JP6744145B2 - Control device, control method, and computer program - Google Patents

Description

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

In recent years, a technique called extreme value control has attracted attention as a plant control method. The extreme value control is a control technique capable of searching the optimum value of the manipulated variable in real time without using a complicated model that simulates the plant. The outline of extreme value control is based on the control amount based on the control amount of the control target process generated by forcibly changing the operation amount given to the process to be controlled (hereinafter referred to as “control target process”). This is to search for an operation amount with which the evaluation amount has an optimum value. When such extreme value control is applied to plant control, it is necessary to set various parameters (hereinafter, referred to as “control parameters”) related to extreme value control. Conventionally, some guidelines have been proposed for appropriately setting control parameters according to the characteristics of a control target process.

Conventional setting guidelines generally set control parameters in advance based on process-specific characteristics such as time constants, manipulated variables, and evaluation variables of the process to be controlled (hereinafter referred to as "process characteristics"). It is set based on the measured information of the controlled process. However, in some cases, it may be difficult to control a control target process whose process characteristics change in the process of searching for an optimum value, using control parameters uniquely determined in advance. If a control target process having such a property is to be controlled with a control parameter uniquely determined in advance, the control parameter may not match the state of the control target process, and the control may become unstable. The current situation is that the guideline for setting control parameters used when a process having such a property is set as a control target has not been sufficiently established. Therefore, it is desired to establish a setting guideline that can appropriately set the control parameter for the control target process having such a property that the process characteristic changes according to the change in the process characteristic.

JP, 2014-135851, A JP, 2005-102876, A

The problem to be solved by the present invention is to provide a control device, a control method, and a computer program capable of setting appropriate control parameters according to changes in process characteristics.

The control device according to the embodiment includes an extreme value control unit, an evaluation amount correction unit, and an integration coefficient update unit. The extreme value control unit is an optimum value of the operation amount based on the 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. Perform extremum control to search for. The evaluation amount correction unit corrects the evaluation amount with a predetermined correction function. The integral coefficient updating unit updates the integral coefficient, which is a control parameter for the extreme value control, based on the corrected evaluation amount. The extreme value control unit executes the extreme value control based on the corrected evaluation amount.

The block diagram which shows the operation example of extreme value control. The figure which shows the specific example of the evaluation function which takes the 2nd-order differential value which changes with operating points. The figure which shows the specific example at the time of applying the control apparatus 1 of 1st Embodiment to control of the water treatment plant 300. The figure which shows the specific example of a functional structure of the control apparatus 1 of 1st Embodiment. The figure which shows the example of correction|amendment of an evaluation function when a sigmoid function is used for a correction function. The figure which shows the example which the convergence speed of optimal value search improves by correction|amendment of an evaluation function. The figure which shows the 2nd specific example regarding correction|amendment of an evaluation function. The figure which shows the 3rd specific example regarding correction|amendment of an evaluation function. The figure which shows the 3rd specific example regarding correction|amendment of an evaluation function. The figure which shows the specific example of a functional structure of the control apparatus 1a of 2nd Embodiment. The figure which shows the specific example of calculation of the second-order differential value by the change rate calculation part 16. The figure which shows the specific example of calculation of the second-order differential value by the 3rd modification.

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

(First embodiment)
[Outline]
The extreme value control is a control method that adaptively searches for the optimum value of the operation amount based on the operation amount of the control target process and the evaluation amount based on the control amount that changes according to the operation amount. The evaluation amount is an index value related to optimization of the control target process, and is determined based on the control amount of the control target process. 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 standard as long as it is a function based on the control amount. The evaluation amount may be the control amount itself. Generally, in the process to be controlled in the extreme value control, this evaluation function is an unknown function with respect to the manipulated variable.

Generally, in the extreme value control, the operation amount is forcibly vibrated by applying a dither signal, and the evaluation amount that changes according to the operation amount is observed. Then, the operation amount is changed so that the evaluation amount approaches the optimum value of the evaluation function. The concept of process control by extreme value control is to approach the evaluation amount to the optimum value of the evaluation function by repeating such increase and decrease of the operation amount. The dither signal that affects the manipulated variable is often given as a sine wave.

