdoor unit 1202 is located outside the building (eg, the rooftop) and the indoor unit 1206 is distributed throughout the building (eg, to various rooms or zones of the building). In some embodiments, the VRF system 1200 includes a number of heat recovery units 1204. The heat recovery unit 1204 can control the flow rate of refrigerant between the outdoor unit 1202 and the indoor unit 1206 (eg, by opening and closing valves) to minimize the heating or cooling load provided by the outdoor unit 1202. .

  Outdoor unit 1202 is shown to include a compressor 1214 and a heat exchanger 1220. The compressor 1214 circulates the refrigerant between the heat exchanger 1220 and the indoor unit 1206. The heat exchanger 1220 functions as a condenser (allows the refrigerant to exhaust heat to the outside air) when the VRF system 1200 operates in the cooling mode, or when the VRF system 1200 operates in the heating mode. Can also function as an evaporator (which allows the refrigerant to absorb heat from the outside air). The fan 1218 provides an airflow that flows through the heat exchanger 1220. The speed of the fan 1218 can be adjusted to adjust the heat transfer rate into or out of the refrigerant in the heat exchanger 1220.

  Each indoor unit 1206 is shown to include a heat exchanger 1226 and an expansion valve 1224. Each of the heat exchangers 1226 can function as a condenser (which allows the refrigerant to exhaust heat into the air in the room or zone) when the indoor unit 1206 operates in the heating mode, or the indoor unit 1206. When operating in cooling mode, it can also function as an evaporator (allowing refrigerant to absorb heat from the air in the room or zone). Fan 1222 provides an airflow that flows through heat exchanger 1226. The speed of the fan 1222 can be adjusted to adjust the heat transfer rate into or out of the refrigerant in the heat exchanger 1226. The temperature sensor 1228 can be used to measure the temperature of the refrigerant in the indoor unit 1206.

  In FIG. 12A, the indoor unit 1206 is shown to operate in a cooling mode. In the cooling mode, the refrigerant is provided to the indoor unit 1206 via the cooling pipe 1212. The refrigerant is expanded to a low temperature and low pressure state by an expansion valve 1224 and flows through a heat exchanger 1226 (acting as an evaporator) to absorb heat from a room or zone in the building. Next, the heated refrigerant is refluxed to the outdoor unit 1202 through the reflux pipe 1210 and compressed to a high temperature and high pressure state by the compressor 1214. The compressed refrigerant flows through the heat exchanger 1220 (functioning as a condenser) and exhausts heat to the outside air. The cooled refrigerant can then be provided to indoor unit 1206 via cooling tube 1212. In the cooling mode, the flow control valve 1236 can be closed and the expansion valve 1234 can be fully opened.

  In the heating mode, the refrigerant is provided to the indoor unit 1206 at a high temperature via the heating pipe 1208. The hot refrigerant flows through the heat exchanger 1226 (which functions as a condenser) and exhausts heat to the air in the building room or zone. The refrigerant then flows back to the outdoor unit via the cooling pipe 1212 (as opposed to the flow direction shown in FIG. 12A). The refrigerant can be expanded to a low temperature and low pressure state by an expansion valve 1234. The expanded refrigerant flows through the heat exchanger 1220 (functioning as an evaporator) and absorbs heat from the outside air. The heated refrigerant can be compressed by the compressor 1214 and provided to the indoor unit 1206 through the heating pipe 1208 in a high-temperature compressed state. In the heating mode, the flow control valve 1236 can be fully opened so that the refrigerant from the compressor 1214 can flow into the heating tube 1208.

Extremum search controller 502, power input represents the total power _{P indoor} consumed by the total power _{P outdoor} and the indoor unit 1206, which is consumed by the outdoor unit 1202 _{P total (i.e., P total = P outdoor + P} indoor) receive Shown to be. The outdoor unit power _Poutdoor may include the power consumption of the compressor 1214 and / or the fan 1218. Indoor unit power P _indoor may include the power consumption of fan 1222 and / or any other power consuming device or heat recovery unit 1204 (eg, electronic valve, pump, fan, etc.) within indoor unit 1206. As shown in FIG 12A, the power input _{P outdoor} and _{P indoor,} in order to provide a combined signal representative of the total power _{P total,} it is possible to sum outside the summation block 1230 extremum search controller 502. In other embodiments, the extremum search controller 502 receives the individual power inputs P _outdoor and P _indoor and performs the summation of the summation block 1230. In either case, extreme value search controller 502, even if the single sum or power input as a combination signal _{P total} representing the total system power is provided, receiving power input _{P outdoor} and _{P indoor} I can say.

In some embodiments, the total system power P _total is a performance variable that the extremum search controller 502 seeks to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the VRF system 1200. In the embodiment shown in FIG. 12A, the total system power _{P total includes P outdoor} and _{P indoor.} However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total may include the recovery unit 1204, the indoor unit 1206, the outdoor unit 1202, pump power consumption and / or any other power consumption that occurs within the VRF system 1200.

The extreme value search controller 502 is shown to provide the pressure setpoint P _sp to the outdoor unit controller 1232. In some embodiments, the pressure setpoint _Psp is an manipulated variable that the extreme value search controller 502 adjusts to affect the _total system power _Ptotal . The pressure setpoint _{P sp} is the set point for the pressure _{P r} of the refrigerant in the suction or discharge of the compressor 1214. Refrigerant pressure _{P r} is the suction side of the compressor 1214 (e.g., upstream of the compressor 1214) can be measured or the discharge side of the compressor 1214 (e.g., downstream of the compressor 1214) by a pressure sensor 1216 located. Outdoor unit controller 1232 is shown to receive the refrigerant pressure P _r as a feedback signal.

The outdoor unit controller 1232 can operate the outdoor unit 1202 to achieve the pressure set point P _sp provided by the extreme value search controller 502. Operating the outdoor unit 1202 may include adjusting the speed of the compressor 1214 and / or the speed of the fan 1218. For example, the outdoor unit controller 1232 can increase the speed of the compressor 1214 to increase the compressor discharge pressure or decrease the compressor suction pressure. The outdoor unit controller 1232 can increase the speed of the fan 1218 to increase heat transfer in the heat exchanger 1220 or decrease the speed of the fan 1218 to decrease heat transfer in the heat exchanger 1220. .

The extreme value search controller 502 dynamically searches for an unknown input (eg, pressure set point P _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement a search control strategy. Although outdoor unit controller 1232 and extreme value search controller 502 are shown as separate devices, in some embodiments, outdoor unit controller 1232 and extreme value search controller 502 can be combined into a single device (eg, extreme value). It is contemplated that it can be a single controller that performs the functions of both the search controller 502 and the outdoor unit controller 1232. For example, the extreme value search controller 502 can be configured to directly operate the compressor 1214 and / or the fan 1218 without the need for the intermediate outdoor unit controller 1232.

Referring now to FIGS. 12B and 12C, a pair of flow diagrams 1250 and 1270 illustrating the operation of the extreme value search controller 502 of the VRF system 1200 are shown in accordance with some embodiments. In both flow diagrams 1250 and 1270, the extreme value search controller 502 provides a pressure setpoint P _sp to a controller (eg, outdoor unit controller 1232) that operates to control the refrigerant pressure of the outdoor unit 1202 of the VRF system 1200. (Blocks 1252 and 1272). The refrigerant pressure can be a compressor suction pressure or a compressor discharge pressure. The extreme value search controller 502 may receive the total power consumption P _total of the VRF system 1200 as a feedback signal (blocks 1254 and 1274).

In the flow diagram 1250, the extreme value search controller 502 estimates the slope of the _total power consumption _Ptotal relative to the refrigerant pressure set point _Psp (block 1256). The extreme value search controller 502 can provide control on the VRF system 1200 by bringing the slope obtained by adjusting the pressure setpoint P _sp to zero (block 1258). In some embodiments, the extreme value search controller 502 generates a stochastic excitation signal (block 1260) and uses the stochastic excitation signal to generate a new refrigerant pressure setpoint _Psp . For example, the extreme value search controller 502 can generate a new pressure set point P _sp by perturbing the refrigerant pressure set point P _sp using a stochastic excitation signal (block 1262).

In the flow diagram 1270, the extreme value search controller 502 estimates a normalized correlation coefficient that relates the total power consumption P _total to the refrigerant pressure set point P _sp (block 1276). The extreme value search controller 502 can provide control on the VRF system 1200 by bringing the estimated correlation coefficient to zero by adjusting the refrigerant pressure set point P _sp (block 1278). In some embodiments, the extreme value search controller 502 generates an excitation signal (block 1280) and uses the excitation signal to generate a new refrigerant pressure setpoint _Psp . For example, the extreme value search controller 502 can generate a new pressure set point P _sp by perturbing the refrigerant pressure set point P _sp using the excitation signal (block 1282).

Variable refrigerant flow system 1300
Referring now to FIG. 13A, another variable refrigerant flow (VRF) system 1300 is shown according to some embodiments. VRF system 1300 may include some or all of the components of VRF system 1200 as described with reference to FIG. 12A. For example, the VRF system 1300 is shown to include an outdoor unit 1302, several heat recovery units 1304, and several indoor units 1306.

  Outdoor unit 1302 is shown to include a compressor 1314 and a heat exchanger 1320. The compressor 1314 circulates the refrigerant between the heat exchanger 1320 and the indoor unit 1306. The heat exchanger 1320 functions as a condenser (allows the refrigerant to exhaust heat to the outside air) when the VRF system 1300 operates in the cooling mode, or when the VRF system 1300 operates in the heating mode. Can also function as an evaporator (which allows the refrigerant to absorb heat from the outside air). Fan 1318 provides an airflow that flows through heat exchanger 1320. The speed of the fan 1318 can be adjusted to adjust the heat transfer rate into or out of the refrigerant in the heat exchanger 1320.

Each indoor unit 1306 is shown to include a heat exchanger 1326 and an expansion valve 1324. Each of the heat exchangers 1326 can function as a condenser (which allows the refrigerant to exhaust heat into the air in the room or zone) when the indoor unit 1306 operates in the heating mode. When operating in cooling mode, it can also function as an evaporator (allowing refrigerant to absorb heat from the air in the room or zone). Fan 1322 provides an airflow that flows through heat exchanger 1326. The speed of the fan 1322 can be adjusted to adjust the heat transfer rate into or out of the refrigerant in the heat exchanger 1326. The temperature sensor 1328 can be used to measure the temperature _Tr of the refrigerant in the indoor unit 1306.

Extremum search controller 502, power input represents the total power _{P indoor} consumed by the total power _{P outdoor} and the indoor unit 1306 consumed by the outdoor unit 1302 _{P total (i.e., P total = P outdoor + P} indoor) receive Shown to be. The outdoor unit power _Poutdoor may include the power consumption of the compressor 1314 and / or the fan 1318. Indoor unit power P _indoor may include the power consumption of fan 1322 and / or any other power consuming device or heat recovery unit 1304 (eg, electronic valve, pump, fan, etc.) within indoor unit 1306.

In some embodiments, the total system power P _total is a performance variable that the extremum search controller 502 seeks to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the VRF system 1300. In the embodiment shown in FIG. 13A, the total system power _{P total includes P outdoor} and _{P indoor.} However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, total system power P _total may include recovery unit 1304, indoor unit 1306, outdoor unit 1302, pump power consumption and / or any other power consumption that occurs within VRF system 1300.

The extreme value search controller 502 is shown to provide a pressure set point P _sp to the outdoor unit controller 1332 and a superheat temperature set point T _sp to the indoor unit controller 1338. In some embodiments, the pressure set point P _sp and the superheat temperature set point T _sp are manipulated variables that the extremum search controller 502 adjusts to affect the _total system power P _total . The pressure setpoint _{P sp} is the set point for the pressure _{P r} of the refrigerant in the suction or discharge of the compressor 1314. The superheat temperature set point T _sp is a set point for the amount of refrigerant superheat at the outlet of the heat exchanger 1326 (that is, the refrigerant temperature T _r -the refrigerant saturation temperature).

