WO2017018227A1 - Optimum control device, optimum control method, computer program and optimum control system - Google Patents

Abstract

An optimum control system of an embodiment of the present invention includes a controlled parameter determination unit, an extreme value control parameter determination unit, and an extreme value control unit. The controlled parameter determination unit determines a controlled parameter indicating a characteristic of a process to be controlled, such determination being made on the basis of an operation amount and an evaluation amount representing an indicator pertaining to the optimization of the process to be controlled on the basis of a control amount which varies in accordance with the operation amount. The extreme value control parameter determination unit determines an extreme value control parameter on the basis of the controlled parameter determined by the controlled parameter determination unit. The extreme value control unit executes extreme value control using the extreme value control parameter determined by the extreme value control parameter determination unit.

Description

Optimal control device, optimal control method, computer program, and optimal control system

Embodiments described herein relate generally to an optimal control device, an optimal control method, a computer program, and an optimal control system.

In recent years, a technique called extreme value control has attracted attention as a plant control method. Extreme value control is a model-free real-time optimal control technique that does not use a complex model of a plant. The outline of extreme value control is to search for an operation amount that optimizes an evaluation amount based on a control amount of a process to be controlled by forcibly changing the operation amount. When such extreme value control is applied to plant control, it is necessary to appropriately set various parameters related to extreme value control (hereinafter referred to as “control parameters”) according to the characteristics of the process to be controlled. However, the current situation is that the guidelines for the setting are not well established. In particular, when it is necessary to consider a temporal change in the process to be controlled (hereinafter referred to as “dynamics”), there is a possibility that extreme value control does not function unless the control parameters are set appropriately. Therefore, establishment of a guideline for appropriately setting control parameters necessary for extreme value control according to the characteristics of the process to be controlled is desired.

JP 2012-215575 A Japanese Patent Publication No. 8-23332 Japanese Patent Publication No. 8-23329 Japanese Patent Publication No. 6-60594 JP 2009-258068 A Japanese Patent No. 4286880 Japanese Patent No. 4309326 Japanese Patent No. 5300827 Japanese Patent Laid-Open No. 2004-171531

The problem to be solved by the present invention is to provide an optimum control device, an optimum control method, a computer program, and an optimum control system capable of executing extreme value control with a control parameter corresponding to the characteristics of a process to be controlled. .

The optimal control system of the embodiment includes a control target parameter determination unit, an extreme value control parameter determination unit, and an extreme value control unit. The control target parameter determination unit is configured to control the control target process based on an operation amount of the control target process and an evaluation amount indicating an index related to optimization of the control target process based on the control amount that changes according to the operation amount. The control target parameter indicating the characteristic is determined. The extreme value control parameter determining unit determines an extreme value control parameter for executing the extreme value control based on the controlled object parameter determined by the controlled object parameter determining unit. The extreme value control unit executes extreme value control of the process to be controlled using the extreme value control parameter determined by the extreme value control parameter determination unit. The extreme value control unit executes extreme value control for changing the manipulated variable so that the evaluation value is directed to an optimum value using the extreme value control parameter determined by the extreme value control parameter determining unit.

The figure explaining the concept of extreme value control. The block diagram which shows the structural example of an extreme value controller. The functional block diagram which shows the function structure of the optimal control apparatus of embodiment. The figure which shows the outline of a water treatment plant. The figure which put together the adjustment method of the control object parameter and extreme value control parameter in embodiment. The figure which shows the specific example of a display of prediction information.

Hereinafter, an optimum control device, an optimum control method, a computer program, and an optimum control system according to embodiments will be described with reference to the drawings.

FIG. 1 is a diagram for explaining the concept of extreme value control.

Extreme value control is a control method that adaptively searches for the optimum value of the evaluation amount based on the change in the evaluation amount according to the change in the manipulated variable. The evaluation amount is a value serving as an optimization index for a process to be controlled (hereinafter referred to as “control target process”). The evaluation amount is an index value determined based on the control amount of the process to be controlled, and the relationship between the evaluation amount and the control amount is represented by a predetermined evaluation function. This evaluation function may be set based on an arbitrary evaluation criterion as long as it is based on the control amount. The evaluation amount may be the control amount itself. Generally, in the process to be controlled in extreme value control, this evaluation function is an unknown function with respect to the manipulated variable.

In extreme value control, the manipulated variable is changed by a periodic signal called a dither signal. Usually, this dither signal is often given as a sine wave. In extreme value control, the manipulated variable is continuously vibrated by a dither signal, and the change (increase / decrease) in the evaluation value is observed. Then, based on the change in the evaluation amount with respect to the change in the operation amount, the operation amount is changed in such a direction that the evaluation amount approaches the optimum value of the evaluation function. The optimum value of the evaluation function is searched by repeating such changes in the operation amount.

