JP7154774B2 - Optimal control device, control method and computer program - Google Patents

Description

Embodiments of the present invention relate to an optimum control device, control method, and computer program.

In recent years, a technique called extremum control has attracted attention as a method of plant control. Extremum control is a model-free real-time optimal control technique that does not use a complex model of the plant. The outline of extreme value control is to forcibly change the manipulated variable to search for the manipulated variable that optimizes the evaluation amount based on the controlled variable of the controlled process. When such extreme value control is applied to plant control, it is necessary to appropriately set various parameters (hereinafter referred to as "control parameters") related to extreme value control according to the characteristics of the process to be controlled. Conventionally, some guidelines for designing control parameters have been presented, but all of them are designed to adapt to temporal changes in the controlled process (hereinafter referred to as "dynamics") and to stably operate extremum control. It has not reached the point where it can be done.

JP 2017-33104 A

D. Nesic et. al., 'A Unifying Approach to Extremum Seeking: Adaptive Schemes Based on Estimation of Derivatives', Proc. 49th IEEE Conference on Decision and Control, December 15-17, 2010 W.H.Moase et al, 'Newton-Like Extremum-Seeking Part I: Theory', Proc. Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, December 16-18, 2009 Yan et al, On the choice of dither in extremum seeking systems: A case study, Automatica, 44, pp.1446-1450 (2008)

The problem to be solved by the present invention is to provide an optimum control device, a control method, and a computer program that can adapt to the dynamics of a process to be controlled and operate extremum control more stably.

The optimum control device according to the embodiment is configured such that the evaluation amount is determined based on the operation amount of the controlled process and the evaluation amount indicating the index related to the optimization of the controlled process based on the control amount that changes according to the operation amount. The control device executes extreme value control for changing the manipulated variable so as to move toward the optimum value. The optimum controller has a gradient estimator and a corrector. The gradient estimating unit estimates a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and unknown with respect to the manipulated variable, based on the evaluation quantity observed for the controlled process. do. The correction unit adapts the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control to changes in the evaluation function, based on the estimated value of the gradient obtained by the gradient estimator. to correct.

The figure explaining the basic concept of extreme value control. 1 is a block diagram showing a basic configuration example of an extreme value control system 9 that implements extreme value control; FIG. 2 is a block diagram showing a specific example of the functional configuration of an optimum control device 2 according to the first embodiment; FIG. FIG. 5 is a diagram showing a specific example of an n-order differential value estimation method according to the first embodiment; The figure which shows an example of the determination method of the control parameter in 1st Embodiment. 1 is a block diagram showing a configuration example of an extreme value control system 1 realized by an optimum control device 2 of the first embodiment; FIG. The figure which shows the specific example of the water treatment plant 3 which implement|achieves a biological waste water treatment process as an example of the plant P in 1st Embodiment. 4 is a flow chart showing the flow of processing in which the optimum control device 2 according to the first embodiment controls the process to be controlled by extreme value control; The block diagram which shows the specific example of the functional structure of the optimal control apparatus 2a in 2nd Embodiment. The block diagram which shows the structural example of the extreme value control system 1a implement|achieved by the optimal control apparatus 2a of 2nd Embodiment. The block diagram which shows the specific example of the functional structure of the optimal control apparatus 2b in 3rd Embodiment. The figure which shows an example of the estimation method of the nth order differential value in 3rd Embodiment. The block diagram which shows the structural example of the extreme value control system 1b implement|achieved by the optimal control apparatus 2b of 3rd Embodiment. FIG. 5 is a diagram showing a specific example of effects obtained by the optimum control devices of the first to third embodiments; The figure which shows the specific example of the screen displayed by the display information in the optimal control apparatus 2 of a modification.

BEST MODE FOR CARRYING OUT THE INVENTION An optimum control device, a control method, and a computer program according to embodiments will be described below with reference to the drawings.

(outline)
FIG. 1 is a diagram for explaining the basic concept of extreme value control. Extreme value control is a control method that brings the evaluation amount closer to the optimum value by updating the manipulated variable based on the change in the evaluation amount. The evaluation amount is a value that serves as an optimization index for a process to be controlled (hereinafter referred to as "controlled 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 any evaluation criteria as long as it is based on the control amount. Also, the evaluation amount may be the control amount itself. Generally, in extreme value control, the evaluation function of the controlled process 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, first, the operation amount is continuously oscillated by a dither signal, and the resulting change (increase or decrease) in the evaluation amount is observed. Then, based on the observed change in the evaluation amount, calculate the operation amount that brings the evaluation amount closer to the optimum value (maximum value or minimum value) of the evaluation function, and update the current operation amount with the calculated operation amount. do. The extreme value control is a control method that searches for the optimum value of the evaluation function by repeating such observation of the evaluation amount and updating of the manipulated variable.

An evaluation function curve EV in FIG. 1A represents an unknown evaluation function with respect to the manipulated variable. Here, for convenience of explanation, the unknown evaluation function is assumed to be a downwardly convex quadratic function. FIG. 1(B) shows a case where an evaluation amount opposite in phase to the phase of the dither signal is obtained when the manipulated variable is changed with the dither signal for the process to be controlled having such an evaluation function. In this case, since the evaluation amount decreases as the operation amount increases, it can be seen that the operating point has changed to the left of the minimum point Pmin of the evaluation function curve EV. On the other hand, FIG. 1(C) shows a case where an evaluation amount having the same phase as the dither signal is obtained for a dither signal similar to that of FIG. 1(B). In this case, since the evaluation amount also increases with an increase in the manipulated variable, it can be seen that the operating point has changed to the right of the minimum point Pmin.

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 variable is decreased. By increasing the evaluation amount, the evaluation amount can be brought closer 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 system that controls the manipulated variable so that the controlled variable follows a preset target value. It was a mold control method. On the other hand, since extreme value control is an optimum value search type control method that searches for an operation amount that optimizes the evaluation amount, it expresses the relationship between the operation amount and the control amount like PID control. No process model is required in advance. Therefore, extreme value control is an effective control method even for a controlled process for which a target value cannot be set in advance, and has the potential to become widely used in the future. An extreme value control controller that performs extreme value control based on such a principle can be realized with a relatively simple configuration.

FIG. 2 is a block diagram showing a basic configuration example of an extreme value control system 9 that implements extreme value control. The extremum control system 9 (extremum control unit) in FIG. Prepare. Thus, the configuration of the extreme value control system 9 is as complicated as a conventional PID controller. Therefore, the extreme value control system 9 can be easily implemented using hardware such as a PLC (Programmable Logic Controller), like the PID controller. An outline of the operation of the extreme value control system 9 of FIG. 2 will be described below. Here, an example of searching for the minimum value of the evaluation function as the optimum value will be described.

The extremum control system 9 forcibly changes the manipulated variable of the controlled process TP by applying a dither signal M (M means Modulation) having periodic changes. This operation is hereinafter referred to as modulation. Due to this modulation, the manipulated variable of the controlled process TP changes periodically, and the controlled variable changes according to the change in the manipulated variable. The controlled process TP acquires an evaluation amount based on the control amount, and feeds back the acquired evaluation amount to the extreme value control system 9 .