Refrigerant pressure _{P r} is the suction side of the compressor 1314 (e.g., upstream of the compressor 1314) can be measured by a pressure sensor 1316 located in or discharge side of the compressor 1314 (e.g., downstream of the compressor 1314). Outdoor unit controller 1332 is shown to receive the refrigerant pressure P _r as a feedback signal. The outdoor unit controller 1332 can operate the outdoor unit 1302 to achieve the pressure set point P _sp provided by the extreme value search controller 502. Operating the outdoor unit 1302 may include adjusting the speed of the compressor 1314 and / or the speed of the fan 1318. For example, the outdoor unit controller 1332 can increase the speed of the compressor 1314 to increase the compressor discharge pressure or decrease the compressor suction pressure. The outdoor unit controller 1332 can increase the speed of the fan 1318 to increase heat transfer in the heat exchanger 1320 and can decrease the speed of the fan 1318 to decrease heat transfer in the heat exchanger 1320. .

The refrigerant superheat T _super can be calculated (by the indoor unit controller 1338) by subtracting the refrigerant saturation temperature T _sat from the refrigerant temperature T _r (ie, T _super = T _r −T _sat ). The refrigerant temperature _Tr can be measured by a temperature sensor 1328 located at the outlet of the heat exchanger 1326. The indoor unit controller 1338 is shown to receive the refrigerant pressure _Tr as a feedback signal. Indoor unit controller 1338 can operate the indoor unit 1306 so as to achieve a superheating temperature setpoint _{T sp} provided by extremum search controller 502. Operating the indoor unit 1306 may include adjusting the speed of the fan 1322 and / or adjusting the position of the expansion valve 1324. For example, the indoor unit controller 1338 increases the speed of the fan 1322 to increase heat transfer in the heat exchanger 1326 and decreases the speed of the fan 1322 to decrease heat transfer in the heat exchanger 1326. You can also. Similarly, the indoor unit controller 1338 moves the valve 1324 closer to the open position to increase the refrigerant flowing through the indoor unit 1306, or moves the valve 1324 closer to the closed position to decrease the refrigerant flowing through the indoor unit 1306. You can also.

The extreme value search controller 502 may provide unknown inputs (eg, pressure set point P _sp and / or superheat temperature set point T _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach an optimal value. Implement an extreme value search control strategy that dynamically searches for Although the outdoor unit controller 1332, the indoor unit controller 1338, and the extreme value search controller 502 are shown as separate devices, in some embodiments, the outdoor unit controller 1332, the indoor unit controller 1338, and the extreme value search controller 502 are combined. It is contemplated that a single device (e.g., a single controller that performs the functions of extreme search controller 502, outdoor unit controller 1332, and indoor unit controller 1338) can be used. For example, the extreme value search controller 502 may be configured to directly operate the compressor 1314, fan 1318, fan 1322 and / or valve 1324 without the need for an intermediate outdoor unit controller 1332 or indoor unit controller 1338. it can.

Referring now to FIGS. 13B and 13C, a pair of flow diagrams 1350 and 1370 illustrating the operation of the extreme value search controller 502 of the VRF system 1300 are shown in accordance with some embodiments. In both flow diagrams 1350 and 1370, extreme search controller 502 provides a pressure setpoint P _sp to a controller (eg, outdoor unit controller 1332) that operates to control the refrigerant pressure of outdoor unit 1302 of VRF system 1300. (Blocks 1352 and 1372). The refrigerant pressure can be a compressor suction pressure or a compressor discharge pressure. The extreme value search controller 502 also provides an overheat temperature setpoint to a controller (eg, indoor unit controller 1338) that operates to control the refrigerant temperature of the indoor units of the VRF system 1300 (blocks 1353 and 1373). The extreme value search controller 502 may receive the total power consumption P _total of the VRF system 1300 as a feedback signal (blocks 1354 and 1374).

In flow diagram 1350, extremum search controller 502, the first total power consumption _{P total} for refrigerant pressure setpoint _{P sp} gradient and, the total power consumption _{P total} for refrigerant superheat setpoint _{T sp} second The gradient is estimated (block 1356). Extremum search controller 502, by bringing the slope obtained by adjusting the pressure setpoint P _sp and superheat setpoint T _sp to zero, it is possible to provide a control on the VRF system 1300 (Block 1358). In some embodiments, the extreme search controller 502 generates a stochastic excitation signal (block 1360) and uses the stochastic excitation signal to create a new refrigerant pressure setpoint _Psp and a new refrigerant superheat temperature setpoint. T _sp is generated. For example, the extreme value search controller 502 can generate a new pressure set point P _sp by perturbing the refrigerant pressure set point P _sp using the first stochastic excitation signal, and the second probability by perturbing the temperature set point T _sp using logical excitation signal, it is possible to generate a new superheating temperature setpoint T _sp (block 1362).

In flow diagram 1370, extremum search controller 502, first and normalized correlation coefficient, the refrigerant superheat setpoint total power consumption _{P total} relating the total power consumption _{P total} refrigerant pressure setpoint _{P sp} estimating a second normalized correlation coefficient which relates the T _sp (block 1376). The extreme value search controller 502 can provide control on the VRF system 1300 by bringing the estimated correlation coefficient to zero by adjusting the refrigerant pressure set point P _sp and the refrigerant superheat temperature set point T _sp. (Block 1378). In some embodiments, the extreme value search controller 502 generates an excitation signal (block 1380) and uses the excitation signal to generate a new refrigerant pressure set point P _sp and a new refrigerant superheat temperature set point T _sp . For example, the extreme value search controller 502 can generate a new pressure set point P _sp by perturbing the refrigerant pressure set point P _sp using the first excitation signal, and using the second excitation signal. by perturbing the temperature setpoint _{T sp} Te, it is possible to generate a new superheating temperature setpoint _{T sp} (block 1382).

Vapor compression system 1400
Referring now to FIG. 14A, a vapor compression air conditioning system 1400 is shown according to some embodiments. System 1400 is shown to include a refrigerant circuit 1410. The refrigerant circuit 1410 includes a condenser 1412, an evaporator 1414, an expansion valve 1424, and a compressor 1406. The compressor 1406 is configured to circulate refrigerant between the evaporator 1414 and the condenser 1412. The refrigerant circuit 1410 operates using a vapor compression cycle. For example, the compressor 1406 compresses the refrigerant into a high temperature and high pressure state. The compressed refrigerant flows through the condenser 1412, and the refrigerant exhausts heat in the condenser 1412. Condenser fan 1432 can be used to adjust the heat transfer rate within condenser 1412. The cooled refrigerant is expanded to a low pressure and low temperature state by an expansion valve 1424. The expanded refrigerant flows in the evaporator 1414, and the refrigerant absorbs heat in the evaporator 1414. The evaporator fan 1416 can be used to adjust the heat transfer rate within the evaporator 1414.

  In some embodiments, the refrigerant circuit 1410 is located in a rooftop unit 1402 (eg, a rooftop air treatment unit), as shown in FIG. 14A. Rooftop unit 1402 can be configured to provide cooling to air supply 1420 flowing through air duct 1422. For example, the evaporator 1414 is located in the air duct 1422 so that the charge 1420 can flow through the evaporator 1414 and be cooled by transferring heat to the expanded refrigerant in the evaporator 1414. . The cooled airflow can then be sent to the building to provide cooling to the building room or zone. The temperature of the supply air 1420 can be measured by a temperature sensor 1418 located downstream of the evaporator 1414 (eg, in the duct 1422). In other embodiments, the refrigerant circuit 1410 is in any of a variety of other systems or devices (eg, refrigerators, heat pumps, heat recovery refrigerators, refrigeration devices, etc.) that transfer heat using a vapor compression cycle. Can be used.

The extreme value search controller 502 has a power input P _total representing the total power consumed by the compressor 1406 P _comp , the evaporator fan 1416 P _{fan, evap} and the condenser fan 1432 P _{fan, cond} (ie, P _total = P _comp + P _{fan, evav} + P _{fan, cond} ). As shown in FIG. 14A, power inputs P _comp , P _{fan, evap} and P _{fan, cond} are summation block 1408 external to extremum search controller 502 to provide a combined signal representative of total power P _total. Can be summed up. In other embodiments, the extreme value search controller 502 receives the individual power inputs P _comp , P _{fan, evap} and P _{fan, cond} and _performs the summation of the summation block 1408. In any case, the extremum search controller 502 may provide power inputs P _comp , P _{fan, evap} and P even if the power inputs are provided as a single sum representing the total system power or a combined signal P _total. It can be said that _{fan and cond} are received.

In some embodiments, the total system power P _total is a performance variable that the extremum search controller 502 seeks to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the vapor compression system 1400. In the embodiment shown in FIG. 14A, the total system power _{P total includes} P _{comp, P fan, evap} and _{P fan,} a _cond. However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total may include the power consumption of various other fans in the rooftop unit 1402, the power consumption of the fluid pump, and / or any other power consumption that occurs in the vapor compression system 1400. .

The extreme value search controller 502 is shown to provide a temperature setpoint T _sp to the feedback controller 1404. In some embodiments, the temperature setpoint _Tsp is an manipulated variable that the extreme value search controller 502 adjusts to affect the _total system power _Ptotal . The temperature set point T _sp is a set point for the temperature of the charge air 1420 exiting the evaporator 1414. The supply air temperature _Tsa can be measured by a temperature sensor 1418 located downstream of the evaporator 1414. The feedback controller 1404 is shown to receive the supply air temperature _Tsa as a feedback signal.

The feedback controller 1404 can operate the evaporator fan 1416, the condenser fan 1432, and / or the compressor 1406 to achieve the temperature set point _Tsp provided by the extreme value search controller 502. For example, the feedback controller 1404 increases the speed of the evaporator fan 1416 to increase the amount of heat removed from the charge 1420 in the evaporator 1414 and is also removed from the charge 1420 in the evaporator 1414. The speed of the evaporator fan 1416 can also be reduced to reduce the amount of heat. Similarly, the feedback controller 1404 can increase the speed of the condenser fan 1432 to increase the amount of heat removed from the refrigerant in the condenser 1412, or the amount of heat removed from the refrigerant in the condenser 1412. The speed of the condenser fan 1432 can also be reduced to reduce.

The extreme value search controller 502 dynamically inputs an unknown input (eg, optimal supply air temperature set point T _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement extremal search control strategy to search. Although feedback controller 1404 and extreme value search controller 502 are shown as separate devices, in some embodiments, feedback controller 1404 and extreme value search controller 502 are combined into a single device (eg, extreme value search controller). It is contemplated that it can be a single controller that performs the functions of both 502 and feedback controller 1404. For example, the extreme value search controller 502 can be configured to directly control the evaporator fan 1416, the condenser fan 1432, and / or the compressor 1406 without the need for the intermediate feedback controller 1404.

Referring now to FIGS. 14B and 14C, a pair of flow diagrams 1450 and 1470 illustrating the operation of the extreme value search controller 502 of the vapor compression system 1400 are shown in accordance with some embodiments. In both flow diagrams 1450 and 1470, the extreme value search controller 502 provides a temperature setpoint T _sp to a feedback controller 1404 that operates to control the charge air temperature T _sa of the vapor compression system 1400 (blocks 1452 and 1472). ). The extreme value search controller 502 may receive the total power consumption P _total of the vapor compression system 1400 as a feedback signal (blocks 1454 and 1474).