FIG. 1 is a block diagram showing an operation example of extreme value control. FIG. 1 shows a control target process 100 that is a control target process, and a control system 200 that realizes extreme value control of the control target process 100. The control system 200 includes an evaluation amount calculation unit 210 and an extreme value control unit 220, and realizes the extreme value control of the control target process 100 by repeating the flow of the process as described below.

First, the manipulated variable output from the extreme value control unit 220 is input to the control target process 100 (step S11). Hereinafter, for the sake of simplicity, the operation amount input in step S11 is referred to as a first operation amount. The controlled process 100 outputs the first controlled variable as a response to the first manipulated variable (step S12). The first control amount is input to the evaluation amount calculation unit 210. The evaluation amount calculation unit 210 calculates the first evaluation amount based on the first control amount. The evaluation amount calculation unit 210 outputs the calculated first evaluation amount to the extreme value control unit 220 (step S13).

The extreme value control unit 220 determines a second operation amount that brings the evaluation amount closer to an optimum value, based on the first evaluation amount. The extreme value control unit 220 outputs the second operation amount determined based on the first evaluation amount to the control target process 100 as a new operation amount (step S14). The controlled process 100 outputs the second controlled variable as a response to the second manipulated variable (step S15). The second control amount is input to the evaluation amount calculation unit 210 as in step S12. The evaluation amount calculation unit 210 calculates the second evaluation amount based on the second control amount.

With such a processing flow, the second evaluation amount becomes an evaluation amount closer to the optimum value than the first evaluation amount. In the extreme value control, the calculation of the evaluation amount based on such a control amount and the determination of the new manipulated variable based on the evaluation amount are repeatedly executed, so that the evaluation amount is controlled to converge to the optimum value. The operation amount of the target process is controlled.

The function of determining the second operation amount based on the first evaluation amount is realized by the following configuration of the extreme value control unit 220. The extreme value control unit 220 includes a high pass filter 221 (HPF: High-Pass Filter), a dither signal output unit 222, a multiplier 223, a low pass filter 224 (LPF: Low-Pass Filter), an integrator 225, and an adder 226. Prepare In FIG. 1, s is the Laplace operator, ω is the angular frequency of the dither signal, a is the amplitude of the dither signal, ω1 is the angular frequency of the low-pass filter 224, ω2 is the angular frequency of the high-pass filter, and k is the integration coefficient of the integrator 225. Represents.

The high-pass filter 221 inputs the fed-back evaluation amount signal, and removes a constant value bias corresponding to the minimum value from the evaluation amount signal. The high-pass filter 221 outputs the evaluation amount signal with the bias removed to the multiplier 223.

The dither signal output unit 222 outputs a dither signal to the multiplier 223 and the adder 226. The dither signal output unit 222 outputs a first dither signal represented by sinωt (t is a variable representing time) to the multiplier 223, and a to the adder 226. And a dither signal output unit 222-2 that outputs a second dither signal represented by ×sinωt. Note that sin ωt (sine wave) is an example of a dither signal, and the dither signal may have any shape as long as it is a periodic signal.

The multiplier 223 multiplies the bias-removed evaluation amount signal output from the high-pass filter 221 by the first dither signal. The multiplier 223 outputs the evaluation amount signal multiplied by the first dither signal to the low pass filter 224.

The low pass filter 224 extracts low frequency components from the evaluation signal multiplied by the dither signal. The low pass filter 224 outputs a signal indicating a low frequency component of the evaluation amount signal to the integrator 225. The low frequency component of this evaluation amount signal is considered to represent the frequency component of the evaluation amount signal that has changed according to the vibration of the dither signal. Therefore, it can be determined from the low frequency component of the evaluation amount signal whether the evaluation amount has increased or decreased with respect to the change in the operation amount.