1A is an unknown evaluation function with respect to the manipulated variable. Here, for convenience of explanation, an unknown evaluation function is assumed as a downward convex quadratic function. Assume that when the manipulated variable is changed by the dither signal shown in FIG. 1B with respect to such an assumed evaluation function, the evaluated quantity changes as shown in FIG. In this case, since the evaluation amount decreases with respect to the increase in the operation amount, it can be seen that the operating point has changed on the left side of the minimum value 101 of the evaluation function curve 100. On the other hand, when the operation amount is changed with the same dither signal, the evaluation amount is changed as shown in FIG. In this case, since the evaluation amount increases with respect to the increase in the operation amount, it can be seen that the operating point has changed on the right side from the minimum value 101.

Therefore, as a result of periodically increasing / decreasing the manipulated variable, if the increase / decrease in the evaluation amount moves in the same phase as the increase / decrease in the manipulated variable, the manipulated value is decreased, and if the operation amount moves in the opposite phase, the manipulated variable is decreased. By increasing the value, the evaluation amount can be brought close to the optimum value. Conventionally, PID control (Proportional-Integral-Derivative Control), which has been generally used as a control method for industrial plants, is a target value tracking that controls the manipulated variable so that the controlled variable follows a preset target value. It was a mold control system. In contrast, extreme value control is an optimal value search type control method that searches for an operation amount that optimizes the evaluation amount, and therefore represents the relationship between the operation amount and the control amount as in PID control. No process model is required in advance. Therefore, extreme value control is an effective control method even for a process to be controlled in which a target value cannot be set in advance, and has the potential to be widely used in the future. An extreme value controller that performs extreme value control based on this principle can be realized with a relatively simple configuration.

FIG. 2 is a block diagram showing a configuration example of the extreme value controller.
2 includes a high-pass filter 21 (LPF: Low-Pass Filter), a dither signal output unit 22, a low-pass filter 23 (HPF: High-Pass Filter), and an integrator 24. Prepare. Thus, the configuration of the extreme value controller 2 is as complex as the conventional PID controller. Therefore, the extreme value controller 2 can be easily mounted using hardware such as a PLC (Programmable Logic Controller), like the PID controller. Hereinafter, an outline of the operation of the extreme value controller 2 of FIG. 2 will be described. Here, the case where the minimum value of the evaluation function is searched for as the optimum value will be described as an example.

The extreme value controller 2 forcibly changes the operation amount of the process 200 to be controlled by applying a dither signal (M) having a periodic change. Hereinafter, this operation is referred to as modulation. By this modulation, the operation amount of the control target process 200 periodically changes. The control target process 200 outputs a control amount in accordance with the input of the modulated operation amount. The control target process 200 acquires and outputs the evaluation amount that has changed in accordance with the change in the control amount. The evaluation amount output from the control target process 200 is fed back to the extreme value controller 2. Usually, the change (response) of the evaluation amount with respect to the change of the operation amount appears with a certain time delay.

As described above, extreme value control is a control method for searching for an extreme value of an unknown evaluation function with respect to an operation amount. Therefore, the evaluation function of the control target process 200 is premised on having a minimum value, but the value is unknown. The high-pass filter 21 removes a constant bias corresponding to the unknown minimum value from the feedback evaluation amount. In other words, this process is a process for always adjusting the unknown local minimum value to zero, and is a preprocess necessary for determining the direction of change (increase or decrease) that the integrator 24 gives to the manipulated variable. .

The dither signal output unit 22 causes the dither signal (D) to act on the evaluation amount adjusted in this way. Thereby, the same frequency component as that of the dither signal (M) is extracted from the evaluation amount changed by the modulation. Hereinafter, this operation is referred to as demodulation (demodulation). The role of demodulation is as follows.

As described above, the evaluation function for the operation amount of the control target process 200 is unknown. Therefore, the evaluation function may include a non-linear element. In this case, the evaluation function is assumed to be a non-linear function convex downward (convex upward in the case of local maximum search). Due to such a non-linear element, there is a high possibility that a harmonic component or a subharmonic component corresponding to the frequency ω of the dither signal (M) appears in the evaluation amount. Demodulation is a process for removing the influence of such harmonics and subharmonics. By this demodulation, a component having the same frequency ω as that of the dither signal (M) in which the evaluation amount is changed is extracted from the components included in the evaluation amount.

The demodulated evaluation amount is input to the low-pass filter 23. The low-pass filter 23 extracts a steady component (low frequency component) from the evaluation amount. The steady component is considered to indicate whether the evaluation amount has changed in the increasing direction or the decreasing direction due to the application of the dither signal (M). The integrator 24 functions as an estimator that estimates the direction (gradient) of the operation amount to be moved to bring the evaluation amount close to the minimum value by integrating the steady component extracted by the low-pass filter 23.

This kind of gradient estimation is based on the most basic gradient method as an adaptive control system estimation method. The dither signal (M) is adjusted by the gradient estimated by the integrator 24 so as to give a change that brings the evaluation amount close to the minimum value with respect to the operation amount. The maximum value search can be realized, for example, by inverting the sign of the integrator 24.

FIG. 3 is a functional block diagram illustrating a functional configuration of the optimum control apparatus according to the embodiment.
In the example of FIG. 3, the plant 300 and the evaluation amount acquisition unit 400 correspond to the control target process 200 of FIG. The evaluation amount acquisition unit 400 acquires the evaluation amount J based on the control amount Y output from the plant 300. The optimal control device 1 performs extreme value control of the plant 300 based on the evaluation amount J output from the evaluation amount acquisition unit 400.