It should be noted that the function of acquiring the evaluation amount based on the control amount (hereinafter referred to as the "evaluation amount acquisition function") does not necessarily have to be included in the controlled process TP. For example, the evaluation value acquisition function may be included in the extreme value control system 9, or another device having the evaluation value acquisition function may be interposed between the controlled process TP and the extreme value control system 9.

Normally, the change in the evaluation amount with respect to the change in the manipulated variable appears with some time delay. As described above, extreme value control is a control method for searching for extreme values of unknown evaluation functions with respect to manipulated variables. Therefore, it is assumed that the evaluation function of the controlled process TP has a minimum value, but the value is unknown with respect to the manipulated variable.

A high-pass filter 11 removes a constant bias corresponding to an unknown minimum value from the feedback evaluation quantity. This processing is processing for always adjusting an unknown minimum value to zero, and is preprocessing necessary for determining the direction of change (increase or decrease) given by the estimator 14 to the manipulated variable. .

The dither signal output unit 12 applies a dither signal D (D means demodulation) to the evaluation amount thus adjusted. As a result, the same frequency component as the dither signal M is extracted from the evaluation amount changed according to the modulation of the manipulated variable. This operation is hereinafter referred to as demodulation. The role of demodulation is as follows.

As described above, the evaluation function for the manipulated variable of the controlled process TP is unknown. Therefore, the evaluation function may contain nonlinear elements. In this case, the evaluation function is assumed to be a downwardly convex (or upwardly convex in case of local maximum search) nonlinear function. Due to such non-linear elements, there is a high possibility that harmonic components and subharmonic components corresponding to the frequency ω of the dither signal M appear in the evaluation quantity. Demodulation is processing for removing the effects of such harmonics and subharmonics. By this demodulation, among the components included in the evaluation amount, the component with the same frequency ω as that of the dither signal M whose evaluation amount is changed is extracted.

The demodulated evaluation quantity is input to the low-pass filter 13 . A low-pass filter 13 extracts a stationary component (low-frequency component) from the evaluation quantity. The stationary component is considered to represent whether the evaluation amount has changed in the increasing direction or the decreasing direction due to the application of the dither signal M. FIG.

The estimator 14 is an integrator that integrates stationary components extracted by the low-pass filter 13 . The estimator 14 functions as an estimator for estimating the direction of the manipulated variable (hereinafter referred to as "manipulated direction") to move the evaluated quantity closer to the minimum value based on the integral value of the stationary component. Such an operation direction estimation method is based on the most basic gradient method as an operation direction estimation method in an adaptive control system. When the estimator 14 determines the operation direction (hereinafter also referred to as "gradient"), the operation amount is adjusted according to the gradient so that the evaluation amount approaches the minimum value. The manipulated variable adjusted in this way is again applied with a dither signal and input to the controlled process TP.

Here, an example of the configuration of the extreme value control system 9 has been described assuming a case of searching for a local minimum value. Just do it.

Also, since an integrator generally has a low-pass characteristic, the extremal value control system 9 need not include the low-pass filter 13 if the estimator 14 has a sufficiently low-pass characteristic. For simplicity, the estimator 14 will be described below as having sufficient low-pass characteristics and including the function of the low-pass filter 13 .

The optimum control device of the embodiment described below is configured using the above-described extreme value control system 9 and functions as a device that controls the controlled process by extreme value control. The optimum control device of the embodiment can be applied to control any process that outputs a controlled variable in response to an input of a manipulated variable. For example, the controlled process may be a sewage treatment process, a combustion process, a petrochemical process, or the like. Hereinafter, the details of the optimal control device of the embodiment will be described by appropriately taking the biological wastewater treatment process as an example.

(First embodiment)
FIG. 3 is a block diagram showing a specific example of the functional configuration of the optimum control device 2 in the first embodiment. A plant P shown in FIG. 3 is an example of means for realizing a process to be controlled, and is, for example, a water treatment plant for realizing a biological wastewater treatment process. The plant P includes various equipment for realizing the controlled process, and operates the various equipment based on the manipulated variables given by the optimum control device 2 . In addition, the plant P includes various measuring instruments for measuring the response of the controlled process to the manipulated variable (that is, the controlled variable), and the measurement data acquired by the measuring instrument is used as information indicating the controlled variable of the controlled process (hereinafter referred to as " (referred to as "measurement information") to the optimum control device 2. Based on the measurement information acquired from the controlled process, the optimum control device 2 updates the manipulated variable in such an operating direction that the evaluation amount of the controlled process approaches the optimum value. Such operations are realized by the optimum control device 2 having the following configuration.

The optimum control device 2 includes a CPU (Central Processing Unit), a memory, an auxiliary storage device, etc. connected via a bus, and executes an extremum control program. Optimum control device 2 executes dither signal output unit 21, manipulated variable output unit 22, measurement information acquisition unit 23, evaluation amount calculation unit 24, gradient estimation unit 25, parameter determination unit 26, and extreme value control by executing the extreme value control program. It functions as a device having a portion 27 . All or part of each function of the optimum control device 2 may be realized using hardware such as an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), or an FPGA (Field Programmable Gate Array). . The control program may be recorded on a computer-readable recording medium. Computer-readable recording media include portable media such as flexible disks, magneto-optical disks, ROMs and CD-ROMs, and storage devices such as hard disks incorporated in computer systems. A control program may be transmitted via an electric communication line.

The dither signal output section 21 generates a dither signal and outputs the generated dither signal to the extreme value control section 27 . Specifically, the dither signal output unit 21 generates a dither signal M for modulation of the manipulated variable and a dither signal D for demodulation of the evaluation amount.

The manipulated variable output unit 22 and the measurement information acquisition unit 23 are configured including a communication interface that connects the optimum control device 2 and the plant P so as to be able to communicate with each other. The manipulated variable output unit 22 transmits to the plant P the manipulated variable output from the extreme value control unit 27 . The measurement information acquisition unit 23 also acquires measurement information from the plant P, and outputs the control amount indicated by the acquired measurement information to the evaluation amount calculation unit 24 .

The evaluation amount calculator 24 calculates an evaluation amount used for extreme value control based on the control amount output from the measurement information acquisition unit 23 . The evaluation amount calculator 24 outputs the calculated evaluation amount to the gradient estimator 25 and the extreme value controller 27 .

The gradient estimator 25 estimates the gradient of the evaluation function based on the evaluation quantity output from the evaluation quantity calculator 24 . Specifically, the gradient estimating unit 25 estimates gradients (that is, differential values) from the first order to the Nth order (where N is an integer equal to or greater than 1) with respect to the manipulated variable, based on changes in the evaluation amounts that are sequentially acquired. . Here, as an example, a case of estimating a first-order differential value will be described. Here, the control cycle of the optimum control device 2 is T, and the time at which control is performed for each control cycle T is called control time. In this case, the gradient estimating unit 25 calculates the difference between the evaluation amount J(t) at a certain control time t and the evaluation amount J(tT) at the control time tT one control cycle earlier, at both times. By dividing by the difference between the manipulated variables U(t) and U(tT), it is possible to obtain an approximate value of the first derivative of the evaluated quantity with respect to the manipulated variable. That is, the first order differential value dJ/dU of the evaluation quantity is approximated by the following equation (1).