The integrator 225 functions as an estimator that estimates the direction of the operation amount to move in order to bring the evaluation amount closer to the optimum value, based on the low-frequency component of the evaluation amount signal output from the low-pass filter 224. Specifically, the integrator 225 integrates the low frequency component of the evaluation amount signal and outputs the integrated signal of the low frequency component. The integrated signal output here gives the direction (increase or decrease) to move with respect to the current manipulated variable.

The adder 226 generates a manipulated variable signal to be input next to the controlled process 100 based on the current manipulated variable signal and the integrated signal output from the integrator 225. The adder 226 adds a second dither signal (a×sin ωt) for vibrating the operation amount signal to the generated operation amount signal and outputs the sum to the controlled process 100.

Such an extreme value control by the control system 200 is performed by setting the angular frequency ω of the dither signal, the amplitude a of the dither signal, the angular frequency ω1 of the low pass filter 224, each frequency ω2 of the high pass filter 221, and the integration coefficient k of the integrator 225 to 5 Characterized by one control parameter. Of these control parameters, the integration coefficient k is a parameter that influences the property of the integrator 225 that determines the direction of the manipulated variable to be changed in the extreme value search, and is an important parameter that affects the performance of the extreme value control. .. In general, the integration coefficient k is a parameter determined based on the characteristics of the manipulated variable and the evaluated variable, and is determined using, for example, the following equation (1).

In Expression (1), τ is a constant for adjustment, a is the amplitude of the dither signal, and G is the second-order differential value of the evaluation function. Note that τ and a are constants that are set based on static information indicating the characteristics of the controlled process. On the other hand, the value of G cannot be uniquely determined in advance because the evaluation function is an unknown function for the manipulated variable. Therefore, the value of G is generally determined based on the actual measurement values of the operation amount and the evaluation amount. However, when the evaluation function is a function having different second-order differential values in places, the integration coefficient k may not be set appropriately in such a determination method.

FIG. 2 is a diagram showing a specific example of an evaluation function that takes a second-order differential value that differs depending on the operating point. FIG. 2A shows an example of an evaluation function whose second-order differential value is constant, and FIG. 2B shows an example of an evaluation function taking a second-order differential value that differs depending on the operating point. Specifically, FIG. 2A shows an example in which the evaluation function is represented by a quadratic function. As shown in FIG. 2A, when the evaluation function is expressed as a quadratic function in which the tangent slope always increases at a constant rate as the manipulated variable increases, the second derivative of the evaluation function is always constant. Becomes Therefore, in such a case, continuously stable extreme value control can be realized by the integration coefficient k determined at a certain operating point.

On the other hand, as shown in FIG. 2B, the evaluation function is expressed as a function in which the slope of the tangent line changes with respect to the change in the manipulated variable and becomes discontinuous before and after the point where the change occurs. In this case, the second-order differential value of the evaluation function may be different depending on the manipulated variable. In such a case, the integration coefficient k may deviate from an appropriate value due to a change in the operation amount, and the stability of the extreme value control may be impaired. Specifically, the speed until the evaluation amount converges to the optimum value may decrease, or the evaluation amount may change away from the optimum value in some cases. As described above, the probability of the method of setting an appropriate integration coefficient k for the evaluation function such that the second-order differential value calculated from the actual values of the operation amount and the evaluation amount does not become constant is desired.

In order to solve such a problem, the control device of the embodiment has the following two functions. One is a function of paying attention to the shape of the evaluation function and correcting the evaluation function so that the second-order differential value is always constant with respect to the change in the operation amount. The other is a function of sequentially updating the value of the integration coefficient k according to changes in the operation amount and the evaluation amount. With such a function, the control device of the embodiment can always keep the value of the integration coefficient k at an appropriate value.

[Details]
FIG. 3 is a diagram showing a specific example in which the control device 1 of the first embodiment is applied to control of the water treatment plant 300. For example, the water treatment plant 300 is a plant that realizes a biological wastewater treatment process. Solid arrows in FIG. 3 represent the flow of sewage to be treated (hereinafter referred to as “treated water”) and the flow of sludge separated from the treated water. Here, first, the outline of the water treatment plant 300 will be described. The water treatment plant 300 includes storage facilities of a first settling tank 310, a biological reaction tank 320, a final settling tank 330, a filter tank 340, and an excess sludge storage tank 350. In addition, the water treatment plant 300 includes a sludge extraction pump 311, an excess sludge pump 331, a return sludge pump 332, and a sludge treatment pump 351 that deliver the treated water or sludge between the storage facilities, and the treated matter in the biological reaction tank 320. And a blower 321 for aerating water.