In the flow diagram 1450, the extreme value search controller 502 estimates the slope of the _total power consumption P _total relative to the supply air temperature set point T _sp (block 1456). Extremum search controller 502, by bringing the slope obtained by adjusting the temperature set point T _sp to zero, it is possible to provide a control on the vapor compression system 1400 (block 1458). In some embodiments, the extreme value search controller 502 generates a stochastic excitation signal (block 1460) and uses the stochastic excitation signal to generate a new charge air temperature setpoint _Tsp . For example, the extremum search controller 502, by perturbing supply air temperature set point T _sp using stochastic excitation signal, can generate a new temperature setpoint T _sp (block 1462).

In flow diagram 1470, extremum search controller 502 estimates the normalized correlation coefficient relating the total power consumption _{P total} and the supply air temperature set point _{T sp} (block 1476). Extremum search controller 502, by bringing the estimated correlation coefficient to zero by adjusting the temperature set point T _sp, it is possible to provide a control on the vapor compression system 1400 (block 1478). In some embodiments, the extreme value search controller 502 generates an excitation signal (block 1480) and uses the excitation signal to generate a new charge air temperature setpoint _Tsp . For example, the extremum search controller 502, by perturbing supply air temperature set point T _sp using an excitation signal, it is possible to generate a new temperature setpoint T _sp (block 1482).

Vapor compression system 1500
Referring now to FIG. 15A, another vapor compression air conditioning system 1500 according to some embodiments is shown. System 1500 may include some or all of the components of vapor compression system 1400 as described with reference to FIG. 14A. For example, system 1500 is shown to include a refrigerant circuit 1510. The refrigerant circuit 1510 includes a condenser 1512, an evaporator 1514, an expansion valve 1524 and a compressor 1506. The compressor 1506 is configured to circulate refrigerant between the evaporator 1514 and the condenser 1512. The refrigerant circuit 1510 operates using a vapor compression cycle. For example, the compressor 1506 compresses the refrigerant into a high temperature and high pressure state. The compressed refrigerant flows through the condenser 1512, and the refrigerant exhausts heat in the condenser 1512. Condenser fan 1532 can be used to adjust the heat transfer rate within condenser 1512. The cooled refrigerant is expanded to a low pressure and low temperature state by an expansion valve 1524. The expanded refrigerant flows through the evaporator 1514, and the refrigerant absorbs heat in the evaporator 1514. The evaporator fan 1516 can be used to adjust the heat transfer rate within the evaporator 1514.

  In some embodiments, the refrigerant circuit 1510 is located in a rooftop unit 1502 (eg, a rooftop air treatment unit), as shown in FIG. 15A. Rooftop unit 1502 can be configured to provide cooling for air supply 1520 flowing through air duct 1522. For example, the evaporator 1514 is located in the air duct 1522 so that the charge 1520 can flow through the evaporator 1514 and be cooled by transferring heat to the expanded refrigerant in the evaporator 1514. . The cooled airflow can then be sent to the building to provide cooling to the building room or zone. The temperature of the supply air 1520 can be measured by a temperature sensor 1518 located downstream of the evaporator 1514 (eg, in the duct 1522). In other embodiments, the refrigerant circuit 1510 is in any of a variety of other systems or devices (eg, refrigerators, heat pumps, heat recovery refrigerators, refrigeration devices, etc.) that transfer heat using a vapor compression cycle. Can be used.

The extreme value search controller 502 is a power input P _total representing the total power consumed by the compressor 1506 P _comp , the evaporator fan 1516 P _{fan, evap} and the condenser fan 1532 P _{fan, cond} (ie, P _total = P _comp + P _{fan, evav} + P _{fan, cond} ). As shown in FIG. 15A, power inputs P _comp , P _{fan, evap} and P _{fan, cond} are summation block 1508 external to extremum search controller 502 to provide a combined signal representative of total power P _total. Can be summed up. In other embodiments, the extreme value search controller 502 receives the individual power inputs P _comp , P _{fan, evap} and P _{fan, cond} and _performs the summation of the summation block 1508. In any case, the extremum search controller 502 may provide power inputs P _comp , P _{fan, evap} and P even if the power inputs are provided as a single sum representing the total system power or a combined signal P _total. It can be said that _{fan and cond} are received.

In some embodiments, the total system power P _total is a performance variable that the extremum search controller 502 seeks to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the vapor compression system 1500. In the embodiment shown in FIG. 15A, the total system power _{P total includes} P _{comp, P fan, evap} and _{P fan,} a _cond. However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total may include various other fan power consumption in the rooftop unit 1502, fluid pump power consumption and / or any other power consumption that occurs in the vapor compression system 1500. .

The extreme value search controller 502 is shown to provide the evaporator fan 1516 with a control signal that regulates the fan speed _Ssp . In some embodiments, the fan speed _Ssp is an manipulated variable that the extreme value search controller 502 adjusts to affect the _total system power _Ptotal . Increasing the fan speed _Ssp can increase the amount of heat removed from the supply air 1520 in the evaporator 1514 and increase the total system power consumption _Ptotal . Similarly, decreasing the fan speed _Ssp reduces the amount of heat removed from the charge 1520 in the evaporator 1514 and can reduce the total system power consumption _Ptotal . The extreme value search controller 502 dynamically searches for unknown inputs (eg, optimal evaporator fan speed S _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement an extreme value search control strategy.

Referring now to FIGS. 15B and 15C, a pair of flow diagrams 1550 and 1570 illustrating the operation of the extreme value search controller 502 of the vapor compression system 1500 are shown, according to some embodiments. In both flow diagrams 1550 and 1570, extremum search controller 502 provides a control signal for regulating the fan speed _{S sp} evaporator fan 1516 of the vapor compression system 1500 (blocks 1552 and 1572). The extreme value search controller 502 may receive the total power consumption P _total of the vapor compression system 1500 as a feedback signal (blocks 1554 and 1574).

In the flow diagram 1550, the extreme value search controller 502 estimates the slope of the _total power consumption _{Ptotal with} respect to the evaporator fan speed _Ssp (block 1556). The extreme value search controller 502 can provide control on the vapor compression system 1500 by bringing the gradient obtained by adjusting the evaporator fan speed _Ssp to zero (block 1558). In some embodiments, the extreme search controller 502 generates a stochastic excitation signal (block 1560) and uses the stochastic excitation signal to generate a new evaporator fan speed _Ssp . For example, the extremum search controller 502 can generate a new evaporator fan speed S _sp by perturbing the evaporator fan speed S _sp using a stochastic excitation signal (block 1562).

In flow diagram 1570, extremum search controller 502 estimates the normalized correlation coefficient relating the total power consumption _{P total} and evaporator fan speed _{S sp} (block 1576). The extreme value search controller 502 can provide control on the vapor compression system 1500 by bringing the estimated correlation coefficient to zero by adjusting the evaporator fan speed _Ssp (block 1578). In some embodiments, the extreme search controller 502 generates an excitation signal (block 1580) and uses the excitation signal to generate a new control signal for the evaporator fan. For example, the extreme value search controller 502 can generate a new speed control signal by perturbing the evaporator fan speed S _sp with the excitation signal (block 1582).

Vapor compression system 1600
Referring now to FIG. 16A, a vapor compression air conditioning system 1600 according to some embodiments is shown. System 1600 is shown to include a refrigerant circuit 1610. The refrigerant circuit 1610 includes a condenser 1612, an evaporator 1614, an expansion valve 1624 and a compressor 1606. The compressor 1606 is configured to circulate refrigerant between the evaporator 1614 and the condenser 1612. The refrigerant circuit 1610 operates using a vapor compression cycle. For example, the compressor 1606 compresses the refrigerant into a high temperature and high pressure state. The compressed refrigerant flows through the condenser 1612, and the refrigerant exhausts heat in the condenser 1612. Condenser fan 1632 can be used to adjust the heat transfer rate within condenser 1612. The cooled refrigerant is expanded to a low pressure and low temperature state by an expansion valve 1624. The expanded refrigerant flows through the evaporator 1614, and the refrigerant absorbs heat in the evaporator 1614. The evaporator fan 1616 can be used to adjust the heat transfer rate within the evaporator 1614.

  In some embodiments, the refrigerant circuit 1610 is located in a rooftop unit 1602 (eg, a rooftop air treatment unit), as shown in FIG. 16A. Rooftop unit 1602 can be configured to provide cooling for air supply 1620 flowing through air duct 1622. For example, the evaporator 1614 is located in the air duct 1622 so that the charge air 1620 can flow through the evaporator 1614 and be cooled by transferring heat to the expanded refrigerant in the evaporator 1614. . The cooled airflow can then be sent to the building to provide cooling to the building room or zone. The temperature of the supply air 1620 can be measured by a temperature sensor 1618 located downstream of the evaporator 1614 (eg, in the duct 1622). In other embodiments, the refrigerant circuit 1610 is in any of a variety of other systems or devices (eg, refrigerators, heat pumps, heat recovery refrigerators, refrigeration devices, etc.) that transfer heat using a vapor compression cycle. Can be used.

The extreme value search controller 502 includes a power input P _total representing the total power consumed by the compressor 1606 P _comp , the evaporator fan 1616 P _{fan, evap} and the condenser fan 1632 P _{fan, cond} (ie, P _total = P _comp + P _{fan, evav} + P _{fan, cond} ). As shown in FIG. 16A, power inputs P _comp , P _{fan, evap} and P _{fan, cond} are summation block 1608 external to extremum search controller 502 to provide a combined signal representing the total power P _total. Can be summed up. In other embodiments, the extreme value search controller 502 receives the individual power inputs P _comp , P _{fan, evap} and P _{fan, cond} and _performs the summation of the summation block 1608. In any case, the extremum search controller 502 may provide power inputs P _comp , P _{fan, evap} and P even if the power inputs are provided as a single sum representing the total system power or a combined signal P _total. It can be said that _{fan and cond} are received.

In some embodiments, the total system power P _total is a performance variable that the extremum search controller 502 seeks to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the vapor compression system 1600. In the embodiment shown in FIG. 16A, the total system power _{P total includes} P _{comp, P fan, evap} and _{P fan,} a _cond. However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total may include the power consumption of various other fans in the rooftop unit 1602, the power consumption of the fluid pump, and / or any other power consumption that occurs in the vapor compression system 1600. .

The extreme value search controller 502 is shown to provide a temperature set point T _sp to the feedback controller 1604 and to provide a control signal to the condenser fan 1632 that regulates the fan speed S _sp . In some embodiments, the temperature setpoint _Tsp and the condenser fan speed _Ssp are manipulated variables that the extremum search controller 502 adjusts to affect the _total system power _Ptotal . The temperature set point T _sp is a set point for the temperature of the charge 1620 exiting the evaporator 1614. The supply air temperature _Tsa can be measured by a temperature sensor 1618 located downstream of the evaporator 1614. The feedback controller 1604 is shown to receive the supply air temperature _Tsa as a feedback signal. The fan speed S _sp is the speed of the condenser fan 1632.

Feedback controller 1604 can operate the evaporator fan 1616 and / or the compressor 1606 to achieve the temperature set point _{T sp} provided by extremum search controller 502. For example, the feedback controller 1604 increases the speed of the evaporator fan 1616 to increase the amount of heat removed from the charge 1620 in the evaporator 1614 and is also removed from the charge 1620 in the evaporator 1614. The speed of the evaporator fan 1616 can be reduced to reduce the amount of heat. Similarly, the extreme value search controller 502 adjusts the condenser fan speed _Ssp to increase the amount of heat removed from the refrigerant in the condenser 1612 (eg, by increasing the condenser fan speed _Ssp) . ) Or the amount of heat removed from the refrigerant in the condenser 1612 can be reduced (eg, by reducing the condenser fan speed _Ssp ).