The optimal control device 1 includes a CPU (Central Processing Unit) connected via a bus, a memory, an auxiliary storage device, and the like, and executes an optimal control program. The optimal control device 1 functions as a device including a control target parameter determination unit 11, an extreme value control parameter adjustment unit 12, and an extreme value control controller 13 by executing an optimal control program. All or some of the functions of the optimal control device 1 may be realized by using hardware such as ASIC (Application Specific Integrated Circuit), PLD (Programmable Logic Device), and FPGA (Field Programmable Gate Array). . The optimal control program may be recorded on a computer-readable recording medium. The computer-readable recording medium is, for example, a portable medium such as a flexible disk, a magneto-optical disk, a ROM, a CD-ROM, or a storage device such as a hard disk built in the computer system. The optimal control program may be transmitted via a telecommunication line.

The control target parameter determination unit 11 determines a control target parameter indicating the characteristics of the plant 300. For example, the control target parameter is a parameter such as a time constant or dead time of the plant 300. The control target parameter determination unit 11 determines the control target parameter based on the operation amount U input to the plant 300 and the evaluation amount J output from the evaluation amount acquisition unit 400.

The extreme value control parameter adjustment unit 12 (extreme value control parameter determination unit) determines an extreme value control parameter for executing extreme value control on the plant 300. For example, the extreme value control parameters are parameters such as the frequency of the low-pass filter and the high-pass filter, the frequency and amplitude of the dither signal, and the gain of the integrator. The extreme value control parameter adjustment unit 12 determines an extreme value control parameter based on the control target parameter determined by the control target parameter determination unit 11.

The extreme value controller 13 executes extreme value control of the process to be controlled based on the extreme value control parameter determined by the extreme value control parameter adjustment unit 12. Details of the configuration of the extreme value controller 13 are the same as those of the extreme value controller 2 shown in FIG.

Note that the process to be controlled that is the control target of the optimal control device 1 is not limited to the plant. The controlled process may be an arbitrary process having an evaluation amount to be optimized. Hereinafter, the function of the optimal control apparatus 1 will be described in detail by taking a water treatment plant that realizes a biological wastewater treatment process as an example of the plant 300 as an example.

FIG. 4 is a diagram showing an outline of a water treatment plant.
The water treatment plant 500 of FIG. 4 includes an anaerobic tank 510, an oxygen-free tank 520, an aerobic tank 530, and a final sedimentation basin 540. Anaerobic tank 510 is equipment for activating microorganisms. The anoxic tank 520 is equipment for removing nitrogen. The aerobic tank 530 is equipment for decomposing organic substances, removing phosphorus, and nitrifying ammonia. The final sedimentation basin 540 is equipment for precipitating activated sludge.

The water treatment plant 500 is equipped with facilities such as a pump for conveying water and sludge between the above facilities, a blower for supplying air into the tank, and a sensor for measuring the concentration of substances in the air or water. The chemical injection pump 511 is a pump that supplies chemicals such as a carbon source that activates microorganisms to the anaerobic tank 510. The circulation pump 531 is a pump that controls the circulation amount of the water to be treated that circulates between the aerobic tank 530 and the anoxic tank 520. The blower 532 controls the amount of aeration by supplying air to the aerobic tank 530. The return sludge pump 541 is a pump that returns the sludge from the final sedimentation basin 540 to the anoxic tank 520. The excess sludge extraction pump 542 is a pump that extracts excess sludge from the final sedimentation basin 540. The sensor 512 and the sensor 543 measure the quality of discharged water in the anaerobic tank 510 and the final sedimentation basin 540, respectively.

In general, in such a biological wastewater treatment process, the manipulated variable is the return rate of the returned sludge, and the controlled variable is the concentration of nitrogen and phosphorus contained in the discharged water (hereinafter referred to as “discharged nitrogen concentration” and “released phosphorus, respectively”). Called "concentration"). The return rate is obtained by dividing the discharge flow rate of the return sludge pump 541 by the inflow amount. The released nitrogen concentration and the released phosphorus concentration are acquired by the sensor 512 and the sensor 543. The control amount may be the amount of nitrogen and phosphorus contained in the discharge water (hereinafter referred to as “discharge nitrogen amount” and “discharge phosphorus amount”, respectively). In this case, the released nitrogen amount and the released phosphorus amount can be obtained by multiplying the released nitrogen concentration and the released phosphorus concentration by the released flow rate, respectively.

In the evaluation amount acquisition unit 400, an evaluation function for acquiring the evaluation amount based on the control amount output from the water treatment plant 500 is set in advance. The evaluation function here defines an unknown evaluation function for the manipulated variable as a function of the control amount. For example, the evaluation function is a function representing the relationship between the released nitrogen concentration and released phosphorus concentration and the evaluation amount. This evaluation function needs to be set so as to take an extreme value between the control amount at the upper limit of the operation amount (return rate) and the control amount at the lower limit of the operation amount. As an example of the method for setting the evaluation function in this way, the evaluation amount is expressed as the sum of the water quality cost based on the concept of drainage levy and the power cost of the return sludge pump 541 (hereinafter referred to as “total cost”). Can be considered. The power cost of the return sludge pump 541 can be calculated from the return sludge flow rate, the rated power of the return sludge pump 541, and the like. In general, in the concept of drainage levy, water quality cost is expressed by the following equation.