First, the water to be treated is first stored in the settling tank 310. First, in the settling basin 310, unnecessary substances having a relatively large specific gravity are settled and settled by gravity. The sludge that first settled in the settling tank 310 is drawn by the sludge drawing pump 311 and sent to the surplus sludge storage tank 350. On the other hand, the supernatant water to be treated is sent to the biological reaction tank 320.

In the biological reaction tank 320, microorganisms are added to the water to be treated. The microorganisms introduced into the water to be treated are activated by the aeration of the water to be treated by the blower 321, decompose organic substances in the water to be treated, and absorb phosphorus in the water to be treated. By the action of this microorganism, the nitrogen component and the phosphorus component are separated from the water to be treated. The water to be treated that has passed through the biological reaction tank 320 is sent to the final settling tank 330.

In the final settling tank 330, the activated sludge in the water to be treated is settled and settled by gravity. The activated sludge settled in the final settling tank 330 is extracted by the excess sludge pump 331 and sent to the excess sludge storage tank 350. Here, part of the activated sludge is returned to the biological reaction tank 320 by the return sludge pump 332, and is recycled in a cyclic manner. On the other hand, the supernatant treated water is sent to the filtration basin 340.

In the filtration basin 340, the final stage purification treatment for the water to be treated is performed, such as removal of small unnecessary substances by filtration and disinfection. The water to be treated that has been subjected to the purification treatment in the filtration pond 340 is discharged to a river or the like as treated water.

The excess sludge storage tank 350 is a facility for temporarily storing unnecessary sludge generated in the biological wastewater treatment process. The sludge stored in the excess sludge storage tank 350 is delivered to the sludge treatment process by the sludge treatment pump 351.

For such a water treatment plant 300, the control device 1 uses, for example, the total cost represented by the sum of the operating cost of the blower 321 and the return sludge pump 332 and the water quality cost of the discharged water as the evaluation amount. Control the operation amount so that the cost is minimized. For example, the operating cost is a cost due to power consumption of the blower 321 and the returning sludge pump 332. The operating cost is calculated based on the power consumption and power unit price of the blower 321 and the returning sludge pump 332. The water quality cost is, for example, a cost due to a charge (generally called “drainage charge”) imposed for drainage. With the increasing awareness of environmental conservation in recent years, the idea of imposing such wastewater charges on drainers is becoming widespread. For example, the water quality cost in the water treatment plant 300 is calculated by the following equation (2).

In the formula (2), the TN load represents the amount of nitrogen component (TN) contained in the discharged water, and the TP load represents the amount of phosphorus component (TP) contained in the discharged water. Further, the TN cost conversion coefficient represents a coefficient for converting the TN load amount into the water quality cost, and the TP cost conversion coefficient represents a coefficient for converting the TP load amount into the water quality cost. The TN load amount and the TP load amount are calculated based on the concentration of each component dissolved in the discharged water and the discharged water amount.

When minimizing the above-mentioned total cost, the operation amount can be defined as a return rate of sludge (hereinafter, referred to as “return sludge”) returned to the biological reaction tank 320 by the return sludge pump 332. The return rate is the ratio of the amount of returned sludge to the amount of treated water that flows into the biological reaction tank 320 from the first settling basin 310. This is because the removal performance of TP and TN in biological wastewater treatment largely depends on the amount of returned sludge. Further, generally, the amount of aeration air of the blower 321 is determined according to the amount of sludge returned by the returned sludge pump 332. Therefore, by inputting the return rate as the operation amount, a specific operation amount for each of the blower 321 and the return sludge pump 332 is determined.