The extreme value search controller 502 may provide an unknown input (eg, optimal supply air temperature setpoint T _sp and / or optimal) to obtain system performance (eg, total power consumption P _total ) that tends to approach an optimal value. Implement an extreme value search control strategy that dynamically searches for the condenser fan speed S _sp ). Although feedback controller 1604 and extreme value search controller 502 are shown as separate devices, in some embodiments, feedback controller 1604 and extreme value search controller 502 are combined into a single device (eg, extreme value search controller). It is contemplated that it can be a single controller that performs the functions of both 502 and feedback controller 1604. For example, the extreme value search controller 502 can be configured to directly control the evaporator fan 1616, the condenser fan 1632, and / or the compressor 1606 without the need for the intermediate feedback controller 1604.

Referring now to FIGS. 16B and 16C, a pair of flow diagrams 1650 and 1670 illustrating the operation of the extreme value search controller 502 of the vapor compression system 1600 are shown, according to some embodiments. In both flow diagrams 1650 and 1670, the extreme search controller 502 provides a temperature setpoint T _sp to a feedback controller 1604 that operates to control the charge air temperature T _sa of the vapor compression system 1600 (blocks 1652 and 1672). ). The extreme value search controller 502 also provides a control signal to restrict the fan speed to the condenser fan 1632 of the vapor compression system 1600 (blocks 1653 and 1674). The extreme value search controller 502 may receive the total power consumption P _total of the vapor compression system 1600 as a feedback signal (blocks 1654 and 1674).

In flow diagram 1650, extremum search controller 502, a first total power consumption _{P total} for the supply air temperature set point _{T sp} slope and, the condenser fan relative to the speed _{S sp} second total power consumption _{P total} The gradient is estimated (block 1656). The extreme value search controller 502 may provide control on the vapor compression system 1600 by bringing the slope obtained by adjusting the temperature setpoint _Tsp and / or the condenser fan speed _Ssp to zero. Yes (block 1658). In some embodiments, the extreme search controller 502 generates a stochastic excitation signal (block 1660) and uses the stochastic excitation signal to create a new charge air temperature setpoint _Tsp and condenser fan speed S. A new control signal that regulates _sp is generated. For example, the extremum search controller 502, by perturbing supply air temperature set point T _sp using a first stochastic excitation signal to generate a new temperature setpoint T _sp, a second stochastic A new control signal for the condenser fan 1632 may be generated by perturbing the condenser fan speed S _sp with the excitation signal (block 1662).

In flow diagram 1670, extremum search controller 502, a first normalized correlation coefficient relating the total power consumption _{P total} and the supply air temperature set point _{T sp,} condenser fan speed total power consumption _{P total} A second normalized correlation coefficient related to S _sp is estimated (block 1676). The extreme value search controller 502 may provide control on the vapor compression system 1600 by bringing the estimated correlation coefficient to zero by adjusting the temperature setpoint _Tsp and / or the condenser fan speed _Ssp. Yes (block 1678). In some embodiments, the extreme search controller 502 generates an excitation signal (block 1680) and uses the excitation signal to control a new charge air temperature setpoint _Tsp and a condenser fan speed _Ssp. Generate a signal. For example, the extremum search controller 502, by perturbing supply air temperature set point T _sp using a first excitation signal to generate a new temperature setpoint T _sp, using the second excitation signal condensate A new control signal for the condenser fan 1632 may be generated by perturbing the condenser fan speed S _sp (block 1682).

Extreme Value Search Control System with Multivariable Optimization Referring now to FIG. 17, another extreme value search control system 1700 according to an exemplary embodiment is shown. System 1700 is shown to include a multiple input single output (MISO) system 1702 and a multivariable extreme value search controller (ESC) 1704. The MISO system 1702 can be any system or device that uses multiple manipulated variables u ₁ ... U _N to affect a single performance variable y. The MISO system 1702 includes a plant 304, 404 or 504 as described with reference to FIGS. 3-5, a cooling water plant 1000 or 1100 as described with reference to FIGS. A variable refrigerant flow system 1200 or 1300 as described with reference and / or a vapor compression system 1400, 1500 or 1600 as described with reference to FIGS. It may be a thing.

In some embodiments, the MISO system 1702 is a combination of a process and one or more machine control outputs. For example, the MISO system 1702 may be an air treatment unit configured to control the temperature in a building space via one or more machine control actuators and / or dampers. In various embodiments, the MISO system 1702 may include a chiller operating process, a damper conditioning process, a mechanical cooling process, a ventilation process, a refrigeration process, or multiple inputs to the MISO system 1702 (eg, operational variables u ₁ ... U _N ) may include any other process that is adjusted to affect the output from the MISO system 1702 (ie, the performance variable y). Some examples of control systems that can be used as the MISO system 1702 are described in detail with reference to FIGS.

を決定することができる。同様に、多変数ＥＳＣ １７０４は、残りの操作変数ｕ_２…ｕ_Ｎに対する性能変数ｙの偏導関数

を決定することができる。いくつかの実施形態では、多変数ＥＳＣ １７０４は、以下の方程式に示されるように、偏導関数のベクトルＤを生成する。

式中、ベクトルＤの各要素は、操作変数ｕ_１…ｕ_Ｎのうちの１つに対する性能変数ｙの勾配である。多変数ＥＳＣ １７０４は、ベクトルＤをゼロに至らせるために、操作変数ｕ_１…ｕ_ＮのＤＣ値を調整することができる。 Multivariable ESC 1704 uses extreme value search control techniques to determine the optimum values of manipulated variables u ₁ ... U _N. In some embodiments, the multivariable ESC 1704 perturbs each manipulated variable u ₁ ... U _N using a different excitation signal (eg, a periodic dither signal or a stochastic excitation signal) Observe the effect of the excitation signal. Multivariable ESC 1704 in order to determine the slope of the performance variable y for each manipulated variable _u 1 ... _{u N,} it is possible to perform a dither demodulation process for each operation variable _u 1 ... _{u N} (Fig. 4 As explained). In some embodiments, each gradient is a partial derivative of the performance variable y for one of the manipulated variables u ₁ ... U _N. For example, the multivariable ESC 1704 is a partial derivative of the performance variable y with respect to the manipulated variable u ₁ .

Can be determined. Similarly, multivariate ESC 1704 is the partial derivative of the performance variable y for the remainder of the manipulated variable _u 2 ... _{u N}

Can be determined. In some embodiments, the multivariable ESC 1704 generates a partial derivative vector D, as shown in the following equation:

Wherein each element of the vector D, is the slope of the performance variable y with respect to one of the manipulated variables u ₁ ... u _N. The multi-variable ESC 1704 can adjust the DC value of the manipulated variable u ₁ ... U _N to bring the vector D to zero.

多変数ＥＳＣ １７０４は、ヘッセ行列Ｈを使用して、ヘッセ行列Ｈが正定値（極大）であるかまたは負定値（極小）であるかを判断することによって、局所的極値を識別することができる。ベクトルＤをゼロに至らせることおよび／またはヘッセ行列Ｈを評価することにより、多変数ＥＳＣ １７０４は、性能変数ｙの極値（すなわち、最大または最小）を達成することができる。 In some embodiments, the multi-variable ESC 1704 uses the partial derivative Hessian H to adjust the manipulated variables u ₁ ... U _N. The Hessian matrix H describes the local curvature of the performance variable y as a function of a plurality of manipulated variables u ₁ ... U _N (ie, y = f (u ₁ , u ₂ ,... U _N )). In some embodiments, the Hessian matrix H is a square matrix of second order partial derivatives, as shown in the following equation:

The multivariable ESC 1704 may identify local extrema by using the Hessian matrix H to determine whether the Hessian matrix H is positive definite (local maximum) or negative definite (local minimum). it can. By bringing the vector D to zero and / or evaluating the Hessian H, the multivariable ESC 1704 can achieve the extreme value (ie, maximum or minimum) of the performance variable y.

Multivariable ESC 1704 can use the vector and matrix based calculations outlined above to implement extreme value search control in multidimensional domains. This approach is the most sophisticated mathematical solution to multivariable problems, but can be problematic in practice because it is difficult to construct and debug controllers that operate in multidimensional domains. For example, adjusting the feedback gain K for each manipulated variable u ₁ ... U _N (ie, each control channel) can be complicated due to variable interactions. In some embodiments, variable interaction causes the feedback gain K for each control channel to depend on all other feedback gains K for all other control channels. Also, interdependencies between manipulated variables can complicate troubleshooting of multivariable ESC 1704. For example, the interaction between manipulated variables u ₁ ... U _N may cause ambiguity when attempting to identify the control channel responsible for the observed behavior of performance variable y.

Referring now to FIG. 18, another extreme value search control system 1800 according to an exemplary embodiment is shown. The control system 1800 is shown to include a MISO system 1702 and a plurality of single variable extreme value search controllers (ESCs) 1804, 1806 and 1808. Although only three single variable ESCs 1804-1808 are shown, it should be understood that any number of single variable ESCs can be included in the control system 1800. Each single variable ESC 1804-1808 can be configured to be assigned to a different manipulated variable u ₁ ... U _N to determine the optimum value of the assigned manipulated variable using extreme value search control techniques. For example, a single variable ESC 1804 can be configured to be assigned to the manipulated variable u ₁ and u ₁ to reach its optimal value, and a single variable ESC 1806 can be assigned to the manipulated variable u ₂ and u ₂ can be configured to reach its optimal value, and a single variable ESC 1808 can be configured to assign the manipulated variable u _N to bring u _N to its optimal value.

）を抽出することができ、極値探索制御技法を使用して、抽出した勾配をゼロに至らせることができる。 Each single variable ESC 1804-1808 can receive the same performance variable y as input from the MISO system 1702. However, each single variable ESC 1804-1808 can correspond to a different control channel (ie, a different manipulated variable) and can be configured to provide the corresponding manipulated variable value as an output to the MISO system 1702. it can. In some embodiments, each single variable ESC 1804-1808 applies a separate uncorrelated perturbation to the corresponding manipulated variable output. The perturbation can be a periodic dither signal or a stochastic excitation signal, as previously described. If a periodic dither signal is used, each single variable ESC 1804-1808 can use a different dither frequency to uniquely identify the effect of each manipulated variable u ₁ ... U _N in performance variable y. Can be configured. If stochastic excitation signals are used, the correlations of the stochastic signals will naturally disappear. This eliminates the requirement for communication or coordination between single variable ESCs 1804-1808 in generating the perturbation signal. Each single variable ESC 1804-1808 is the slope of the performance variable y relative to the corresponding manipulated variable (eg,

) And extreme value search control techniques can be used to bring the extracted gradient to zero.

Although system 1800 is shown to include a MISO system 1702, it should be understood that in some embodiments, a multiple input multiple output (MIMO) system can be used instead of MISO system 1702. When a MIMO system is used instead of the MISO system 1702, each single variable ESC 1804-1808 can receive the same performance variable y or a different performance variable y ₁ ... Y _M as a feedback output from the MIMO system. . Each single variable ESC 1804-1808 can extract the gradient of one of the performance variables for one of the manipulated variables and uses extreme value search control techniques to bring the extracted gradient to zero. Can be made.

を推定するように構成することができる。同様に、単一変数ＥＳＣ １８０６内の再帰的勾配推定器５０６の実例は、第２の操作変数ｕ_２に対する性能変数ｙの勾配または傾き

を推定するように構成することができ、単一変数ＥＳＣ １８０８内の再帰的勾配推定器５０６の実例は、第Ｎの操作変数ｕ_Ｎに対する性能変数ｙの勾配または傾き

を推定するように構成することができる。再帰的勾配推定器５０６の複数の実例は、互いに独立して動作することができ、そのそれぞれの再帰的勾配推定プロセスを実行するための通信または調整を必要としない。 In some embodiments, each single variable ESC 1804-1808 is an illustration of ESC 502 and may include all components and functions of ESC 502 as described with reference to FIG. Each single variable ESC 1804-1808 may include an example of a recursive gradient estimator 506 and a feedback controller 508. Each instance of the recursive gradient estimator 506 can be configured to perform a recursive gradient estimation process to estimate the slope of the performance variable y relative to the corresponding manipulated variable u ₁ ... U _N. For example, an example of a recursive slope estimator 506 in a single variable ESC 1804 is the slope or slope of the performance variable y relative to the first manipulated variable u ₁ .