Formula (1) shows the simplest example of a method of obtaining the differential value of the evaluation quantity. It is susceptible to noise due to measured or calculated values of In addition, when obtaining a high-order differential value of the second order or higher, the influence of noise increases, and there is a high possibility that the gradient cannot be estimated substantially. Regarding such a problem, the following documents propose a method of estimating the gradient with higher accuracy, focusing on the fact that the dither signal is usually given as a sine wave.

Non-Patent Document 1 describes a gradient estimation method using a filter, and Non-Patent Document 2 describes a gradient estimation method using the observer concept. In this embodiment, the gradient estimator 25 preferably estimates the gradient of the evaluation function based on such conventional technology. Here, the basic idea of the gradient estimation method described in Non-Patent Document 1 will be described.

In general, the manipulated variable may include harmonic components and subharmonic components, but when the dither signal is given as a sine wave, the manipulated variable changes sinusoidally at approximately the same frequency as the dither signal. Therefore, it is assumed that the manipulated variable U changes sinusoidally as U(t)=U ₀ +a×sinωt, and that the evaluation value obtained by this change is represented by the evaluation function J shown in the following equation (2). .

where f is an unknown function. In practice, f contains the dynamics of the plant, so rather f should be considered the operator of the dynamic system. However, if the frequency ω of the dither signal provides a sufficiently gradual change in the dynamics of the plant, then f can be approximated as a function. Under this premise, f is regarded as a function here. The following equation (3) is obtained by Taylor-expanding this equation (2).

Here, D ^k f (where k is an integer equal to or greater than 1) means the k-th differential of the function f with respect to U. The following equation (4) is obtained by multiplying this equation (3) by sin ⁿ ωt (where n is an integer of 1 or more).

Here, the following equation (5) is obtained by performing the periodic averaging process on the equation (4).

Here, A ₀ is defined by the following equation (6).

Focusing on the fact that the amplitude a and the exponent n of the dither signal are constants, it is assumed that the value of the ⁿ -th order differential Dnf does not change significantly in one control cycle, and µn is _given by the following equation (7): Defined.

Subsequently, by defining the following equations (8) and (9) and using the relationship of the equation (5), the differentials D ⁰ f to D ⁿ f from 0 to nth order are as shown in the following equation (10) is represented by

Here, _An is defined by the following equation (11).

Therefore, by using equation (10), it is possible to estimate the n-th order differential value (or the 0th to n-th order differential values) of any order. Furthermore, Non-Patent Document 1 describes a method of estimating the n-th order differential value with some modifications along with such a basic idea.

FIG. 4 is a diagram showing a specific example of a method of estimating the n-order differential value in the first embodiment. In FIG. 4, G(t) is defined by the following equation (12).

Here, X(t) is a vector signal in which x ₁ (t) to x _n (t) in FIG. 4 are arranged. That is, equation (12) can be considered as approximating (substituting) the signals defined by equations (5) and (8) with X(t) shown in FIG.

Thus, the gradient of the evaluation function J can be estimated by the gradient estimator G(t) using a filter. The optimum control device 2 of the present embodiment determines control parameters for extreme value control based on the estimated value of the gradient estimated using such a method. The gradient estimating section 25 outputs the gradient estimated value obtained in this manner to the parameter determining section 26 .

Returning to the description of FIG. The parameter determining unit 26 determines control parameters for extreme value control based on the gradient estimation value of the evaluation function acquired by the gradient estimating unit 25 . More specifically, the parameter determination unit 26 determines five control parameters: low-pass filter frequency, high-pass filter frequency, dither signal frequency, dither signal amplitude, and integral gain.

FIG. 5 is a diagram illustrating an example of a control parameter determination method according to the first embodiment. Specifically, FIG. 5 shows the control parameter adjustment rule described in Patent Document 1. As shown in FIG. This adjustment rule is basically assumed to be used when determining control parameters in the design stage before applying extreme value control to the control of the controlled process. That is, Patent Document 1 does not assume that the control parameters determined based on this adjustment rule are changed after the application of the extreme value control.

In the optimum control device 2 of this embodiment, the parameter determination unit 26 selects No. 1 shown in FIG. 5 for parameters other than the integral gain among the five parameters shown in FIG. 1 to No. 4 based on each adjustment rule. On the other hand, the parameter determining unit 26 adaptively determines the integral gain according to the state of the controlled process based on the gradient estimation value obtained by the gradient estimating unit 25, and reflects it in the extreme value control. A method of determining the integral gain will be described later.

Returning to the description of FIG. The extreme value control unit 27 performs extreme value control of the controlled process using the control parameters determined by the parameter determination unit 26 . Specifically, first, the extremum control unit 27 applies a dither signal to the manipulated variable given to the plant P, and observes the evaluation quantity that changes accordingly. Based on the observed value of the evaluation amount, the extreme value control unit 27 updates the operation amount so that the evaluation amount approaches the optimum value. The extreme value control unit 27 repeatedly applies the dither signal, observes the evaluation amount, and updates the manipulated variable, thereby bringing the evaluation amount of the controlled process closer to the optimum value.

FIG. 6 is a block diagram showing a configuration example of the extreme value control system 1 realized by the optimum control device 2 of the first embodiment. The extreme value control system 1 differs from the extreme value control system 9 having the basic configuration shown in FIG. This is the point at which it works. Specifically, the integral gain KI calculated by the parameter determination unit 26 (not shown) based on the gradient estimation value is adaptively reflected in the estimator 14 . As a result, the optimum control device 2 can adapt to the dynamics of the process to be controlled and operate the extreme value control more stably. The details of the method of determining the integral gain will be described later.

The extreme value control system 1 shown in FIG. 6 functions as the dither signal output section 21 and the extreme value control section 27 of the optimum control device 2 shown in FIG. Also, the extreme value control system 1 may be configured to include the manipulated variable output section 22 , the measurement information acquisition section 23 and the evaluation amount calculation section 24 .

FIG. 7 is a diagram showing a specific example of a water treatment plant 3 that implements a biological wastewater treatment process, as an example of the plant P in the first embodiment. For example, the water treatment plant 3 shown in FIG. The anaerobic tank 31 is equipment for activating microorganisms. The anoxic tank 32 is equipment for removing nitrogen. The aerobic tank 33 is equipment for decomposing organic matter, removing phosphorus, and nitrifying ammonia. The final sedimentation tank 34 is equipment for precipitating the activated sludge.