In this case, the evaluation amount calculation unit 210 sets the water quality of the discharge water discharged from the filtration basin 340 (that is, the TN load amount and the TP load amount, which will be referred to as “discharge water quality” below) as the control amount. To get from. The evaluation amount calculation unit 210 calculates the evaluation amount as the above total cost based on the acquired discharged water quality. The evaluation amount calculation unit 210 outputs the calculated total cost to the control device 1. The evaluation amount calculation unit 210 may be configured by a device different from the control device 1 or may be configured as a part of the control device 1.

Based on the return rate input to the return sludge pump 332 and the total cost output from the evaluation amount calculation unit 210, the control device 1 changes the return rate so as to decrease the total cost in the water treatment plant. It is determined as a new operation amount to be input to 300. The control device 1 inputs the new manipulated variable thus determined to the return sludge pump 332.

In this way, by defining the total cost based on the water quality cost and the operating cost, it is possible to operate the extreme value control so as to minimize the operating cost while maintaining the water quality of the discharged water. The evaluation amount may be any amount as long as it can be calculated based on the control amount. For example, when optimization of the control amount is the purpose of the extreme value control, the control amount itself may be defined as the evaluation amount. Further, when the operating cost does not matter, the evaluation amount may be defined only by the water quality cost.

On the other hand, it is known that the water quality cost of TN and the water quality cost of TP have a trade-off relationship. Specifically, as the amount of returned sludge increases, the TN removal performance improves, and as the amount of returned sludge decreases, the TP removal performance improves. In this way, when the water quality costs of the respective dissolved components are in a trade-off relationship, the total cost may be defined based on only the water quality costs. Since the total cost is defined only by the water quality cost, the extreme value control can be operated so that the balance between TP and TN contained in the discharged water can be controlled more accurately.

When the water treatment plant 300 in which the evaluation amount is defined as such a total cost is the control target process, the control device 1 of the embodiment uses the return rate as the operation amount and the total cost as the evaluation amount. By executing, the return rate that gives the optimum total cost is searched.

It should be noted that the controlled process often has a constraint condition according to the nature and environment of the process. For example, in a water treatment plant, a target value of water quality, a permissible range, and the like for treated water are set based on discharge rules and the like. In some cases, an allowable upper limit for the total cost, the water quality cost, and the operating cost may be set. In such a case, the control device 1 may control the manipulated variable such that these constraint conditions are satisfied with respect to various variables related to the extreme value control such as the manipulated variable, the controlled variable, and the evaluation amount.

Further, the control device 1 may weight the evaluation amount according to the state of the control target process. For example, the control device 1 may perform weighting to further increase the water quality cost when the discharged water quality exceeds a predetermined regulation value. By performing such weighting, it is possible to more reliably prevent the discharged water quality from exceeding the regulation value.

Although the application example of the extreme value control in the water treatment plant 300 has been described above, the process targeted for the extreme value control is not limited to the biological wastewater treatment process. The extreme value control can be applied to any process having an evaluation amount to be optimized.

FIG. 4 is a diagram showing a specific example of the functional configuration of the control device 1 of the first embodiment. The control device 1 includes a CPU (Central Processing Unit), a memory, an auxiliary storage device, and the like connected by a bus, and executes a control program. The control device 1 functions as a device including the extreme value control unit 11, the evaluation function estimation unit 12, the evaluation amount correction unit 13, and the integration coefficient update unit 14 by executing the control program. Note that all or part of each function of the control device 1 may be realized using hardware such as an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), and an FPGA (Field Programmable Gate Array). The control program may be recorded in 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 a computer system. The control program may be transmitted via a telecommunication line.

The extreme value control unit 11 outputs an operation amount that brings the evaluation amount closer to the optimum value based on the input evaluation amount. Such a function of the extreme value control unit 11 is realized by the same configuration as the extreme value control unit 220 shown in FIG. Therefore, here, the same reference numerals as those in FIG. 1 are used to omit the description of the configuration of the extreme value control unit 11.

The evaluation function estimation unit 12 estimates an evaluation function representing the correspondence between the operation amount and the evaluation amount, based on the evaluation amount output from 210 and the operation amount input to the control target process. The evaluation function estimation unit 12 outputs the estimated evaluation function to the evaluation amount correction unit 13.