In the formula (1), COD means chemical oxygen demand, BOD means biochemical oxygen demand, TN means released nitrogen, and TP means released phosphorus. The conversion factor for each cost may be determined based on the actual drainage levy, or may be determined by other methods. In general, it is known that, among COD, BOD, TN, and TP, those that greatly change by changing the return rate are TN and TP. Therefore, here, the water quality cost is expressed by the following equation (2).

In general, it is known that when the return rate is increased, the nitrogen removal rate increases and the water quality cost related to TN decreases, and conversely, when the return rate is lowered, the phosphorus removal rate increases and the water quality cost related to TP decreases. In such a case, the evaluation function may be set based only on the water quality cost. However, when the cost between water qualities that do not have such a trade-off relationship is used as an index, the evaluation function is expressed as the total cost including the operation cost (electric power cost). (Return rate) It is set to take an extreme value between the control amount at the upper limit and the control amount at the lower limit of the operation amount.

Also, instead of such total cost, a function that directly represents the evaluation of water quality may be set as the evaluation function. For example, the evaluation amount may be calculated as in the following formula (3).

In Expression (3), TN _lim and TP _lim are parameters representing a threshold level corresponding to the regulation value and management value of the discharged water quality. When such an evaluation function is used, the evaluation amount rapidly increases when the threshold level is exceeded. Therefore, it can be expected that the extreme value control functions so as to suppress the evaluation amount within the threshold level.

As described above, the evaluation function setting method necessary for extreme value control has been described using the water treatment plant 500 as shown in FIG. 4 as an example. However, depending on the plant 300 to be controlled, setting of the evaluation function is not necessary. In some cases. An example of this is the control of wind turbine blades in a wind power plant. When extreme value control is applied to control that maximizes the amount of power generation by moving the windmill blade direction along with the wind direction, the evaluation amount is the power generation amount, and the operation amount is the rotation angle of the windmill blade. . In this case, since the control amount becomes the evaluation amount as it is, it is not necessary to set the evaluation function. In such a case, the evaluation amount acquisition unit 400 may not be provided. On the other hand, extreme value control may be applicable by acquiring the evaluation amount.

The control target parameter determination unit 11 determines the control target parameter based on the control amount and the evaluation amount acquired as described above. Hereinafter, control target parameters determined by the control target parameter determination unit 11 will be described.

[1. Time constant]
One of the control target parameters to be determined by the control target parameter determination unit 11 is a time constant of the control target process. The time constant of the process to be controlled is the time until the control amount reaches 63% (= 100 × {1-exp (−1)}%) of the step response when the manipulated variable is changed in steps. Defined. This time constant is normally used as a control parameter for PID control. In addition, when the evaluation amount is acquired based on one control amount, the time constant may be simply set based on the above definition, but the evaluation amount includes a plurality of control amounts as in the water treatment plant 500 described above. When acquired based on (TN concentration and TP concentration), the larger time constant (that is, the slower response speed) is set as a representative value. Although the time constant may be identified by actually changing the manipulated variable and measuring the response time, it can be identified using any open-loop (open-loop) or closed-loop (closed-loop) system identification method. Also good.

[2. Dead time]
One of the control target parameters to be determined by the control target parameter determination unit 11 is a dead time (until the response of the control amount is obtained from the input of the operation amount or until the evaluation amount is acquired from the input of the operation amount ( Delay time). The dead time can be identified by any identification method, but the simplest method is to collect time-series data for manipulated variables and time-series data for controlled variables and calculate the correlation coefficient while shifting the time. It is. In this case, the time difference until the value of the correlation coefficient becomes maximum is the dead time.

[3. Second derivative of evaluation function]
One of the control target parameters to be determined by the control target parameter determination unit 11 is the second-order differential value G = d ² J / d ² U of the evaluation amount J when the operation amount U is changed. This can be estimated by obtaining the amount of change in the evaluation amount J when the manipulated variable U is changed at some operating points of the control target process in a state where the disturbance to the control target process can be regarded as almost constant. it can. Note that the value of the second order differential value G is not always constant. Therefore, in such a case, a representative value such as an average value or a median value is used, or a second-order differential value G is determined for each of several operating points. When the control amount and the evaluation amount can be acquired individually as in the present embodiment, parameter identification is performed using the process model represented by the following equations (4) and (5). It is also possible.

Equation (4) is a model representing “first-order lag + dead time process” that is also commonly used in PID control. Expression (5) represents the evaluation function of the model represented by Expression (4) as a quadratic function having the simplest convex shape. Y (t) in Expression (4) represents a control amount at time t. u represents an operation amount. _Ku represents the process gain. T represents a time constant, and s represents a Laplace operator. L represents the dead time. J (t) in Equation (5) represents the evaluation amount at time t. K _y represents the gain of the evaluation function. K _arg represents the control amount y giving the optimum value, and K _min represents the optimum value (minimum value) of the evaluation function.