Can be configured to estimate. Similarly, an example of a recursive slope estimator 506 in a single variable ESC 1806 is the slope or slope of the performance variable y relative to the second manipulated variable u ₂ .

An example of a recursive slope estimator 506 in a single variable ESC 1808 is the slope or slope of the performance variable y with respect to the Nth manipulated variable u _N.

Can be configured to estimate. The multiple instances of recursive gradient estimator 506 can operate independently of each other and do not require communication or coordination to perform their respective recursive gradient estimation processes.

のうちの１つ）を受信することができる。フィードバックコントローラ５０８の各実例は、操作変数の最適値（すなわち、ゼロの勾配をもたらす操作変数の値）に達するまで、対応する勾配をゼロに至らせる方向に対応する操作変数（すなわち、ｕ_１…ｕ_Ｎのうちの１つ）の値を調整することができる。例えば、単一変数ＥＳＣ １８０４内のフィードバックコントローラ５０８の実例は、操作変数ｕ_１のＤＣ値ｗ_１を調整することによって勾配

をゼロに至らせるように構成することができる。同様に、単一変数ＥＳＣ １８０６内のフィードバックコントローラ５０８の実例は、操作変数ｕ_２のＤＣ値ｗ_２を調整することによって勾配

をゼロに至らせるように構成することができ、単一変数ＥＳＣ １８０８内のフィードバックコントローラ５０８の実例は、操作変数ｕ_ＮのＤＣ値ｗ_Ｎを調整することによって勾配

をゼロに至らせるように構成することができる。フィードバックコントローラ５０８の複数の実例は、互いに独立して動作することができ、そのそれぞれの勾配をゼロに至らせるための操作変数ｕ_１…ｕ_Ｎ間の相互作用についてのいかなる情報も必要としない。 Each instance of the feedback controller 508 is deduced from the corresponding instance of the recursive slope estimator 506 (ie,

Can be received). Each instance of the feedback controller 508 corresponds to an manipulated variable (ie, u ₁ ... Corresponding to the direction in which the corresponding slope is brought to zero until the optimum value of the manipulated variable (ie, the value of the manipulated variable that results in a slope of zero) is reached. it is possible to adjust the value of one) of the u _N. For example, an example of a feedback controller 508 in a single variable ESC 1804 is a gradient by adjusting the DC value w ₁ of the manipulated variable u _1.

Can be configured to reach zero. Gradient Similarly, examples of the feedback controller 508 in a single variable ESC 1806, by adjusting the DC value _{w 2} of manipulated variables _{u 2}

Can be configured to reach zero, and an example of a feedback controller 508 in a single variable ESC 1808 can be obtained by adjusting the DC value w _N of the manipulated variable u _N

Can be configured to reach zero. The multiple instances of the feedback controller 508 can operate independently of each other and do not require any information about the interaction between the manipulated variables u ₁ ... U _{N to} bring their respective slopes to zero.

In some embodiments, each single variable ESC 1804-1808 includes an instance of a stochastic signal generator 512, an integrator 514, and an excitation signal element 510. Each instance of the stochastic signal generator 512 can be configured to generate a persistent excitation signal q for one of the manipulated variables u ₁ ... U _N. For example, an example of a stochastic signal generator 512 within a single variable ESC 1804 can generate a _first stochastic excitation signal q _1, and a probabilistic signal generator 512 within a single variable ESC 1806 can be generated. An example can generate a _second stochastic excitation signal q _2, and an example of a stochastic signal generator 512 in a single variable ESC 1808 generates an _Nth stochastic excitation signal q _N. be able to. Each stochastic excitation signal q ₁ ... q _N, as shown in the following equation, in order to form a manipulated variable u ₁ ... u _N, DC value w manipulated variable corresponding in the excitation signal elements 510 ₁ ... it can be added to the w _N.
u ₁ = w ₁ + q ₁
u ₂ = w ₂ + q ₂
...
u _N = w _N + q _N

One advantage of the stochastic excitation signals q ₁ ... Q _N is that adjustment of the single variable ESCs 1804-1808 is easier because the dither frequency ω _v is no longer an essential parameter. ESC 1,804-1,808, even need to know the natural frequency of the MISO system 1702 in generating a stochastic excitation signal _q 1 ... _{q N,} there is no need to estimate. In addition, each of the stochastic excitation signal q ₁ ... q _N is to obtain a random, it is not necessary to ensure that the stochastic excitation signals q ₁ ... q _N are not correlated with each other. Multiple instances of the stochastic signal generator 512 can operate independently of each other and communicate or coordinate to ensure that the stochastic excitation signals q ₁ ... Q _N are distinct and uncorrelated. Do not need.

と関連付ける（例えば、

に比例する）ことができるが、性能変数ｙの範囲に基づいてスケーリングされる。例えば、各相関係数ρ_１…ρ_Ｎは、対応する性能勾配

の正規化尺度であり得る（例えば、範囲０≦ρ≦１にスケーリングされる）。 In some embodiments, each single variable ESC 1804-1808 includes an example of a correlation coefficient estimator 528. Each instance of correlation coefficient estimator 528 can be configured to estimate a correlation coefficient ρ for one of the manipulated variables u ₁ ... U _N. For example, an example of correlation coefficient estimator 528 in single variable ESC 1804 can generate a _first correlation coefficient ρ _1, and an example of correlation coefficient estimator 528 in single variable ESC 1806 is The second correlation coefficient ρ ₂ can be generated, and an example of the correlation coefficient estimator 528 in the single variable ESC 1808 can generate the Nth correlation coefficient ρ _N. Each correlation coefficient ρ ₁ ... Ρ _N is the performance gradient of the corresponding manipulated variable.

Associated with (for example,

Scaled based on the range of performance variable y. For example, each correlation coefficient ρ ₁ ... Ρ _N is a corresponding performance gradient.

(For example, scaled to the range 0 ≦ ρ ≦ 1).

の代わりに相関係数ρ_１…ρ_Ｎを使用する。例えば、単一変数ＥＳＣ １８０４は、操作変数ｕ_１のＤＣ値ｗ_１を調整して相関係数ρ_１をゼロに至らせることができる。同様に、単一変数ＥＳＣ １８０６は、操作変数ｕ_２のＤＣ値ｗ_２を調整して相関係数ρ_２をゼロに至らせることができ、単一変数ＥＳＣ １８０８は、操作変数ｕ_ＮのＤＣ値ｗ_Ｎを調整して相関係数ρ_Ｎをゼロに至らせることができる。性能勾配

の代わりに相関係数ρ_１…ρ_Ｎを使用する利点の１つは、単一変数ＥＳＣ １８０４〜１８０８によって使用される調整パラメータが、性能変数ｙのスケールに基づいてカスタマイズまたは調整する必要のない調整パラメータの一般集合であり得ることである。この利点により、各単一変数ＥＳＣ １８０４〜１８０８に対する制御ループ特有の調整を実行する必要性が排除され、各ＥＳＣ １８０４〜１８０８は、多くの異なる制御ループおよび／またはプラントにわたって適用可能な調整パラメータの一般集合を使用できるようになる。 In some embodiments, the single variable ESC 1804-1808 is used to perform a performance gradient when performing its extreme value search control process.

Is used instead of correlation coefficients ρ ₁ ... Ρ _N. For example, the single variable ESC 1804 can adjust the DC value w ₁ of the manipulated variable u ₁ to bring the correlation coefficient ρ ₁ to zero. Similarly, the single variable ESC 1806 can adjust the DC value w ₂ of the manipulated variable u ₂ to bring the correlation coefficient ρ ₂ to zero, and the single variable ESC 1808 is the DC of the manipulated variable u _N. it is possible to adjust the value w _N bring the correlation coefficient [rho _N to zero. Performance gradient

One advantage of using correlation coefficients ρ ₁ ... Ρ _N instead of is that the tuning parameters used by single variable ESCs 1804-1808 need not be customized or adjusted based on the scale of performance variable y. It can be a general set of tuning parameters. This advantage eliminates the need to perform control loop specific adjustments for each single variable ESC 1804-1808, and each ESC 1804-1808 has a number of adjustment parameters applicable across many different control loops and / or plants. The general set can be used.

  Referring now to FIG. 19, another extreme value search control system 1900 according to an exemplary embodiment is shown. The control system 1900 is shown to include a MISO system 1702 and a multivariable controller 1902. Multivariable controller 1902 is shown to include a plurality of single variable extreme value search controllers (ESC) 1904, 1906 and 1908. In some embodiments, single variable ESCs 1904-1908 are implemented as separate control modules or components of multivariable controller 1902. Although only three single variable ESCs 1904-1908 are shown, it should be understood that any number of single variable ESCs can be included in the multivariable controller 1902.

Single variable ESCs 1904-1908 may be configured to perform some or all of the same functions as single variable ESCs 1804-1808 as described with reference to FIG. Each single variable ESC 1904-1908 can be configured to be assigned to a different manipulated variable u ₁ ... U _N to determine the optimum value of the assigned manipulated variable using extreme value search control techniques. For example, a single variable ESC 1904 can be assigned to the manipulated variable u ₁ to configure u ₁ to reach its optimal value, and a single variable ESC 1906 can be assigned to the manipulated variable u ₂ and u ₂ can be configured to reach its optimal value, and a single variable ESC 1908 can be configured to assign the manipulated variable u _N to bring u _N to its optimal value. In some embodiments, each of the single variable ESCs 1904-1908 includes a recursive gradient estimator 506, a feedback controller 508, a correlation coefficient estimator 528, a stochastic signal generator 512, an integrator 514 and / or an excitation. An example of signal element 510 is included. These components can be configured to operate as described with reference to FIG.

Although the system 1900 is shown to include a MISO system 1702, it should be understood that in some embodiments, a multiple input multiple output (MIMO) system can be used in place of the MISO system 1702. When a MIMO system is used instead of the MISO system 1702, each single variable ESC 1904-1908 can receive the same performance variable y or a different performance variable y ₁ ... y _M as a feedback output from the MIMO system. . Each single variable ESC 1904-1908 can extract the gradient of one of the performance variables for one of the manipulated variables and uses extreme value search control techniques to bring the extracted gradient to zero. Can be made.

In some embodiments, multivariable controller 1902 is configured to operate in a plurality of different modes of operation. For example, the multivariable controller 1902 can operate as a finite state machine or hybrid controller configured to evaluate state transition conditions and switch between a plurality of different operating states when the state transition conditions are met. An example of such a hybrid controller is described in detail in U.S. Pat. No. 6,057,009, filed Aug. 9, 2016, the entire disclosure of which is incorporated herein by reference. In some embodiments, each mode of operation of multivariable controller 1902 is associated with a different subset of manipulated variables u ₁ ... U _N. For example, the multivariable controller 1902, when operating in the first mode of operation, MISO instrumental variables _u 1 ... first subset of _{u N S 1 = {u 1} , u 4, u 5, u 7} provided to the system 1702, when operating in the second mode of operation, operation variables _u 1 ... second subset _S of _{u N 2 = {u 1,} u 2, u 3, u 6} MISO system 1702 Can be provided. Each manipulated variable u ₁ ... U _N can be controlled by a different single variable ESC 1904-1908.