The water treatment plant 3 is equipped with equipment such as pumps for conveying water and sludge between the above equipment, blowers for supplying air to tanks, and sensors for measuring concentrations of substances in the air or water. The chemical feed pump 311 is a pump that feeds a chemical such as a carbon source for activating microorganisms into the anaerobic tank 31 . The circulation pump 331 is a pump that controls the amount of water to be treated that circulates between the aerobic tank 33 and the anoxic tank 32 . The blower 332 supplies air to the aerobic tank 33 to control the amount of aeration. The return sludge pump 341 is a pump that returns sludge from the final sedimentation basin 34 to the anoxic tank 32 . The excess sludge extraction pump 342 is a pump that extracts excess sludge from the final sedimentation tank 34 . A sensor 312 and a sensor 343 measure the water quality of the effluent in the anaerobic tank 31 and the final sedimentation tank 34, 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 effluent (hereinafter referred to as "effluent nitrogen concentration" and "effluent phosphorus concentration", respectively). concentration”). The return rate is obtained by dividing the discharge rate of the return sludge pump 341 by the inflow rate. The effluent nitrogen concentration and the effluent phosphorus concentration are obtained by sensors 312 and 343 . The amount of control may be the amount of nitrogen and phosphorus contained in the discharged water (hereinafter referred to as the "discharged nitrogen amount" and the "discharged phosphorus amount", respectively). In this case, the effluent nitrogen amount and the effluent phosphorus amount are obtained by multiplying the effluent nitrogen concentration and the effluent phosphorus concentration by the effluent amount, respectively.

An evaluation function for obtaining an evaluation amount based on the control amount output from the water treatment plant 3 is preset in the evaluation amount calculation unit 24 . The evaluation function here is defined as an unknown evaluation function for the manipulated variable as a function of the controlled variable. For example, the evaluation function is a function representing the relationship between the effluent nitrogen concentration and the effluent phosphorus concentration and the evaluation amount. This evaluation function must be set so as to take an extreme value between the controlled variable at the upper limit of the manipulated variable (return rate) and the controlled variable at the lower limit of the manipulated variable. As an example of the method of setting the evaluation function in this way, there is a method of expressing the evaluation amount as the sum of the water quality cost based on the concept of the wastewater levy and the power cost of the return sludge pump 341 (hereinafter referred to as "total cost"). Conceivable. The power cost of the return sludge pump 341 can be calculated from the return sludge flow rate, the rated power of the return sludge pump 341, and the like. In general, in the concept of wastewater levy, the water quality cost is expressed by the following formula.

In formula (13), COD means chemical oxygen demand, BOD means biochemical oxygen demand, TN means effluent nitrogen, and TP means effluent phosphorus. The conversion factor for each cost may be determined based on the actual waste water charge, or may be determined by other methods. Generally, among COD, BOD, TN and TP, it is known that TN and TP are greatly changed by changing the return rate. Therefore, here, the water quality cost is represented by the following equation (14).

It is generally known that increasing the return rate increases the nitrogen removal rate and reduces the water quality cost related to TN, and conversely, decreasing the return rate increases the phosphorus removal rate and reduces the water quality cost related to TP. In such a case, the evaluation function may be set based only on the water quality cost. However, when the cost of water quality that does not have such a trade-off relationship is used as an index, by expressing the evaluation amount as a total cost that takes into account the operation cost (electricity cost), the evaluation function can be expressed as the operation amount (Return rate) Set so as to take an extreme value between the controlled variable at the upper limit and the controlled variable at the manipulated variable lower limit.

Moreover, instead of such a total cost, a function that directly expresses the evaluation of water quality may be set as the evaluation function. For example, the evaluation amount may be calculated as in Equation (15) below.

In Equation (15), TN _lim and TP _lim are parameters that represent threshold levels corresponding to regulation values and management values for effluent water quality. When such an evaluation function is used, the evaluation amount rises sharply when the threshold level is exceeded. Therefore, it can be expected that extremal value control functions so as to keep the evaluation quantity within the threshold level.

The method of setting the evaluation function required for extreme value control has been described above using the water treatment plant 3 as shown in FIG. 4 as an example. In some cases. One such example is the control of wind turbine blades in wind power plants. When extreme value control is applied to control that maximizes power generation by moving the direction of the wind turbine blades in accordance with the wind direction, the evaluation amount is the power generation amount, and the operation amount is the rotation angle of the wind turbine blades. . In this case, it is not necessary to set an evaluation function because the control amount becomes the evaluation amount as it is. In such a case, the evaluation amount calculation unit 24 may not be provided. On the other hand, it may be possible to apply extremum control by obtaining an evaluation quantity.

[Determination method of integral gain]
The method by which the parameter determination unit 26 determines the integral gain based on the gradient estimate will be described below. The above adjustment rule proposed in Patent Document 1 is based on the average system described in Non-Patent Document 3. An average system is a system that expresses the dynamic behavior of a system that takes the periodic average (average) when a periodic input is applied to a system, and is used for stability analysis of extreme control systems. .

In particular, Non-Patent Document 3 specifically describes an averaging system of an extreme value control system that controls a static plant without dynamics. The average system is represented by the following equation (16).

where DJ represents the slope of the input of the evaluation function J with respect to the periodic mean UU _* . U _* is the equilibrium point of U. τ is a scaled function of time at the frequency ω of the dither signal and is a value represented by the following equation (17).

KI ₀ is the integral gain on the time axis τ, and the actual integral gain KI on the time axis t is converted by the following equation (18).

Note that P in Equation (16) represents the power of the dither signal. As described in Non-Patent Document 3, when using a sine wave as a dither signal, P=1/2, when using a triangular wave, P=1/3, and when using a square wave, P=1. is. In the average system shown by equation (16), when the evaluation amount converges to the minimum value (minimum value) while the operation amount is periodically oscillated by the dither signal, how does the evaluation amount oscillate periodically? It expresses the dynamics of convergence of extremum control that the minimum value (minimum value) converges at a high speed.

In Non-Patent Document 3, it is assumed that the plant is static, and the period of the dither signal is set sufficiently longer than the time constant of the plant. This is the case when the frequency ω of the dither signal is set sufficiently lower than the cutoff frequency 2π/ω of the plant. In such cases, even though the plant has dynamics, it can be considered to be approximately static. This is supported by the singular perturbation theory used in the stability analysis of extremal control. Therefore, here we show how to determine the integral gain using the average system of equation (16) under the assumption that the frequency ω of the dither signal is set appropriately.

Equation (16) shows the behavior of the extremal control system on the time axis τ=ωt scaled by the frequency of the dither signal. It is thought that it corresponds to the time constant on the time axis τ until . Therefore, if the parameters ω, a, and _KI0 are determined so that the time constant T _ave of the average system represented by Equation (16) is sufficiently longer than the dither signal period T=2π/ω, the evaluation amount is dither It is expected to gradually converge to the minimum value (minimum value) according to the increase/decrease of the manipulated variable by the signal.

Here, since the frequency ω and the amplitude a of the dither signal are determined based on the adjustment rule of FIG. will adjust KI ₀ . However, since Equation (16) is generally a nonlinear differential equation, the concept of time constant cannot be defined directly. Therefore, Patent Document 1 proposes an adjustment rule for determining a control parameter by defining a time constant under the assumption that the evaluation function J is a quadratic function. For example, assume that the evaluation function J(t) is represented by the following equation (19).

In this case, DJ(U+U _* )=G×U(t), so equation (14) is expressed as the following equation (20).