In general, K _arg and K _min in equation (5) are often not known. On the other hand, the process model of Expression (4) can be identified using a normal identification method if the control amount can be measured. Further, if the K _y of formula (5) is calculated directly from the relational expression between the control amount and the evaluation value, or be estimated by measuring the variation of the evaluation value J when changing a control amount it can. If K _u and K _y can be estimated in this way, the second-order differential value G (in the steady state) can be calculated by a simple calculation formula as shown in the following formula (6). it can.

[4. Upper and lower limits of operation amount]
One of the control target parameters to be determined by the control target parameter determination unit 11 is an upper limit value and a lower limit value of the operation amount. For these parameters, the upper and lower limit values of the operation amount implemented in the plant monitoring control system or the like may be used as they are, or the maximum value and the minimum value in the past operation data of the plant are respectively set as upper limit values. And it may be used as a lower limit. Moreover, you may set based on the knowledge regarding a plant. In general, when the return rate is the manipulated variable in the water treatment plant 500, the lower limit can be set to approximately 20%, and the upper limit can be set to approximately 100%.

Note that the control target parameter determination unit 11 may automatically determine the control target parameter using the plant measurement data, or input a parameter identified by performing a necessary test such as a step response test. It may be configured to accept. Moreover, when identification using plant data is difficult, it may be configured to accept input of assumed values for some or all of the control target parameters.

The extreme value control parameter adjustment unit 12 determines an extreme value control parameter based on the control target parameter determined by the control target parameter determination unit 11. Hereinafter, the extreme value control parameters determined by the extreme value control parameter adjusting unit 12 will be described.

[1. Dither signal amplitude and frequency]
Extreme control parameter adjustment unit 12 calculates the fluctuation range U _R of the operation amount from the upper limit value and the lower limit value of the manipulated variable. The extreme control parameter adjusting section 12, with respect to the variation range U _R of the manipulated variables, in advance set the parameters k ₁ indicating whether to allow the oscillating at how much variation width dither signal. The extreme value control parameter adjusting unit 12 determines the amplitude a of the dither signal based on the set parameter k ₁ as shown in the following equation (7).

Specifically, the parameter k ₁ is the ratio of the amplitude a to the variation range U _R of the manipulated variables. Usually, the parameter k ₁ may be set to about 0.01 to 0.1. For example, when k ₁ = 0.01 is set, the dither signal is allowed to constantly oscillate with a fluctuation range of about 1% with respect to the fluctuation range of the manipulated variable, and k ₁ = 0.1 is set. In this case, it is allowed to constantly vibrate with a fluctuation range of about 10% with respect to the fluctuation range of the manipulated variable.

The reason why the amplitude a of the dither signal is determined based on the parameter k ₁ is as follows. As can be seen from FIG. 2, the amplitude a of the dither signal is a signal that is forcibly added for modulation of the manipulated variable, and the signal fed back is input to the low-pass filter. It is assumed that the signal output from the low-pass filter hardly oscillates, and the amplitude of the steady operation amount vibration is assumed to be approximately the same as the amplitude a of the dither signal. Therefore, by determining the amplitude a of the dither signal based on the ratio of the manipulated variable with respect to the fluctuation range, the extreme value control parameter adjusting unit 12 does not adversely affect the normal control of the process to be controlled, and the extreme value The amplitude can be determined so as to produce a change in the evaluation quantity that is necessary for control.

Note that the value of the parameter k _1, it is preferable that the default value is set. For example, the extreme value control parameter adjustment unit 12 is configured to hold a default value such as k ₁ = 0.05 (= 5%) in advance and change the value within an allowable range as necessary. Is preferred.

[2. Dither signal frequency]
The extreme value control parameter adjustment unit 12 determines the frequency of the dither signal based on two control target parameters, a time constant and a dead time. First, the extreme value control parameter adjustment unit 12 acquires a time constant T _mod as a comprehensive time constant of the process to be controlled. The time constant T _mod is calculated by the following equation (8). T _{mod in} Expression (8) corresponds to a time constant in the case where “first order delay + dead time process” expressed by Expression (4) is approximated by Padé.

Subsequently, the extreme value control parameter adjustment unit 12 acquires the bandwidth of the process to be controlled based on T _mod acquired by Expression (8). The bandwidth ω _{b of the} process to be controlled is calculated by the following equation (9).

Subsequently, the extreme value control parameter adjusting unit 12 determines the frequency of the dither signal based on the bandwidth ω _{b of the} process to be controlled acquired by Expression (9). The frequency ω of the dither signal is calculated by the following equation (10).

k ₂ is a parameter that takes values in the range of 5-10. By setting the frequency ω of the dither signal in this way, it is possible to separate the dynamics of the process to be controlled and the time scale of the search speed in the extreme value search. In other words, this setting makes it possible to regard the process to be controlled as a static process that is stationary as seen from the time scale of the scanning signal for extreme value search (that is, the dither signal). Note that it is preferable that k ₂ has a default value as in k ₁ . For example, the dynamics of the controlled process and the time scale of the scanning of the extremum search set 10 so as to be completely separated as the default value for k _2.