In some embodiments, the multivariable controller 1902 is configured to switch between multiple different sets of single variable ESCs 1904-1908 based on the mode of operation of the multivariable controller 1902. The multi-variable controller 1902 can selectively activate and deactivate individual single variables ESC 1904-1908 based on which manipulated variables u ₁ ... U _N are provided to the MISO system 1702 in each mode of operation. it can. For example, the multivariable controller 1902 can be activated as soon as the transition to the first mode of operation, a single variable ESC configured to control the operation variables of the subset S ₁ selectively. Similarly, multivariable controller 1902 may activate the transition as soon as the second mode of operation, a single variable ESC configured to control the operation variables of the subset S ₂ selectively. The multi-variable controller 1902 can cancel any of the single variable ESCs 1904-1908 that do not need to control the operational variables provided to the MISO system 1702 in the current mode of operation.

Example Test Results Referring now to FIG. 20, an example of an extreme value search control system 2000 used to test the multivariable optimization techniques described herein is shown in accordance with an illustrative embodiment. ing. System 2000 is shown to include two single variable ESCs 2002 and 2004 and MISO system 2012. Each of the single variables ESC 2002, 2004 may be the same as or similar to any of the single variables ESC 1804-1808 or 1904-1908 as described with reference to FIGS. Single variable ESC 2002 provides a first operational variable u ₁ to MISO system 2012 and single variable ESC 2004 provides a second operational variable u ₂ to MISO system 2012.

式中、ωは、

に設定された。入力ダイナミクス２００６は、操作変数ｕ_１を変数ｘ_１に変換し、入力ダイナミクス２００８は、操作変数ｕ_２を変数ｘ_２に変換する。 The MISO system 2012 may be the same as or similar to the MISO system 1702 described with reference to FIG. The MISO system 2012 is shown to include input dynamics 2006, 2008 and a performance map 2010. The input dynamics 2006, 2008 were selected to have the following critically decaying quadratic form.

Where ω is

Was set to The input dynamics 2006 converts the operation variable u ₁ into the variable x ₁ , and the input dynamics 2008 converts the operation variable u ₂ into the variable x ₂ .

性能マップ２０１０の出力は、性能変数ｙ（すなわち、ｙ＝ｆ（ｘ））として単一変数ＥＳＣ ２００２、２００４の両方に提供される。 The performance map 2010 is selected as a continuous, differentiable, non-separable, non-scalable, single-mode Ackley (2) function type 2D nonlinear static map as shown in the equation below. It was.

The output of performance map 2010 is provided to both single variables ESC 2002, 2004 as performance variable y (ie, y = f (x)).

Referring now to FIGS. 21-23, results from tests performed on the system 2000 are presented. For the single variable ESC 2002, 2004, the extreme value search control technique described with reference to FIG. 5 was performed. The optimum values for each manipulated variable u ₁ and u ₂ are u ₁ = 0 and u ₂ = 0, and the optimum value for performance variable y is y = −200. Each manipulated variable u ₁ and u ₂ was set to an initial value at u ₁ = 5 and u ₂ = 5. No adjustment was performed for any control loop. FIG. 21 is a graph 2100 showing that the performance variable y quickly converges to the optimal value of y = −200. 22 and 23 are graphs 2200 and 2300 showing that the manipulated variables u ₁ and u ₂ quickly converge to their optimal values u ₁ = 0 and u ₂ = 0.

  The test results show that despite the difficult inseparable 2D performance map 2010, the multi-loop extreme value search control technique using multiple single variable extreme value search controllers converges quickly. The ability to apply this technique to inseparable problems without having to adjust individual feedback control loops makes this approach particularly attractive for practical implementations.

Multivariable Optimization Process Referring now to FIG. 24, a flowchart of a multivariable optimization process 2400 using multiple single variable extremum search controllers is shown in accordance with an illustrative embodiment. Process 2400 may be performed by one or more components of extreme search control system 1800 or 1900 as described with reference to FIGS. For example, the process 2400 may be performed by a set of single variable extremum search controllers (eg, ESC 1804-1808 or 1904-1908). A single variable ESC can be implemented as a separate controller (as shown in FIG. 18) or as a module of a multivariable controller (as shown in FIG. 19).

Process 2400 is shown to include providing a plurality of manipulated variables u ₁ ... U _N as inputs to the plant (step 2402) and receiving performance variable y as feedback from the plant (step 2404). Yes. In some embodiments, the plant may be the same as or similar to the MISO system 1702. For example, the plant can receive a plurality of manipulated variables u ₁ ... U _N as input and provide a single performance variable y as output. In other embodiments, the plant provides multiple performance variables as outputs. For example, the plant may be a multiple input multiple output (MIMO) system. Each of the manipulated variables u ₁ ... U _N is independently generated and provided by a separate single variable extreme value search controller (eg, one of the single variables ESC 1804 to 1808 or 1904 to 1908). Can do. The performance variable y can be received from the plant and provided as an input to each of the single variable ESCs. In other words, each single variable ESC can receive the same performance variable y as input.

を推定するように構成することができ、第２の単一変数ＥＳＣは、第２の操作変数ｕ_２に対する性能変数ｙの勾配または傾き

を推定するように構成することができ、第Ｎの単一変数ＥＳＣは、第Ｎの操作変数ｕ_Ｎに対する性能変数ｙの勾配または傾き

を推定するように構成することができる。単一変数ＥＳＣは、互いに独立して動作することができ、そのそれぞれの勾配推定プロセスを実行するための通信または調整を必要としない。 Process 2400 is shown to include using a plurality of different single variables ESC (step 2406) to independently determine the slope of performance variable y for each of manipulated variables u ₁ ... U _N. . In some embodiments, each single variable ESC corresponds to one of the manipulated variables u ₁ ... U _N. Each single variable ESC can estimate the slope of the performance variable y relative to the corresponding manipulated variable u ₁ ... U _N. For example, the first single variable ESC is the slope or slope of the performance variable y with respect to the first manipulated variable u ₁

And the second single variable ESC is the slope or slope of the performance variable y with respect to the second manipulated variable u ₂

It can be configured to estimate a single variable ESC of the N, the slope or inclination of the performance variable y with respect to the operation variable u _N of the N

Can be configured to estimate. Single variable ESCs can operate independently of each other and do not require communication or adjustment to perform their respective gradient estimation processes.

をゼロに至らせるように構成することができる。同様に、第２の単一変数ＥＳＣ内の第２のフィードバックコントローラは、操作変数ｕ_２のＤＣ値ｗ_２を調整することによって勾配

をゼロに至らせるように構成することができ、第Ｎの単一変数ＥＳＣ内の第Ｎのフィードバックコントローラは、操作変数ｕ_ＮのＤＣ値ｗ_Ｎを調整することによって勾配

をゼロに至らせるように構成することができる。複数のフィードバックコントローラは、互いに独立して動作することができ、そのそれぞれの勾配をゼロに至らせるための操作変数ｕ_１…ｕ_Ｎ間の相互作用についてのいかなる情報も必要としない。 Process 2400 is shown to include bringing the estimated slope to zero (block 2408) by adjusting the output of the feedback controller for each manipulated variable. Each feedback controller may be a component of a single variable ESC (as shown in FIG. 5). Each feedback controller has an operating variable (ie, u ₁ ... _N of the operating variable corresponding to the direction that brings the corresponding slope to zero until the optimal value of the operating variable (ie, the value of the operating variable that yields a slope of zero) is reached. The value of one of them can be adjusted. For example, the first feedback controller in the first single variable ESC can be graded by adjusting the DC value w ₁ of the manipulated variable u _1.

Can be configured to reach zero. Gradient Similarly, a second feedback controller in the second single variable ESC by adjusting the DC value w ₂ of manipulated variables u ₂

The can be configured to bring to zero, the feedback controller of the N in a single variable ESC of the N, the slope by adjusting the DC value w _N manipulated variable u _N

Can be configured to reach zero. The multiple feedback controllers can operate independently of each other and do not require any information about the interaction between manipulated variables u ₁ ... U _{N to} bring their respective slopes to zero.

Process 2400 is shown to include generating an excitation signal for each manipulated variable (step 2410). Each excitation signal can be generated by a separate excitation signal generator, which can be a component of a single variable ESC (as shown in FIG. 5). In some embodiments, the first excitation signal generator in the first single variable ESC generates a _first excitation signal q ₁ and the second excitation signal generator in the second single variable ESC. Generates a _second excitation signal q2, and an Nth excitation signal generator in the Nth single variable ESC generates an _Nth excitation signal qN. The excitation signal can be a periodic dither signal or a stochastic excitation signal, as previously described. If a periodic dither signal is used, each single variable ESC is configured so that the effect of each manipulated variable u ₁ ... U _N can be uniquely identified in performance variable y using a different dither frequency. be able to. If stochastic excitation signals are used, the correlations of the stochastic signals will naturally disappear. This eliminates the requirement for communication or coordination between single variable ESCs when generating the excitation signal.

Process 2400 is shown to include generating a new value for each manipulated variable by perturbing the output of each feedback controller with a corresponding excitation signal (step 2412). Each excitation signal q ₁ ... q _N, as shown in the following equation, in order to form a manipulated variable u ₁ ... u _N, can be added to the DC value w ₁ ... w _N corresponding manipulated variables.
u ₁ = w ₁ + q ₁
u ₂ = w ₂ + q ₂
...
u _N = w _N + q _N
The new value of the manipulated variable u ₁ ... U _N can then be provided as input to the plant (step 2402) and the process 2400 can be repeated.

  Referring now to FIG. 25, a flowchart of a multivariable optimization process 2500 using a plurality of single variable extreme value search controllers is shown in accordance with an illustrative embodiment. Process 2500 may be performed by one or more components of extreme value search control system 1800 or 1900 as described with reference to FIGS. For example, process 2500 may be performed by a set of single variable extremum search controllers (eg, ESCs 1804-1808 or 1904-1908). A single variable ESC can be implemented as a separate controller (as shown in FIG. 18) or as a module of a multivariable controller (as shown in FIG. 19).

Process 2500 is shown to include providing a first set of manipulated variables to a plant using a first set of single variable ESCs while operating in a first mode of operation (step 2502). ing. In some embodiments, each mode of operation is associated with a different subset of manipulated variables u ₁ ... u _N. For example, a first subset of manipulated variables _{u 1 ... u N S 1 =} {u 1, u 4, u 5, u 7} may be a first mode of operation, the manipulated variable _u 1 ... _{u N} The two subsets S ₂ = {u ₁ , u ₂ , u ₃ , u ₆ } can be associated with the second mode of operation. Each manipulated variable u ₁ ... U _N can be controlled by a different single variable ESC.

  Process 2500 transitions from a first mode of operation to a second mode of operation (step 2504) and identifying a second set of manipulated variables associated with the second mode of operation (step 2506). Is shown to include. In some embodiments, the transition from the first mode of operation occurs as a result of meeting one or more state transition conditions. For example, a multivariable controller can operate as a finite state machine or hybrid controller configured to evaluate state transition conditions and switch between a plurality of different operating states when the state transition conditions are met. Identifying the set of manipulated variables associated with the second mode of operation retrieves such information from the database or automatically identifies the inputs required for the plant in the second mode of operation Can be included.

Process 2500 activates a second set of single variables ESC configured to optimize a second set of manipulated variables (step 2508) and operates in a second mode of operation while Providing a second set of manipulated variables to the plant using a second set of univariate ESCs (step 2510). Each of the second set of manipulated variables can be controlled by a separate single variable ESC. Step 2508 may include selectively activating and / or deactivating one or more single variables ESC based on which operating variables u ₁ ... U _N are provided to the plant in each mode of operation. . Single variable ESC configured to control the operation variables of the subset S ₁ as soon as the transition to the first mode of operation, can be selectively activated. Similarly, a single variable ESC configured to control the operation variables of the subset S ₂ as soon as the transition to the second operating mode, can be activated. Step 2508 may include releasing a single variable ESC that does not need to control the manipulated variable provided to the plant in the current mode of operation.