The time constant T _ave of Equation (20) is 1/(KI ₀ ×a×P×G). This _Tave is a time constant on the time axis τ, and τ=1 is the time corresponding to 1/ω. Therefore, the value of KI ₀ can be determined by determining how many times the period 2π/ω of the dither signal should be set for the time corresponding to the time constant T _ave . Here, since the time constant of the average system needs to be adjusted to be sufficiently longer than the period of the dither signal, for example, the time corresponding to the time constant is set to k3 (=5 to 10) of the period of the dither signal. ). In this case, k3×2π=1/(KI ₀ ×a×P×G) holds, so KI ₀ is determined by the following equation (21).

Patent Literature 1 proposes an adjustment rule for the integral gain as described above, but this adjustment rule is based on the assumption that the evaluation function J(t) is a quadratic function as described above. However, one can hardly expect real-life problems to lie within such assumptions. On the other hand, Patent Document 1 proposes a method of converting the evaluation function so that it can be approximated by a quadratic function. should be clarified to some extent. Acquisition of such a relationship requires observation of several operating points of the controlled process, which requires a large engineering cost.

To address this problem, the present embodiment focuses on the fact that G in equations (19) and (21) is the second-order differential value of the evaluation function, and the parameter determination unit 26 uses the second-order Applying the derivative estimate to equation (21) determines the integral gain. Note that G is a constant when the evaluation function J(t) is a quadratic function, but in most real problems the evaluation function J(t) is not a quadratic function. When the evaluation function J(t) is not a quadratic function in this way, G is a function that changes with time. Therefore, in this case, the integral gain is represented by the following equation (22).

In Equation (19), G(t) is the second order differential value with respect to the manipulated variable of the evaluation function estimated by the gradient estimator 25 . Equation (19) expresses that the integral gain becomes a function of time t by the second-order differential value G(t) at time t. That is, the parameter determining unit 26 can update the integral gain by applying the sequentially acquired gradient estimation values to Equation (22), adapting to the dynamics of the controlled process that changes over time.

FIG. 8 is a flow chart showing the flow of processing in which the optimum control device 2 according to the first embodiment controls the process to be controlled by extreme value control. It is assumed that the controlled process of the plant P is controlled by a control method other than extreme value control such as PID control at the start of the flowchart. First, the measurement information acquisition unit 23 acquires measurement information from the plant P (step S101). The measurement information acquisition unit 23 outputs the control amount indicated by the measurement information to the evaluation amount calculation unit 24 .

The evaluation amount calculation unit 24 calculates the evaluation amount of the controlled process at that time based on the control amount output from the measurement information acquisition unit 23 (step S102). The evaluation amount calculator 24 outputs the calculated evaluation amount to the gradient estimator 25 and the extreme value controller 27 .

The gradient estimation unit 25 estimates the gradient of the evaluation function based on the evaluation amount output from the evaluation amount calculation unit 24 (step S103). The gradient estimator 25 outputs the obtained gradient estimate to the parameter determiner 26 .

The parameter determining unit 26 determines the control parameters based on the slope estimation value output from the slope estimating unit 25 and a predetermined control parameter adjustment rule (step S104). Specifically, the parameter determining unit 26 uses No. 1 in FIG. 1 to No. 4, the frequency ω ₁ of the high-pass filter 11, the frequency ω and amplitude a of the dither signal output from the dither signal output unit 12, and the frequency ω ₂ of the low-pass filter 13 are determined. Information necessary for determining these control parameters according to the adjustment rule shown in FIG. It may be stored in the optimum control device 2 .

On the other hand, the parameter determination unit 26 determines the integral gain KI ₀ by applying the slope estimation value output from the slope estimation unit 25 to Equation (22). The parameter determination unit 26 outputs the control parameter values thus determined to the extreme value control unit 27 .

Subsequently, the extreme value control unit 27 starts extreme value control of the controlled process using each control parameter determined by the parameter determination unit 26 (step S105). Here, it is assumed that the control method for the controlled process is switched to extreme value control at a predetermined timing after the control parameters are determined by the parameter determining unit 26 . This timing may be a predetermined timing or an arbitrary timing by user's operation.

After the extreme value control unit 27 starts extreme value control, the optimum control device 2 repeatedly executes the same processes as steps S101, S102 and S103 (steps S106, S107 and S108), and performs the same method as step S104. to acquire the value of the integral gain (step S109). Then, the parameter determining unit 26 updates the current integral gain value with the acquired integral gain value (step S110).

The optimal control device 2 of the first embodiment configured as described above estimates the gradient of the evaluation function based on the obtained measurement information, and adaptively determines the integral gain based on the obtained estimated gradient value. It has the function to According to such an optimum control device 2, since the integral gain, which is greatly related to the stability of the extreme value control, can be adaptively updated according to the state of the controlled process, it can adapt to the dynamics of the controlled process. Therefore, it becomes possible to operate the extreme value control more stably.

According to the optimum control device 2 that can adjust the control parameters in this way, for example, the total cost is minimized while adapting to the dynamics of the water treatment process, using the amount of sludge returned in the water treatment plant of FIG. 7 as the operation amount. It is possible to realize such extreme value control.

(Second embodiment)
FIG. 9 is a block diagram showing a specific example of the functional configuration of the optimum control device 2a in the second embodiment. The optimum control device 2a is different from the first embodiment in that it includes a gradient estimator 25a instead of the gradient estimator 25, a parameter determiner 26a instead of the parameter determiner 26, and a manipulated variable converter 28. It differs from the optimum control device 2 in form. Other configurations of the optimum control device 2a are the same as those of the optimum control device 2 in the first embodiment. Therefore, here, the same reference numerals as in FIG. 3 are assigned to those similar configurations, and the description thereof is omitted.

The gradient estimating unit 25a is similar to the gradient estimating unit 25 in the first embodiment in that it estimates the gradient of the evaluation function based on the acquired evaluation amount, but the gradient of the evaluation function is not the second derivative value but the linear value. It differs from the gradient estimating section 25 in that it estimates the differential value and outputs the acquired gradient estimated value to the manipulated variable converting section 28 instead of the parameter determining section 26a.

The parameter determination unit 26a is the same as the parameter determination unit 26 in the first embodiment in that it determines five control parameters: low-pass filter frequency, high-pass filter frequency, dither signal frequency, dither signal amplitude, and integral gain. However, it is different from the parameter determining section 26 in that the slope estimation value of the evaluation function is not used to determine the integral gain.

The manipulated variable conversion unit 28 converts the manipulated variable outputted from the extreme value control unit 27 based on the gradient estimated value of the evaluation function outputted from the gradient estimating unit 25a. The manipulated variable conversion unit 28 outputs the converted manipulated variable to the manipulated variable output unit 22 . Specifically, the manipulated variable conversion unit 28 converts the manipulated variable by the following method.

First, assuming that the manipulated variable output from the extreme value control unit 27 is U, the average system for the extreme value control when U is the input (manipulated variable) is expressed by the above equation (16). Equation (16) is re-cited below as Equation (23).