As described above, two extreme value control parameters of the amplitude a and the frequency ω of the dither signal used for extreme value control are determined.

Next, the extreme value control parameter adjusting unit 12 determines the extreme value control parameters related to the low-pass filter and the high-pass filter using the parameters determined above. Hereinafter, a method for determining control parameters related to the low-pass filter and the high-pass filter will be described.

[3. Low-pass filter frequency]
As described above, the low-pass filter is used for the purpose of passing a component that oscillates at the frequency ω of the dither signal and cutting out the harmonic component. Therefore, the extreme value control parameter adjustment unit 12 determines the frequency ω _{1 of the} low-pass filter by the following equation (11).

Note that an integrator subsequent to the low-pass filter can also obtain the effect of cutting off the harmonics as in the low-pass filter. Therefore, the extreme value controller 13 may be configured not to include a low-pass filter. In this case, ω ₁ may be set to ∞ (infinity).

[4. High-pass filter frequency]
As described above, the high-pass filter is used for the purpose of removing the bias component in order to make the minimum value of the evaluation function zero. The high pass filter needs to pass the dither signal. Therefore, the extreme value control parameter adjusting unit 12 determines the frequency ω _{2 of the} high-pass filter by the following equation (12).

Incidentally, the high-pass filter, a bias signal (i.e., zero frequency) for it if it is possible to remove the frequency omega ₂ does not necessarily have to be strictly adjusted. Therefore, ω ₂ may be an arbitrary value as long as it is sufficiently smaller than 0.1 × ω. For example, ω ₂ may be a sufficiently small fluctuation value that satisfies ω ₂ ≦ 0.1 × ω. Further, for example, ω ₂ may be simply set as a fixed value sufficiently small with respect to 0.1 × ω (for example, 0.001 with respect to ω = 0.1).

When the frequency ω _{1 of the} low-pass filter and the frequency ω _{2 of the} high-pass filter are set as fixed values of ∞ and 0.001, respectively, these parameters are set as default values before estimating the frequency ω of the dither signal. May be.

[5. Integrator gain]
The extreme value control parameter adjustment unit 12 determines the gain of the integrator (hereinafter referred to as “integral gain”) based on the control target parameter and the extreme value control parameter determined as described above. The integral gain KI is expressed by the following equations (13) and (14) using the frequency ω of the dither signal.

In the formula (14), _{k 3} is a parameter representing the convergence time of the extreme value control for the period _T d = _2π / _ω of the dither signal. In order to separate the period of the dither signal from the convergence time of the extreme value control, k ₃ is preferably set to 5 to 10. Then, the default value of _{k 3} to set the 10. Further, P in the equation (14) represents the power of the dither signal. It is known that P = 1/2 when the dither signal is a sine wave, and P = 1/3 and P = 1 when the dither signal is a triangular wave and a rectangular wave, respectively.

The above KI ₀ is a factor that greatly affects the performance of extreme value control. Hereinafter, a method for setting the KI ₀ will be described.

Equation (14) is a mathematical formula derived based on an average system (average system) used for stability analysis of the extreme value control system. An average system is a system in which when a periodic input is applied to a certain system, the behavior (output) of the system can be expressed by an average value (average) in that period. When the process to be controlled is a static process having no dynamics, the average system of the extreme value control system is expressed by the following equation (15).

In Expression (15), D _J represents a gradient related to the periodic average (xx ^* ) of the input of the evaluation function J. x ^* is the equilibrium point of x. τ is a time function scaled by the frequency ω of the dither signal. It is a value represented by the following formula (16).

The average system of Equation (15) represents the dynamics related to the convergence of extreme value control. Specifically, it represents how fast the evaluation amount converges to the minimum value (minimum value) with respect to the operation amount given periodic vibration by the dither signal. For example, when the control target process represented by the process model of Expression (4) and Expression (5) can be regarded as a static process having fast dynamics, x in Expression (15) is a steady state control target process. corresponding to the period mean _{u ave} of y (= _{K u} × _u) in. Further, the slope of _{D J} of formula (15) can be expressed from equation (5) as in the following equation (17).

As described above, the frequency ω of the dither signal is set so that the dynamics of the process to be controlled responds sufficiently quickly to changes in the dither signal. Therefore, in this case, there is no problem even if the process to be controlled represented by Expression (4) is regarded as static. Since the equation (15) shows the behavior of the extreme value control system on the time axis τ (= ωt) scaled by the frequency of the dither signal, the time constant of the average system represented by the equation (15) is This is considered to correspond to the time constant on the time axis τ until the extreme value control converges to the extreme value. Therefore, the time constant of the averaging system of the formula (15), so that more long enough period of the dither signal T (= 2π / ω) ω , by adjusting the a and KI _0, accurately evaluate the amount It is thought that it can be converged.

Since the dither signal frequency ω and the amplitude a are determined as described above, the extreme value control parameter adjusting unit 12 sets the time constant of the average system to be sufficiently longer than the period T (= 2π / ω) of the dither signal. ₀ may be determined.