Example Implementations Referring now to FIGS. 26-28, there are shown some example implementations of multivariable optimization using multiple single variable ESCs, according to an exemplary embodiment. The implementation shown in FIGS. 26-28 has multiple single variable ESCs, manipulated variables u that can be provided to MISO system 1702 by a single variable ESC, and performance that can be received as feedback from MISO system 1702. FIG. 6 illustrates various embodiments of a MISO system (eg, MISO system 1702) that can be controlled using a variable y.

Cooling water plant 2600
With particular reference to FIG. 26, a cooling water plant 2600 according to some embodiments is illustrated. The cooling water plant 2600 may include some or all of the components of the cooling water plant 1000 and / or the cooling water plant 1100 as described with reference to FIGS. 10A and 11A. For example, the cooling water plant 2600 is shown to include a refrigerator 2602, a cooling tower 2604, and an air treatment unit (AHU) 2606. The refrigerator 2602 is connected to the cooling tower 2604 by a condenser water supply loop 2622. A condenser water pump 2614 located along the condenser water loop 2622 circulates condenser water between the cooling tower 2604 and the refrigerator 2602. Cooling tower fan system 2636 provides an airflow that flows through cooling tower 2604 to facilitate cooling of the condenser water in cooling tower 2604. The refrigerator 2602 is also connected to the AHU 2606 via a cooling fluid loop 2624. A cooling fluid pump 2616 located along the cooling fluid loop 2624 circulates cooling fluid between the refrigerator 2602 and the AHU 2606.

The cooling water plant 2600 is shown to include a first single variable ESC 2642 and a second single variable ESC 2644. Single variable ESC 2642,2644 Both of cooling tower fan system 2636 P _tower, condenser water pump 2614 P _pump and power representing the total power consumed by the compressor 2634 P _chiller refrigerator 2602 input _{P total} (i.e. It is shown to receive a _{P total = P tower + P pump} + P chiller). As shown in FIG. 26, the power input _{P tower, P pump} and _{P chiller} is to provide a combined signal representative of the total power _{P total,} summing outside the summation block 2640 of a single variable ESC 2642,2644 be able to. In another embodiment, a single variable ESC 2642,2644, the individual power input _{P tower,} receives the _{P pump} and _{P chiller,} to implement the sum of the total block 2640. In either case, the single variable ESC 2642,2644, even if a single sum or power input as a combination signal _{P total} representing the total system power is provided, the power input _{P tower, P pump} and P It can be said that a _chiller is received.

In some embodiments, the total system power P _total is a performance variable that the single variable ESC 2642, 2644 seeks to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the cooling water plant 2600. In the embodiment shown in FIG. 26, the total system power _{P total includes P tower, P pump} and _{P chiller.} However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total may include the power consumption of the fans in the AHU 2606, the power consumption of the cooling fluid pump 2616, and / or any other power consumption that occurs in the cooling water plant 2600.

Single variable ESC 2642 is shown to provide a fan speed control signal to cooling tower fan system 2636. In some embodiments, the cooling tower fan speed Fan _sp is a manipulated variable that adjusts so that the single variable ESC 2642 affects the total system power P _total . For example, the single variable ESC 2642 may also increase the speed of the cooling tower fan system 2636 to increase the amount of heat removed from the condenser water by the cooling tower 2604 and may be removed from the condenser water by the cooling tower 2604. The cooling tower fan system 2636 can be slowed down to reduce the amount of heat generated. By lowering the cooling tower fan speed Fan _sp, can reduce the cooling tower power consumption P _tower, due to additional refrigeration power to transfer heat to the hot condenser water is required, the refrigerator There is a possibility of increasing the power consumption P _chiller . The single variable ESC 2642 dynamically searches for unknown inputs (eg, optimal cooling tower fan speed Fan _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement an extreme value search control strategy.

Similarly, a single variable ESC 2644 is shown to provide a pump power control signal to the condenser water pump 2614. In some embodiments, the pump speed Pump _sp is an manipulated variable that adjusts so that the single variable ESC 2644 affects the total system power P _total . For example, the single variable ESC 2644 may increase the speed of the condenser water pump 2614 to increase the amount of heat removed from the refrigerant in the condenser 2618, or the heat removed from the refrigerant in the condenser 2618. The speed of the condenser water pump 2614 can also be reduced to reduce the amount of water. By reducing the pump speed Pump _sp , the pump power consumption P _pump can be reduced, but because additional refrigerator power is required to transfer heat to the high-temperature condenser water, the refrigerator power consumption P _chiller may be increased. The single variable ESC 2644 is a pole that dynamically searches for unknown inputs (eg, optimal pump speed Pump _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach optimal values. Implement a value search control strategy.

Variable refrigerant flow system 2700
Referring now to FIG. 27, another variable refrigerant flow (VRF) system 2700 is shown according to some embodiments. VRF system 2700 may include some or all of the components of VRF system 1200 and / or VRF system 1300 as described with reference to FIGS. 12A and 13A. For example, the VRF system 2700 is shown to include an outdoor unit 2702, a number of heat recovery units 2704, and a number of indoor units 2706.

  Outdoor unit 2702 is shown to include a compressor 2714 and a heat exchanger 2720. The compressor 2714 circulates the refrigerant between the heat exchanger 2720 and the indoor unit 2706. The heat exchanger 2720 functions as a condenser (allows the refrigerant to exhaust heat to the outside air) when the VRF system 2700 operates in the cooling mode, or when the VRF system 2700 operates in the heating mode. Can also function as an evaporator (which allows the refrigerant to absorb heat from the outside air). Fan 2718 provides an airflow that flows through heat exchanger 2720. The speed of the fan 2718 can be adjusted to adjust the heat transfer rate into or out of the refrigerant in the heat exchanger 2720.

Each indoor unit 2706 is shown to include a heat exchanger 2726 and an expansion valve 2724. Each of the heat exchangers 2726 can function as a condenser (allowing the refrigerant to exhaust heat into the air in the room or zone) when the indoor unit 2706 operates in the heating mode, or the indoor unit 2706. When operating in cooling mode, it can also function as an evaporator (allowing refrigerant to absorb heat from the air in the room or zone). Fan 2722 provides an airflow through heat exchanger 2726. The speed of the fan 2722 can be adjusted to adjust the heat transfer rate into or out of the refrigerant in the heat exchanger 2726. The temperature sensor can be used to measure the temperature _Tr of the refrigerant in the indoor unit 2706.

VRF system 2700 is shown to include a first single variable ESC 2732 and a second single variable ESC 2738. Both single variables ESC 2732 and 2738 are the power input P _total representing the total power _Poutoror consumed by the outdoor unit 2702 and the total power _Pindoor consumed by each indoor unit 2703 (ie, _Ptotal = _Poutor + P _(indoor ). As shown in FIG. 27, power input _{P outdoor} and _{P indoor,} in order to provide a combined signal representative of the total power _{P total,} it is possible to sum outside the summation block 2730 of a single variable ESC 2732 and 2738 . In other embodiments, single variables ESCs 2732 and 2738 receive the individual power inputs P _outdoor and P _indoor and perform the summation of summation block 2730. In either case, the single variable ESC 2732 and 2738, even if a single sum or power input as a combination signal _{P total} representing the total system power is provided, receiving the power input _{P outdoor} and _{P indoor} I can say that.

In some embodiments, the total system power P _total is a performance variable that the single variables ESC 2732 and 2738 seek to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the VRF system 2700. In the embodiment shown in FIG. 27, the total system power _{P total includes P outdoor} and _{P indoor.} However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total represents the power consumption of the fan 2718 in the outdoor unit 2702, the fan 2722 in the indoor unit 2706, the heat recovery unit 2704 and / or any other power consumption that occurs in the VRF system 2700. May be included.

A single variable ESC 2732 is shown to provide the overheat set point SH _sp to the outdoor unit 2702. In some embodiments, the overheat setpoint SH _sp is an manipulated variable that adjusts so that the single variable ESC 2732 affects the total system power P _total . For example, the single variable ESC 2732 may increase the superheat set point SH _sp to increase the refrigerant temperature relative to the saturation temperature, so that the refrigerant temperature in the outdoor unit 2702 is close to the saturation temperature. In addition, the overheat set point SH _sp can be reduced. Reducing the overheat set point SH _sp can reduce the outdoor unit power consumption _Poutdoor , but requires additional fan power to transfer heat from the low temperature refrigerant, so the indoor unit power consumption P There is a possibility of increasing the _door . A single variable ESC 2732 dynamically searches for unknown inputs (eg, optimal overheat setpoint SH _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement extreme value search control strategy.

Similarly, a single variable ESC 2738 is shown to provide the heat recovery unit 2704 with a valve set point Valve _sp . In some embodiments, a valve setpoint Valve _sp is an operation variable single variable ESC 2738 is adjusted to affect the total system power _{P total.} For example, the valve set point Valve _sp can be adjusted to control the position of the bypass valve in the heat recovery unit 2704. The single variable ESC 2738 can increase the valve set point Valve _sp to progressively open the bypass valve or decrease the valve set point Valve _sp to progressively close the bypass valve. A single variable ESC 2738 dynamically searches for an unknown input (eg, optimal valve set point Valve _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement extreme value search control strategy.

Vapor compression system 2800
Referring now to FIG. 28, another vapor compression air conditioning system 2800 is shown according to some embodiments. System 2800 may include some or all of the components of vapor compression systems 1400, 1500 and / or 1600 as described with reference to FIGS. 14A, 15A and 16A. For example, system 2800 is shown to include a refrigerant circuit 2810. The refrigerant circuit 2810 includes a condenser 2812, an evaporator 2814, an expansion valve 2824 and a compressor 2806. The compressor 2806 is configured to circulate refrigerant between the evaporator 2814 and the condenser 2812. The refrigerant circuit 2810 operates using a vapor compression cycle. For example, the compressor 2806 compresses the refrigerant into a high temperature and high pressure state. The compressed refrigerant flows through the condenser 2812, and the refrigerant exhausts heat in the condenser 2812. Condenser fan 2832 can be used to adjust the heat transfer rate within condenser 2812. The cooled refrigerant is expanded to a low pressure and low temperature state by an expansion valve 2824. The expanded refrigerant flows in the evaporator 2814, and the refrigerant absorbs heat in the evaporator 2814. The evaporator fan 2816 can be used to adjust the heat transfer rate within the evaporator 2814.

  In some embodiments, the refrigerant circuit 2810 is located in a rooftop unit 2802 (eg, a rooftop air treatment unit), as shown in FIG. The rooftop unit 2802 can be configured to provide cooling for the air supply 2820 flowing through the air duct 2822. For example, the evaporator 2814 is located in the air duct 2822 so that the charge air 2820 can flow through the evaporator 2814 and be cooled by transferring heat to the expanded refrigerant in the evaporator 2814. . The cooled airflow can then be sent to the building to provide cooling to the building room or zone. The temperature of the supply air 2820 can be measured by a temperature sensor 2818 located downstream of the evaporator 2814 (eg, in the duct 2822). In other embodiments, the refrigerant circuit 2810 is in any of a variety of other systems or devices (eg, refrigerators, heat pumps, heat recovery refrigerators, refrigeration devices, etc.) that transfer heat using a vapor compression cycle. Can be used.