The evaluation amount correction unit 13 corrects the evaluation function estimated by the evaluation function estimation unit 12 into a function that reduces the variance of the second-order differential value within the range of the operation amount domain. Specifically, the evaluation amount correction unit 13 performs variable conversion of the operation amount, and corrects the evaluation function so that the evaluation function is represented by a variable after variable conversion as a quadratic function. In this case, the correction function used for the variable conversion is given by multiplying the function that is the evaluation function after correction by the inverse function of the evaluation function before correction. By expressing the evaluation function as a quadratic function, the second derivative value of the evaluation function becomes constant within the range of the domain. If the second-order differential value is constant, it is possible to define the integration coefficient k as a constant by the equation (1), and the stability of the extreme value control can be improved.

The integration coefficient updating unit 14 calculates the integration coefficient k based on the evaluation function corrected by the evaluation amount correction unit 13, and updates the existing integration coefficient set in the integrator 225 with the calculated integration coefficient k. Specifically, the integration coefficient updating unit 14 calculates the second derivative G of the corrected evaluation function and applies the calculated second derivative G to the equation (1) to calculate the integration coefficient k.

Here, the reason why the evaluation function is corrected to a quadratic function is that the quadratic function takes a constant second-order differential value over the entire domain, and the variance of the second-order differential value is the smallest. As described above, the quadratic function is the most ideal function as the transformed evaluation function. Good. The evaluation amount correction unit 13 outputs the evaluation amount after variable conversion represented by the corrected evaluation function to the extreme value control unit 11.

FIG. 5 is a diagram showing an example of the correction of the evaluation function when the sigmoid function is used as the correction function. FIG. 5A shows an example of the evaluation function before correction. The horizontal axis of FIG. 5A represents the operation amount U, and the vertical axis represents the evaluation amount J. FIG. 5A shows an evaluation function in which the second-order differential value is different between the operation amounts a and b and the operation amounts c to e. In this way, when the evaluation functions are largely different within the range of the domain, if the integration constant k is determined only by the second-order differential value with a certain operation amount, the operation amount that starts the search for the optimum value (hereinafter, " Depending on the "starting point"), the convergence speed to the optimum value varies.

FIG. 5B shows an example in which the evaluation function of FIG. 5A is corrected using the sigmoid function. The sigmoid function E(x) is a function represented by the following expression (3), and has a shape as shown in FIG. 5(C).

As can be seen from FIG. 5C, the change rate of the sigmoid function E(x) increases as x increases in the range of x<0, and the change rate increases as x increases in the range of x>0. It is a function that becomes smaller. By performing variable conversion of the manipulated variable U using such a sigmoid function, the evaluation function is corrected to a shape closer to a quadratic function as shown in FIG. As can be seen from FIG. 5B, in the evaluation function corrected by the sigmoid function, the difference between the second-order differential value between the operation amounts a and b and the second-order differential value between the operation amounts c to e is small. Therefore, by searching for the optimum value based on the corrected evaluation function, that is, by determining the integration constant k based on the second-order differential value of the corrected evaluation function, the optimum value at a more stable convergence speed is obtained. Can be searched.

FIG. 6 is a diagram showing an example in which the convergence speed of the optimum value search is improved by the correction of the evaluation function. FIG. 6A and FIG. 6B show the time required for the operation amount to converge to the optimum value when the search is performed based on the evaluation function before correction shown in FIG. , "Convergence time"). The optimum value of the operation amount is the operation amount that gives the optimum value of the evaluation amount. 6A shows an example in which the operation amount a is used as the starting point, and FIG. 6B shows an example in which the operation amount e is used as the starting point. FIGS. 6A and 6B show that the convergence time is t ₁ when the starting point is the manipulated variable a, and the convergence time is t ₂ when the starting point is the manipulated variable e. Showing.