When the process to be controlled is represented by the process model of Expression (4) and Expression (5), the average system is represented by the following Expression (18). Further, the time constant of the average system expressed by the equation (18) is expressed by the equation (19).

The time constant of the average system indicated by Equation (19) is the time constant on the time axis τ. In this case, τ = 1 is considered to be a time corresponding to 1 / ω. Therefore, the value of KI ₀ can be determined by specifying how many times the response time corresponding to the time constant is 2π / ω of the dither signal.

As described above, KI ₀ needs to be set so that the time constant of the average system is sufficiently longer (converged) than the period of the dither signal. Therefore, the extreme value control parameter adjusting unit 12 determines, for example, the response time corresponding to the time constant to be about k ₃ (= 5 to 10) times the period of the dither signal. In this case, the following equation (20) between the _{k 3} and KI ₀ is established. Then, Expression (14) is obtained by applying Expression (4) to Expression (20).

FIG. 5 summarizes the method for determining the control target parameter, the method for adjusting the extreme value control parameter, and the conventional design guideline in the embodiment described above.

The optimal control apparatus 1 of the embodiment configured as described above is capable of determining an extreme value control parameter and adjusting an extreme value control parameter by only setting five control object parameters. With part 12. Therefore, by using the optimum control device 1 of the embodiment, it is possible to realize extreme value control of the process to be controlled on a scale that can be implemented in the PLC.

Note that the above-described optimal control device 1 may be configured to acquire process data during operation and automatically update the extreme value control parameters. With this configuration, the optimal control device 1 can perform control with extreme value control parameters corresponding to the state of the process to be controlled that changes over time, and improve the performance of searching for the optimum value by extreme value control. Can be made.

Hereinafter, another modification of the optimum control device 1 of the embodiment will be described.
[First Modification]
The optimal control device 1 displays the prediction information indicating the prediction of how the behavior of the control target process changes by setting the control target parameter and the extreme value control parameter determined by the above method. , Not shown).

FIG. 6 is a diagram illustrating a specific example of display of prediction information.
For example, the display screen 600 includes a mode display area 610, a control target parameter display area 620, a pre-adjustment extreme value control parameter display area 630, a post-adjustment extreme value control parameter display area 640, a pre-adjustment control information display area 650, and a post-adjustment control. An information display area 660 is provided. The mode display area 610 is an area in which an extreme value control execution mode is displayed. The example of FIG. 6 shows a case where manual control is selected from two modes of automatic control and manual control. The control target parameter display area 620 is an area in which the value of the control target parameter determined by the optimal control device 1 is displayed. The pre-adjustment extreme value control parameter display area 630 is an area in which the value of the current extreme value control parameter before change is displayed. The adjusted extreme value control parameter display area 640 is an area in which the value of the newly determined extreme value control parameter is displayed. The pre-adjustment control information display area 650 is an area in which a control result with the current extreme value control parameter is displayed. The post-adjustment control information display area 660 is an area in which a prediction of a control result when extreme value control is performed using a newly determined extreme value control parameter is displayed.

In this case, the optimal control device 1 includes a prediction unit (not shown) that simulates the behavior of the control target process based on the process model of the control target process, and a display control unit (not shown) that generates the display screen. With. The display control unit generates a display screen that displays the value of the extreme value control parameter before and after the change by combining the prediction result simulated by the prediction unit and the control result of the current extreme value control parameter.

By displaying such a display screen, workers who need to adjust the parameters of the extremum controller, such as plant managers and maintenance personnel, can verify the validity of the present and changed extremum control parameters. This confirmation can be visually judged.

[Second Modification]
When some or all of the control target parameters change according to the operating point of the control target process, the optimal control device 1 stores a plurality of parameter sets of the control target parameters and the extreme value control parameters, and uses a predetermined switching criterion. It may be configured as a gain scheduling type control device that switches the extreme value control parameter accordingly.

[Third Modification]
The optimal control apparatus 1 may be configured to periodically identify the control target parameter and update the extreme value control parameter when the difference from the current control target parameter value exceeds a predetermined threshold value. . The threshold value for determining the difference between the parameters to be controlled may be set simply based on the absolute value of the difference, or the ratio of the change based on the parameter after the change ((parameter value before adjustment−parameter after adjustment) (Value) ÷ adjusted parameter value × 100 (%)). In the latter case, for example, the threshold value may be α (%), and the extreme value control parameter may be updated when the rate of change becomes ± α% or more. When the prediction unit of the first modification is provided, the extreme value is obtained when the similarity between the actual control result and the prediction result is evaluated by the sum of squares of errors and the response speed is assumed to change greatly. The control parameter may be updated.

[Fourth Modification]
In the above modification, the optimum control device 1 updates the extreme value control parameter as a device that executes extreme value control. However, the optimum control device 1 determines whether the current control state is valid based on the criteria for updating the parameter. A function as a diagnostic device for diagnosing sex may be provided. In this case, for example, when the update of the extreme value control parameter is recommended, the optimal control device 1 may include a notification unit that notifies an operator such as a plant to that effect.