In equation (23), the gradient DJ (U+U _* ) of the evaluation function is generally a nonlinear function with respect to U, so the speed of convergence in equation (23) could not be expressed by the concept of time constant. . Therefore, in the first embodiment, first, the concept of the time constant is defined on the assumption that the evaluation function J(U) is represented by a quadratic function, and the defined time constant is set to a desired value. The integral gain KI ₀ was determined. However, since the evaluation function J(U) is not actually a quadratic function, the integral gain KI ₀ is adaptively adjusted so that the second derivative value is constant.

On the other hand, in this embodiment, the time constant is defined by transforming the input variable U so that the average system expressed by Equation (23) becomes a linear system. That is, the variable conversion shown in the following equation (24) is performed so that the average system for the variable v after conversion becomes a linear system. By this variable transformation, the average system for the variable v is transformed as shown in the following equation (25).

Here, the function v=h(U) for converting equation (23) to equation (25) must satisfy the partial differential equation shown in equation (26) below.

There are many transformation functions h that satisfy this condition, but if the first derivative value DJ(U) of the evaluation function is known, any differential equation can be solved at least approximately. . For example, Equation (26) can be approximated by Equation (27) below.

Using equation (27) approximated in this way, for example, if an appropriate transformation v ₀ =h (U ₀ ) can be given to the initial value of the manipulated variable U ₀ , the change in the manipulated variable by extreme value control h(U) can be updated accordingly. The manipulated variable conversion unit 28 can convert the manipulated variable by applying the gradient estimated value (first order differential value) acquired by the gradient estimating unit 25a to Equation (27).

Further, regarding the initial value v ₀ of the variable v, when DJ(U) can be approximated by a linear function of U, the following formula (28) is used to approximate the formula (22). be able to.

Equation (25) corresponds to the average system represented by Equation (20) in which the second-order differential value G of the evaluation function is set to G=1. Therefore, the integral gain may be calculated by setting G in Equation (22) to G=1.

FIG. 10 is a block diagram showing a configuration example of an extreme value control system 1a realized by the optimum control device 2a of the second embodiment. The extreme value control system 1a differs from the extreme value control system 9 having the basic configuration shown in FIG. () ⁿ ) adaptively acts on the manipulated variable given to the controlled process TP. Specifically, the manipulated variable converted by the manipulated variable converter 28 (not shown) based on the estimated gradient value is given to the controlled process TP. As a result, the optimum controller 2a can adapt to the dynamics of the process to be controlled and operate the extreme value control more stably, like the optimum controller 2 of the first embodiment.

Furthermore, in the second embodiment, it is sufficient to obtain the first derivative of the evaluation function as the gradient estimation value, so that the extreme value control processing can be made simpler than in the first embodiment in which the second derivative is obtained. can be done. Specifically, in estimating a gradient using a filter such as that shown in FIG. 4, the number of filter stages can be reduced. can do. This also means that G(t) after the filter can be realized in smaller dimensions.

On the other hand, in the second embodiment, it may take some time and effort to appropriately set the initial value when converting the manipulated variable. Therefore, which embodiment should be used should be selected according to the characteristics, restrictions, etc. of the target process to be applied.

(Third embodiment)
FIG. 11 is a block diagram showing a specific example of the functional configuration of the optimum control device 2b in the third embodiment. The optimum control device 2b includes an evaluation amount calculation unit 24b instead of the evaluation amount calculation unit 24, a gradient estimation unit 25b instead of the gradient estimation unit 25, and a parameter determination unit 26b instead of the parameter determination unit 26. It differs from the optimum control device 2 in the first embodiment in that it further includes an evaluation amount conversion unit 29 . Other configurations of the optimum control device 2b are the same as those of the optimum control device 2 in the first embodiment. Therefore, here, the same reference numerals as in FIG. 3 are assigned to those similar configurations, and the description thereof is omitted.

The evaluation amount calculation unit 24b is similar to the evaluation amount calculation unit 24b in the first embodiment in that it calculates an evaluation amount used for extreme value control based on the control amount output from the measurement information acquisition unit 23. , differs from the evaluation amount calculation unit 24 in that the calculated evaluation amount is output to the gradient estimation unit 25 b and the evaluation amount conversion unit 29 .

The gradient estimating unit 25b is similar to the gradient estimating unit 25 in the first embodiment in that it estimates the gradient of the evaluation function based on the obtained evaluation amount. It is different from the gradient estimating unit 25 in that it is output to the evaluation amount conversion unit 29 .

The evaluation amount conversion unit 29 converts the evaluation amount output from the evaluation amount calculation unit 24b based on the gradient estimated value of the evaluation function output from the gradient estimation unit 25b. The evaluation amount conversion unit 29 outputs the converted evaluation amount to the extreme value control unit 27 . Specifically, the evaluation amount conversion unit 29 converts the evaluation amount by the following method.

FIG. 12 is a diagram showing an example of a method of estimating the n-order differential value in the third embodiment. First, a conversion function for converting the evaluation amount is determined in advance for the evaluation amount conversion unit 29 . Here, for the sake of simplification, the evaluation function J is converted to a power, and the converted evaluation function J is locally approximated by a quadratic function. Here, J _m can be expressed as J _m =T(J)=J ⁿ , where J _m is the evaluation function after conversion, and n is the exponent used for conversion (hereinafter referred to as "power parameter"). This power parameter n can be estimated as follows.

When converting J _m =J ⁿ , the gradient of J with respect to the manipulated variable U is also converted by the same conversion function, so D ² J _m =(D ² J) ⁿ . At this time, if the power parameter n is determined so that D ² J _m is a constant value, the second derivative value of the evaluation function after conversion will be a constant value, so the evaluation amount after conversion is approximated by a quadratic function. can be considered to have been Therefore, the evaluation amount conversion unit 29 calculates the power parameter n by calculating a power such that the second-order differential value of the evaluation function obtained based on the input evaluation amount is a predetermined constant C=1. to estimate FIG. 12 is a conceptual diagram showing the configuration of such an evaluation amount conversion unit 29. As shown in FIG.

Specifically, the evaluation amount conversion unit 29 includes an estimator 291 and a conversion unit 292 . The estimator 291 searches for a power n that satisfies the transformation function D ² J _m =(D ² J) ⁿ using the constant C=1 as the target value of the second derivative of the evaluation function, and uses the search result as the final power It is output to the conversion unit 292 as the value of the power parameter. The conversion unit 292 converts the evaluation amount J by applying the power parameter n estimated by the estimator 291 to the conversion function of the evaluation amount. The conversion unit 292 outputs the converted evaluation amount J _m to the extreme value control unit 27 .

For example, if the power parameter is estimated by a method such as the method of steepest descent, the estimator 291 can be constructed using an integrator. Also, the estimator 291 regards the power parameter n as a virtual manipulated variable, and sets the error between the constant C=1, which is the target value, and the second-order differential value D ² J _m =(D ² J) ⁿ to zero. It may be configured using a PID controller such as

Here, the case where the gradient estimating unit 25b estimates the second-order differential value has been described, but when the gradient estimating unit 25b estimates the first-order differential value, the evaluation amount conversion unit 29 calculates the gradient estimated value may be configured to transform the evaluation quantity so that is proportional to the manipulated variable.