On the other hand, FIGS. 6C and 6D show the convergence speed when the search is performed based on the corrected evaluation function shown in FIG. 5B. FIG. 6C is an example when the operation amount a is the starting point, and FIG. 6D is an example when the operation amount e is the starting point. 6C and 6D, the convergence time is t ₃ (t ₃ >t ₁ ) when the starting point is the operation amount a, and the convergence time is when the starting point is the operation amount e. Indicates that t ₄ (t ₄ <t ₂ ). In this way, by correcting the evaluation function so that it has a shape close to a quadratic function, the convergence speed of the optimum value search can be stabilized.

FIG. 7 is a diagram showing a second specific example regarding the correction of the evaluation function. 7A shows an evaluation function to be corrected, and FIG. 7B shows a correction function used for correcting the evaluation function shown in FIG. 7A. FIG. 7C shows the evaluation function corrected by the correction function of FIG. 7B. For example, FIG. 7A shows an evaluation function that can be approximated by the following expression (4).

In the equation (4), U ^* represents an operation amount that gives the minimum value of the evaluation function V(U), and n represents an arbitrary real value. The shape of the evaluation function becomes the shape shown in FIG. 7A when n is a positive value and has a real value of 1 or more. On the other hand, the correction function of FIG. 7B is a function represented by the following expression (5). Note that n in the following expression (5) has the same value as n in the expression (4).

The evaluation function V′(U) corrected by such a correction function E(x) becomes a function that can be approximated by a quadratic function like the following expression (6), and has a shape as shown in FIG. 7(C). It becomes a function.

FIG. 8 is a diagram showing a third specific example regarding the correction of the evaluation function. 8A shows an evaluation function to be corrected, and FIG. 8B shows a correction function used for correcting the evaluation function shown in FIG. 8A. FIG. 8C shows the evaluation function corrected by the correction function of FIG. 8B. For example, FIG. 8A shows an evaluation function that can be approximated by the following expression (7).

In Expression (7), U ^* represents the manipulated variable that gives the minimum value of the evaluation function V(U), and n represents an arbitrary real value. The shape of the evaluation function becomes the shape as shown in FIG. 8A when n is a positive value and has a real value of 1 or more. On the other hand, the correction function of FIG. 8B is a function represented by the following expression (8). Note that n in the following formula (8) has the same value as n in the formula (7).

The evaluation function V′(U) corrected by such a correction function E(x) becomes a function that can be approximated by a quadratic function similar to the equation (6), and has a shape as shown in FIG. 8C. Become.

FIG. 9 is a diagram showing a third specific example regarding the correction of the evaluation function. 9A shows an evaluation function to be corrected, and FIG. 9B shows a correction function used for correcting the evaluation function shown in FIG. 9A. FIG. 9C shows the evaluation function corrected by the correction function of FIG. 9B. For example, FIG. 9A shows an evaluation function that can be approximated by the following expression (9).

In Expression (9), U ^* represents a manipulated variable that gives the minimum value of the evaluation function V(U), and n ₁ and n ₂ represent arbitrary real values. The shape of the evaluation function becomes the shape as shown in FIG. 9A when n ₁ and n ₂ are positive and have a real value of 1 or more. On the other hand, the correction function of FIG. 9B is a function represented by the following expression (10). Note that _{n 1} and _{n 2} in the following equation (10) is the same value as _{n 1} and _{n 2} of formula (9).

The evaluation function V′(U) corrected by such a correction function E(x) becomes a function that can be approximated by a quadratic function similar to Expression (6), and has a shape as shown in FIG. 9C. Become.

Since the evaluation functions corrected as shown in FIGS. 7C, 8C, and 9C are all quadratic functions, the second-order differential value of the evaluation function is constant within the range of the domain. Becomes If the second-order differential value is constant, it is possible to define the integration coefficient k as a constant by the equation (1), and the stability of extreme value control can be improved.

The control device 1 of the first embodiment configured as described above includes the evaluation amount correction unit 13 to correct the evaluation function to a function that reduces the variance of the second-order differential value within the range of the domain. be able to. With such a configuration, the control device 1 according to the first embodiment allows the integral coefficient k to be observed in the extreme value control of the process to be controlled such that the process characteristic changes according to the manipulated variable. It can be updated to an appropriate value based on (or control amount).