[Fifth Modification]
Among the functional units included in the optimal control device 1, functional units other than the extreme value controller 13 (second extreme value control device) are devices other than the optimal control device 1 (first extreme value control device). ) May be implemented. For example, if the control target parameter determination unit 11, the extreme value control parameter adjustment unit 12, the evaluation amount acquisition unit 400, and the like are mounted on an apparatus that can communicate with the optimal control device 1 and the control target plant 300 via a network, It is also possible to configure a cloud control system that can control extreme value control from a remote location.

According to at least one embodiment described above, the control target parameter determination unit that determines the control target parameter of the control target process based on the operation amount and the evaluation amount, and the control target determined by the control target parameter determination unit And an extreme value control parameter determination unit for determining an extreme value control parameter for executing extreme value control based on the parameter, thereby enabling extreme values with control parameters appropriately set according to the characteristics of the process to be controlled. Value control can be performed.

Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the spirit of the invention. These embodiments and their modifications are included in the scope and gist of the invention, and are also included in the invention described in the claims and the equivalents thereof.

Claims (9)

1. Based on an operation amount of the control target process and an evaluation amount indicating an index related to optimization of the control target process based on a control amount that changes according to the operation amount, a control target parameter indicating a characteristic of the control target process is A control target parameter determining unit to determine;
   An extreme value control parameter determining unit that determines an extreme value control parameter for executing the extreme value control based on the controlled object parameter determined by the controlled object parameter determining unit;
   Using the extreme value control parameter determined by the extreme value control parameter determining unit, an extreme value control unit that executes extreme value control that changes the manipulated variable so that the evaluation value is directed to an optimum value;
   An optimal control device comprising:
2. The extreme value control unit includes a high-pass filter, a low-pass filter, and an integrator,
   The control target parameter determination unit includes a time constant of the control target process, the control target process dead time, a second-order differential value of the evaluation amount with respect to the operation amount, and an upper limit value and a lower limit value of the operation amount. Determined as the parameter to be controlled,
   The extreme value control parameter determination unit is configured to change an amplitude of the dither signal for changing the operation amount based on the time constant, the dead time, the second-order differential value, and the upper limit value and the lower limit value, and the dither signal. A frequency, a frequency of the low-pass filter and the high-pass filter, and a gain of the integrator are determined as the extreme value control parameters;
   The optimal control device according to claim 1.
3. In a mode in which the display unit can compare information regarding the current extreme value control parameter determined by the extreme value control parameter determination unit and the extreme value control parameter newly determined by the extreme value control parameter determination unit. A display control unit for generating information for display;
   The optimal control apparatus according to claim 1 or 2.
4. The extreme value control parameter determination unit acquires a plurality of parameter sets of the control target parameter and the extreme value control parameter according to an operating point of the control target process,
   The extreme value control unit executes extreme value control with an extreme value control parameter corresponding to an operating point of the process to be controlled.
   The optimal control apparatus as described in any one of Claim 1 to 3.
5. The extreme value control unit has a difference between the extreme value control parameter currently used for extreme value control and the extreme value control parameter newly determined by the extreme value control parameter determination unit exceeds a predetermined threshold value. In this case, the extreme value control is executed with the newly determined extreme value control parameter.
   The optimal control apparatus as described in any one of Claim 1 to 4.
6. A notification unit for notifying that a difference between an extreme value control parameter currently used for extreme value control and the newly determined extreme value control parameter exceeds a predetermined threshold;
   The optimal control apparatus according to claim 5.
7. Based on an operation amount of the control target process and an evaluation amount indicating an index related to optimization of the control target process based on a control amount that changes according to the operation amount, a control target parameter indicating a characteristic of the control target process is A control object parameter determination step to be determined; and
   An extreme value control parameter determining step for determining an extreme value control parameter for executing the extreme value control based on the controlled object parameter determined in the controlled object parameter determining step;
   Using the extreme value control parameter determined in the extreme value control parameter determination step, an extreme value control step for executing extreme value control for changing the manipulated variable so that the evaluation value is directed to an optimum value;
   An optimal control method.
8. Based on an operation amount of the control target process and an evaluation amount indicating an index related to optimization of the control target process based on a control amount that changes according to the operation amount, a control target parameter indicating a characteristic of the control target process is A control object parameter determination step to be determined; and
   An extreme value control parameter determining step for determining an extreme value control parameter for executing the extreme value control based on the controlled object parameter determined in the controlled object parameter determining step;
   Using the extreme value control parameter determined in the extreme value control parameter determination step, an extreme value control step for executing extreme value control for changing the manipulated variable so that the evaluation value is directed to an optimum value;
   A computer program for causing a computer to execute.
9. Based on an operation amount of the control target process and an evaluation amount indicating an index related to optimization of the control target process based on a control amount that changes according to the operation amount, a control target parameter indicating a characteristic of the control target process is A control target parameter determining unit to determine;
   An extreme value control parameter determining unit that determines an extreme value control parameter for executing the extreme value control based on the controlled object parameter determined by the controlled object parameter determining unit;
   A first extreme value control device comprising:
   A second extreme value control device that executes extreme value control for changing the manipulated variable such that the evaluation value is directed to an optimum value using the extreme value control parameter determined by the first extreme value control device; ,
   Comprising
   Optimal control system.

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