The vapor compression system 2800 is shown to include a first single variable ESC 2826, a second single variable ESC 2828 and a third single variable ESC 2830. Each of the single variables ESC 2826-2830 is a power input P _total representing the total power consumed by the compressor 2806 P _comp , the evaporator fan 2816 P _{fan, evap} and the condenser fan 2832 P _{fan, cond} (ie, P _total = P _comp + P _{fan, evap} + P _{fan, cond} ). As shown in FIG. 28, power inputs P _comp , P _{fan, evap} and P _{fan, cond} are external sum blocks of single variable ESCs 2826-2830 to provide a combined signal representing the total power P _total. 2808 can be summed. In other embodiments, the single variable ESC 2826-2830 receives the individual power inputs P _comp , P _{fan, evap} and P _{fan, cond} and _performs the summation of the summation block 2808. In either case, the single variable ESC from 2826 to 2,830, even if a single sum or power input as a combination signal _{P total} representing the total system power is provided, the power input _{P comp, P fan, evap} And P _{fan, cond} can be received.

In some embodiments, the total system power P _total is a performance variable that ESC 2826-2830 seeks to optimize (eg, minimize). The total system power P _total may include the power consumption of one or more components of the vapor compression system 2800. In the embodiment shown in FIG. 28, the total system power _{P total includes} P _{comp, P fan, evap} and _{P fan,} a _cond. However, in various other embodiments, the total system power P _total may include any combination of power inputs. For example, the total system power P _total may include the power consumption of various other fans in the rooftop unit 2802, the power consumption of the fluid pump, and / or any other power consumption that occurs in the vapor compression system 2800. .

A single variable ESC 2830 is shown to provide a temperature setpoint T _sp to the feedback controller 2804. In some embodiments, the temperature set point _{T sp} is an operation variable single variable ESC 2830 is adjusted to affect the total system power _{P total.} The temperature set point T _sp is a set point for the temperature of the charge 2820 exiting the evaporator 2814. Supply air temperature _{T sa} can be measured by a temperature sensor 2818 located downstream of the evaporator 2814. Feedback controller 2804 is shown to receive a supply air temperature T _sa as a feedback signal.

Feedback controller 2804 can operate the evaporator fan 2816 to achieve a temperature set point _{T sp} to be provided by a single variable ESC 2830. For example, the feedback controller 2804 increases the speed of the evaporator fan 2816 to increase the amount of heat removed from the charge 2820 in the evaporator 2814 and is also removed from the charge 2820 in the evaporator 2814. The speed of the evaporator fan 2816 can also be reduced to reduce the amount of heat.

A single variable ESC 2830 dynamically uses unknown inputs (eg, optimal supply air temperature setpoint T _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach optimal values. Implement extremal search control strategy to search. Although feedback controller 2804 and single variable ESC 2830 are shown as separate devices, in some embodiments, feedback controller 2804 and single variable ESC 2830 are combined into a single device (eg, single variable ESC It is contemplated that it can be a single controller that performs the functions of both the 2830 and the feedback controller 2804. For example, the single variable ESC 2830 can be configured to directly control the evaporator fan 2816 without requiring an intermediate feedback controller 2804.

Still referring to FIG. 28, a single variable ESC 2826 is shown to provide the compressor 2806 with a condenser pressure setpoint Pr _sp . The condenser pressure set point Pr _sp defines a set point for the refrigerant pressure in the condenser 2812 that may be the same as the refrigerant pressure at the outlet of the compressor 2806. In some embodiments, the condenser pressure set point Pr _sp is an manipulated variable that adjusts so that the single variable ESC 2826 affects the total system power P _total . The single variable ESC 2826 dynamically sets the unknown input (eg, optimal condenser pressure setpoint Pr _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement extremal search control strategy to search.

Similarly, a single variable ESC 2828 is shown to provide a fan speed set point Fan _sp to the condenser fan 2832. The fan speed set point Fan _sp can indicate a target value for the speed of the fan 2832 and / or a target value for the flow rate of the airflow flowing through the condenser 2812. In some embodiments, the fan speed set point Fan _sp is an manipulated variable that adjusts so that the single variable ESC 2828 affects the total system power P _total . The single variable ESC 2828 dynamically searches for unknown inputs (eg, optimal fan speed set point Fan _sp ) to obtain system performance (eg, total power consumption P _total ) that tends to approach the optimal value. Implement an extreme value search control strategy.

Configuration of Exemplary Embodiments The architecture and configuration of the systems and methods as shown in the various exemplary embodiments is merely exemplary. Although this disclosure has described only a few embodiments in detail, many changes (eg, various element sizes, dimensions, structures, shapes and ratios, parameter values, attachment methods, material usage, colors, orientations) Change) is possible. For example, the position of an element can be reversed, changed in another way, or the nature or number of individual elements or positions can be changed or changed. Accordingly, all such modifications are intended to be included within the scope of this disclosure. The order or sequence of any process or method steps can be varied or rearranged according to alternative embodiments. Other substitutions, changes, changes and omissions in the design, operating conditions and configurations of the exemplary embodiments may be made without departing from the scope of this disclosure.

  The present disclosure contemplates methods, systems, and program products on any machine-readable medium for performing various operations. Embodiments of the present disclosure may be implemented using existing computer processors, or by special purpose computer processors for suitable systems incorporated for this or other purposes, or by wiring systems. Can do. Embodiments within the scope of this disclosure include a program product that includes a machine-readable medium for holding or storing machine-executable instructions or data structures. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can be RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage, or machine-executable instructions or data structures. Any other medium that can be used to hold or store the desired program code in a form and that can be accessed by a general purpose or special purpose computer or other machine with a processor may be included. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machine to perform a certain function or group of functions.

  Although the figure shows a particular order of method steps, the order of the steps may differ from that depicted. Also, two or more steps can be performed simultaneously or partially simultaneously. Such variations will depend on the software and hardware system selected and the choice of the designer. All such variations are within the scope of this disclosure. Similarly, software implementation can be performed using standard programming techniques with rule-based logic and other logic to perform various connection steps, processing steps, comparison steps, and decision steps.

Claims (20)

A building heating, ventilation or air conditioning (HVAC) system,
A plant with HVAC equipment operable to affect the environmental conditions of the building;
A first single variable extremum search configured to perturb a first manipulated variable using a first excitation signal and to provide the first manipulated variable as a first perturbation input to the plant. A controller (ESC);
A second single variable ESC configured to perturb a second manipulated variable using a second excitation signal and to provide the second manipulated variable as a second perturbation input to the plant; Prepared,
The plant uses both perturbation inputs to simultaneously affect the performance variables,
Both single variable ESCs are configured to receive the same performance variable as feedback from the plant;
The first single variable ESC is configured to estimate a first slope of the performance variable relative to the first manipulated variable;
The second single variable ESC is configured to estimate a second slope of the performance variable relative to the second manipulated variable;
The HVAC system, wherein the single variable ESC is configured to independently bring the first and second slopes to zero by independently adjusting the first and second manipulated variables. The HVAC system of claim 1, wherein the first and second excitation signals are stochastic excitation signals that include at least one of an aperiodic signal, a random walk signal, a non-deterministic signal, and a non-repetitive signal. Each of the single variable ESCs is
A stochastic excitation signal generator configured to generate one of the stochastic excitation signals;
3. The HVAC system of claim 2, comprising a feedback controller configured to adjust one of the operational variables to bring one of the estimated slopes of the performance variable to zero. The plant is
A multiple input single output (MISO) system that provides the performance variable as a single output from the plant, or
Multiple input multiple output (MIMO) providing the performance variable and a plurality of other variables as output from the plant
The HVAC system of claim 1, comprising at least one of: The first slope is a first normalized correlation coefficient relating the performance variable to the first manipulated variable;
The HVAC system of claim 1, wherein the second slope is a second normalized correlation coefficient that relates the performance variable to the second manipulated variable. The HVAC system of claim 1, wherein each of the single variable ESCs is configured to perform a recursive estimation process to estimate one of the gradients of the performance variable. A plurality of additional single variable ESCs each corresponding to a different manipulated variable;
Each of the plurality of additional single variable ESCs estimates the slope of the performance variable relative to the corresponding manipulated variable and independently adjusts the corresponding manipulated variable to bring the slope independently to zero. The HVAC system of claim 1, wherein the HVAC system is configured to A building heating, ventilation or air conditioning (HVAC) system,
A plant with HVAC equipment operable to affect the environmental conditions of the building;
A first set of single variable extreme value search controllers (ESCs) configured to provide a first set of manipulated variables as input to the plant while operating in a first mode of operation;
A second set of single variable ESCs configured to provide a second set of manipulated variables as input to the plant while operating in a second mode of operation;
In response to detecting a transition from the first operating mode to the second operating mode, to switch from the first set of single variable ESCs to the second set of single variable ESCs. An HVAC system comprising a configured multi-variable ESC. 9. Each of the single variable ESCs is configured to independently optimize one of the manipulated variables by performing a separate single variable extreme value search control process. HVAC system. Each of the single variable extreme value search control processes includes:
Perturbing one of the manipulated variables using an excitation signal;
Providing the manipulated variable as a perturbation input to the plant;
Receiving performance variables as feedback from the plant;
Estimating a slope of the performance variable relative to the manipulated variable;
10. The HVAC system of claim 9, comprising adjusting the manipulated variable to bring the estimated gradient to zero. The HVAC system of claim 10, wherein the excitation signal is a stochastic excitation signal that includes at least one of an aperiodic signal, a random walk signal, a non-deterministic signal, and a non-repetitive signal. Each of the single variable ESCs is
A stochastic excitation signal generator configured to generate a stochastic excitation signal;
A gradient estimator configured to estimate a gradient of the performance variable relative to one of the manipulated variables;
9. A HVAC system according to claim 8, comprising a feedback controller configured to bring the estimated slope to zero by adjusting one of the manipulated variables. The plant is
A multiple input single output (MISO) system that provides the performance variable as a single output from the plant, or
Multiple input multiple output (MIMO) providing the performance variable and a plurality of other variables as output from the plant
The HVAC system of claim 8, comprising at least one of: 9. The HVAC system of claim 8, wherein each of the single variables ESC is configured to estimate a normalized correlation coefficient that relates the performance variable to one of the manipulated variables. A method for operating a building heating, ventilation or air conditioning (HVAC) system comprising:
Perturbing the first manipulated variable using the first excitation signal;
Perturbing the second manipulated variable using the second excitation signal;
Providing the first manipulated variable and the second manipulated variable as a perturbation input to a plant comprising an HVAC facility, wherein the plant uses both perturbation inputs to simultaneously affect performance variables. , Step and
Receiving the performance variable as feedback from the plant;
Estimating a first slope of the performance variable relative to the first manipulated variable and a second slope of the performance variable relative to the second manipulated variable;
Independently bringing the first and second gradients to zero by independently adjusting the first and second manipulated variables;
Operating the HVAC facility of the plant to influence the environmental conditions of the building using the first and second manipulated variables. 16. The method of claim 15, wherein the first and second excitation signals are stochastic excitation signals that include at least one of an aperiodic signal, a random walk signal, a non-deterministic signal, and a non-repetitive signal. The plant is
A multiple input single output (MISO) system that provides the performance variable as a single output from the plant, or
Multiple input multiple output (MIMO) providing the performance variable and a plurality of other variables as output from the plant
16. The method of claim 15, comprising at least one of: The first slope is a first normalized correlation coefficient relating the performance variable to the first manipulated variable;
16. The method of claim 15, wherein the second slope is a second normalized correlation coefficient that relates the performance variable to the second manipulated variable. The method of claim 15, wherein estimating at least one of the first gradient and the second gradient comprises performing a recursive estimation process. Perturbing a plurality of additional manipulated variables with different excitation signals;
Providing the additional manipulated variable as a perturbation input to the plant, wherein the plant uses all of the perturbation inputs to simultaneously affect the performance variable;
Estimating a slope of the performance variable for each of the plurality of additional manipulated variables;
16. The method of claim 15, further comprising: independently adjusting each of the plurality of additional manipulated variables to independently bring each of the gradients to zero.

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