However, when the target value of the estimator 291 is set to a constant C=1, the integral gain is determined by assuming that the gradient G (second derivative value) of the evaluation function is G=1 in the adjustment rule shown in FIG. . If the target value of estimator 291 is constant C=G, then the value of constant C is used to determine the integral gain.

Returning to the description of FIG. The parameter determination unit 26b is the same as the parameter determination unit 26 in the first embodiment in that it determines five control parameters: low-pass filter frequency, high-pass filter frequency, dither signal frequency, dither signal amplitude, and integral gain. However, it is different from the parameter determining section 26 in that the slope estimation value of the evaluation function is not used to determine the integral gain.

FIG. 13 is a block diagram showing a configuration example of an extreme value control system 1b realized by the optimum control device 2b of the third embodiment. The difference between the extreme value control system 1b and the extreme value control system 9 having the basic configuration shown in FIG. adaptively acts on the evaluation amount obtained based on the control amount of the controlled process TP. Specifically, the evaluation amount converted by the evaluation amount conversion unit 29 (not shown) based on the gradient estimated value is input to the extreme value control system 1b. As a result, the optimum controller 2b can adapt to the dynamics of the process to be controlled and operate the extreme value control more stably, like the optimum controller 2 of the first embodiment.

FIG. 14 is a diagram showing a specific example of effects obtained by the optimum control devices of the first to third embodiments. FIG. 14(A) assumes that the shape of the unknown evaluation function is actually a quadratic function, a cubic function, and a 0.5th order function, and performs extreme value control based on the control parameters adjusted by the conventional adjustment rule. A simulation result is shown. Further, FIG. 14B shows the result of simulating extreme value control based on the control parameters adjusted by the adjustment method of the present embodiment under the same assumption. Specifically, in the simulation of FIG. 14A, the control parameters were adjusted based on the adjustment rule described in Patent Document 1. As can be seen from FIG. 14A, in the conventional adjustment method, the extremum search is successful when the shape of the evaluation function is a quadratic function or a cubic function. In the case of the 0.5th order function, the search performance is remarkably degraded. On the other hand, as can be seen from FIG. 14B, the adjustment method of the present embodiment succeeds in searching for extreme values regardless of the shape of the evaluation function.

In actual extreme value control, the shape of the evaluation function to be optimized cannot be known in advance. Therefore, in the conventional control parameter adjustment method, the search performance for extreme values (local optimum values) changes depending on the shape of the evaluation function, and in the worst case, the control may become unstable. there were. In contrast, according to the control parameter adjustment method of the present embodiment, it is possible to always stably search for the extreme value regardless of the shape of the evaluation function.

(Modification)
The optimum control device 2 of the first embodiment associates gradient information indicating the gradient of the evaluation function estimated by the gradient estimator 25 with manipulated variable information indicating the manipulated variable determined by the extreme value controller 27. Then, a display control unit (not shown) generates information (hereinafter referred to as "display information") for display on a display device such as a CRT (Cathode Ray Tube) display, a liquid crystal display, an organic EL (Electro-Luminescence) display, or the like. ) may be provided. FIG. 15 is a diagram showing a specific example of a screen displayed by the display information in the optimum control device 2 of the modified example. As shown in FIG. 15A, the display information may indicate each value in a separate series on the time axis, or may indicate each value in one series. Moreover, as shown in FIG. 15B, the display information may display each value in a form in which one or both of the values are replaced with another correlated value. FIG. 15B is an example in which gradient information is replaced with information indicating an evaluation amount. In addition, as shown in FIG. 15, the display information may include information indicating the current operating point, the current time, and the like.

In this case, the optimum control device 2 may be provided with a display device for displaying display information, or may be provided with an interface for connecting these display devices to its own device. The optimum control device 2 may also have a communication interface for transmitting display information to other devices. Also, the display control unit may be provided in the optimum control device 2a or 2b in the second or third embodiment, like the optimum control device 2 in the first embodiment. In the second embodiment, the manipulated variable displayed may be the manipulated variable determined by the extreme value control unit 27, or may be the manipulated variable converted by the manipulated variable conversion unit 28. good.

According to at least one embodiment described above, a gradient estimator for estimating a gradient indicating a rate of change of an unknown evaluation function indicating an evaluation amount with respect to a manipulated variable based on an evaluation amount observed for a controlled process; a correction unit that adapts to changes in the evaluation function and corrects the control parameter, the manipulated variable, or the evaluation amount necessary for executing extreme value control based on the estimated value of the gradient obtained by the gradient estimator; Therefore, extremal control can be operated more stably by adapting to the dynamics of the controlled process.

In the first embodiment, the parameter determination section 26 that adaptively updates the integral gain of the estimator 14 based on the gradient estimation value is an example of the correction section. Further, in the second embodiment, the manipulated variable conversion unit 28 that adaptively converts the manipulated variable based on the estimated gradient value is an example of the correction unit. Further, in the third embodiment, the evaluation amount conversion unit 29 that adaptively converts the evaluation amount based on the gradient estimation value is an example of the correction unit.

While several embodiments of the invention have been described, these embodiments have been presented by way of example 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 modifications can be made without departing from the scope of the invention. These embodiments and their modifications are included in the scope and spirit of the invention, as well as the scope of the invention described in the claims and equivalents thereof.

1, 1a, 1b... extremum control system, 11...high pass filter, 12... dither signal output unit, 13... low pass filter, 14... estimator, 9... extremum control system (basic configuration), 2, 2a, 2b... optimum control device, 21... dither signal output unit, 22... operation amount output unit, 23... measurement information acquisition unit, 24, 24b... evaluation amount calculation unit, 25, 25a, 25b... gradient estimation unit, 26, 26a, 26b... parameter determination unit, 27... extreme value control unit, 28... operation amount conversion unit, 29... evaluation amount conversion unit, 291... estimator, 292... conversion unit, 3... water treatment plant, 31... anaerobic tank, 311... Chemical injection pump 312 Sensor 32 Anoxic tank 33 Aerobic tank 331 Circulation pump 332 Blower 34 Final sedimentation tank 341 Return sludge pump 342 Excess sludge extraction pump 343 sensor

Claims (10)

Based on a manipulated variable of the controlled process and an evaluation quantity indicating an index related to optimization of the controlled process based on the controlled quantity that changes according to the manipulated variable, the operation is performed so that the evaluated quantity approaches an optimum value. A control device that performs extreme value control that changes the amount of
a gradient estimator for estimating a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and is unknown with respect to the manipulated variable, based on the evaluation quantity observed with respect to the controlled process; ,
Correction for adaptively correcting the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control based on the estimated value of the gradient obtained by the gradient estimator, in accordance with changes in the evaluation function. Department and
with
The extreme value control unit that executes the extreme value control has an integrator for determining a manipulated variable to be given to the controlled process,
The gradient estimator estimates a second derivative value of the evaluation function as the gradient,
The correcting unit corrects the integral gain of the integrator based on the second order differential value of the evaluation function estimated by the gradient estimating unit.
optimum controller. Based on a manipulated variable of the controlled process and an evaluation quantity indicating an index related to optimization of the controlled process based on the controlled quantity that changes according to the manipulated variable, the operation is performed so that the evaluated quantity approaches an optimum value. A control device that performs extreme value control that changes the amount of
a gradient estimator for estimating a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and is unknown with respect to the manipulated variable, based on the evaluation quantity observed with respect to the controlled process; ,
Correction for adaptively correcting the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control based on the estimated value of the gradient obtained by the gradient estimator, in accordance with changes in the evaluation function. Department and
with
The extreme value control unit that executes the extreme value control is an integrator for determining the manipulated variable given to the controlled process, and the integral gain thereof is obtained by assuming that the evaluation function is a quadratic function. having an integrator determined based on the second derivative of the evaluation function;
The gradient estimator estimates a first derivative value of the evaluation function as the gradient,
The correcting unit corrects the manipulated variable determined by the extremal value control unit based on the integral gain based on the first derivative of the evaluation function estimated by the gradient estimating unit.
optimum controller. Based on a manipulated variable of the controlled process and an evaluation quantity indicating an index related to optimization of the controlled process based on the controlled quantity that changes according to the manipulated variable, the operation is performed so that the evaluated quantity approaches an optimum value. A control device that performs extreme value control that changes the amount of
a gradient estimator for estimating a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and is unknown with respect to the manipulated variable, based on the evaluation quantity observed with respect to the controlled process; ,
Correction for adaptively correcting the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control based on the estimated value of the gradient obtained by the gradient estimator, in accordance with changes in the evaluation function. Department and
with
The extreme value control unit that executes the extreme value control is an integrator for determining the manipulated variable given to the controlled process, and the integral gain thereof is obtained by assuming that the evaluation function is a quadratic function. having an integrator determined based on the second derivative of the evaluation function;
The gradient estimating unit estimates a first-order differential value or a second-order differential value of the evaluation function as the gradient,
The correction unit adjusts the evaluation function unknown with respect to the manipulated variable based on the first-order differential value or the second-order differential value of the evaluation function estimated by the gradient estimating unit. Transform variables so that they change linearly with respect to changes,
optimum controller. Based on a manipulated variable of the controlled process and an evaluation quantity indicating an index related to optimization of the controlled process based on the controlled quantity that changes according to the manipulated variable, the operation is performed so that the evaluated quantity approaches an optimum value. A control device that performs extreme value control that changes the amount of
a gradient estimator for estimating a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and is unknown with respect to the manipulated variable, based on the evaluation quantity observed with respect to the controlled process; ,
Correction for adaptively correcting the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control based on the estimated value of the gradient obtained by the gradient estimator, in accordance with changes in the evaluation function. Department and
with
When the dither signal used for the extreme value control is a sine wave, the gradient estimating unit estimates a differential value of the first or higher order of the evaluation function using a filter or an observer.
optimum controller. Gradient information indicating the gradient of the evaluation function estimated by the gradient estimating unit, and a manipulated variable indicating the manipulated variable determined by the extreme value control unit that executes the extreme value control or the manipulated variable corrected by the correcting unit. Further comprising a display control unit that generates information to be displayed on the display unit in association with the information,
Optimal control device according to any one of claims 1 to 4 . Based on a manipulated variable of the controlled process and an evaluation quantity indicating an index related to optimization of the controlled process based on the controlled quantity that changes according to the manipulated variable, the operation is performed so that the evaluated quantity approaches an optimum value. A control method for extreme value control that changes the amount of
a gradient estimation step of estimating a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and is unknown with respect to the manipulated variable, based on the evaluation quantity observed with respect to the controlled process; ,
Correction for adaptively correcting the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control based on the estimated value of the gradient obtained in the gradient estimation step, in accordance with changes in the evaluation function. a step;
has
estimating a second derivative of the evaluation function as the gradient in the gradient estimation step;
In the correcting step, the integral gain of an integrator that the extreme value control unit that executes the extreme value control has for determining the manipulated variable given to the controlled process is calculated by the gradient estimating step. corrected based on the second derivative of the evaluation function,
control method. Based on a manipulated variable of the controlled process and an evaluation quantity indicating an index related to optimization of the controlled process based on the controlled quantity that changes according to the manipulated variable, the operation is performed so that the evaluated quantity approaches an optimum value. A control method for extreme value control that changes the amount of
a gradient estimation step of estimating a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and is unknown with respect to the manipulated variable, based on the evaluation quantity observed with respect to the controlled process; ,
Correction for adaptively correcting the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control based on the estimated value of the gradient obtained in the gradient estimation step, in accordance with changes in the evaluation function. a step;
has
The extreme value control unit that executes the extreme value control is an integrator for determining the manipulated variable given to the controlled process, and the integral gain thereof is obtained by assuming that the evaluation function is a quadratic function. having an integrator determined based on the second derivative of the evaluation function;
estimating a first derivative of the evaluation function as the gradient in the gradient estimation step;
In the correcting step, the manipulated variable determined by the extremal value control unit based on the integral gain is corrected based on the first derivative of the evaluation function estimated by the gradient estimating step.
control method. Based on a manipulated variable of the controlled process and an evaluation quantity indicating an index related to optimization of the controlled process based on the controlled quantity that changes according to the manipulated variable, the operation is performed so that the evaluated quantity approaches an optimum value. A control method for extreme value control that changes the amount of
a gradient estimation step of estimating a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and is unknown with respect to the manipulated variable, based on the evaluation quantity observed with respect to the controlled process; ,
Correction for adaptively correcting the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control based on the estimated value of the gradient obtained in the gradient estimation step, in accordance with changes in the evaluation function. a step;
has
The extreme value control unit that executes the extreme value control is an integrator for determining the manipulated variable given to the controlled process, and the integral gain thereof is obtained by assuming that the evaluation function is a quadratic function. having an integrator determined based on the second derivative of the evaluation function;
in the gradient estimation step, estimating a first-order differential value or a second-order differential value of the evaluation function as the gradient;
In the correcting step, the evaluation function, which is unknown with respect to the manipulated variable, is corrected based on the first-order differential value or the second-order differential value of the evaluation function estimated by the gradient estimating step. Transform variables so that they change linearly with respect to changes,
control method. Based on a manipulated variable of the controlled process and an evaluation quantity indicating an index related to optimization of the controlled process based on the controlled quantity that changes according to the manipulated variable, the operation is performed so that the evaluated quantity approaches an optimum value. A control method for extreme value control that changes the amount of
a gradient estimation step of estimating a gradient indicating a rate of change of an evaluation function, which is a function representing the evaluation quantity and is unknown with respect to the manipulated variable, based on the evaluation quantity observed with respect to the controlled process; ,
Correction for adaptively correcting the control parameter, the manipulated variable, or the evaluation amount necessary for executing the extreme value control based on the estimated value of the gradient obtained in the gradient estimation step, in accordance with changes in the evaluation function. a step;
has
In the gradient estimation step, if the dither signal used for the extreme value control is a sine wave, a filter or an observer is used to estimate a differential value of the first order or higher of the evaluation function.
control method. the computer,
A computer program for functioning as the optimum control device according to any one of claims 1 to 5 .

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