Hereinafter, a modified example of the control device 1 of the first embodiment will be described.

The evaluation amount correction unit 13 may correct the evaluation function for the entire domain or may correct the evaluation function for a part of the domain.

The evaluation amount correction unit 13 may correct the evaluation function for any section of the evaluation function with a correction function according to each section.

(Second embodiment)
In the first embodiment, a method of updating the integration coefficient k by correcting the evaluation function to a quadratic function or a function having a shape close to a quadratic function (hereinafter, referred to as “first updating method”) has been described. .. However, the first updating method is effective when the process characteristic (that is, the evaluation function) changes relatively slowly with respect to the change in the manipulated variable, but the process characteristic with respect to a small change in the manipulated variable. May not work effectively in the case of a large change. In this case, the evaluation amount is observed corresponding to the local change in the operation amount, and the integration coefficient k is updated adaptively based on the local change in the evaluation amount (hereinafter, referred to as “second updating method”). That is required). Hereinafter, the control device 1a of the second embodiment that realizes the second updating method will be described in detail.

FIG. 10 is a diagram showing a specific example of the functional configuration of the control device 1a according to the second embodiment. The control device 1a does not include the evaluation function estimation unit 12 and the evaluation amount correction unit 13, a point that includes an integration coefficient update unit 14a instead of the integration coefficient update unit 14, a control information acquisition unit 15, a change rate calculation unit 16, and The difference from the control device 1 of the first embodiment is that a time delay unit 17 is further provided. In the description of FIG. 10, among the functional units included in the control device 1a, the same functional units as those of the control device 1 are denoted by the same reference numerals as those in FIG.

The control information acquisition unit 15 measures (or acquires) the operation amount input to the control target process and the evaluation amount calculated based on the control amount of the control target process in real time. The control information acquisition unit 15 outputs the measured operation amount and evaluation amount to the change rate calculation unit 16. In addition, the real-time measurement here means that the measurement is repeated every short period (hereinafter, referred to as “observation cycle”) in which the above-described local fluctuation of the evaluation amount can be observed. To do. In addition, the control information acquisition unit 15 may measure the evaluation amount output from the evaluation amount calculation unit 210, or may acquire the control amount from the control target process and calculate the evaluation amount. That is, the evaluation amount calculation unit 210 may be included in the control device 1a.

The change rate calculation unit 16 calculates the change rate corresponding to the second-order differential value of the evaluation function in each observation period based on the operation amount and the evaluation amount output from the control information acquisition unit 15. The change rate calculating unit 16 outputs the change rate calculated for each observation period to the integration coefficient updating unit 14a.

If the evaluation function can be estimated for each observation cycle, the change rate calculation unit 16 may calculate the second-order differential value itself of the evaluation function. However, when updating the integration coefficient based on the local evaluation amount, it may be difficult to perform the process of estimating the evaluation function for each observation period. Therefore, a configuration for calculating the change rate corresponding to the second-order differential value of the evaluation function based on the measured values of the plurality of evaluation amounts will be described below. In the following description, the "change rate" is intentionally described as "second-order differential value" so that the essential meaning of the change rate can be easily understood.

FIG. 11 is a diagram showing a specific example of calculation of the second-order differential value by the change rate calculation unit 16. 11A illustrates a specific example of the operation amount and the evaluation amount measured by the control information acquisition unit 15, and FIG. 11B illustrates the measurement amount in a certain observation cycle T (time t ₁₁ to time t ₁₂ ). The operation amount and the evaluation amount are expanded. FIG. 11B shows that five manipulated variables g, h, i, l, and m were measured in the observation cycle T. In this case, for example, the change rate calculation unit 16 calculates the second-order differential value G based on the following equations (11) to (15).

In formulas (11) to (14), J(g), J(h), J(i), J(l), and J(m) are operation amounts g, h, i, l, and m, respectively. Indicates the measured evaluation amount. That is, G ₁ in Expression (11) represents the second-order differential value based on the evaluation amounts of the operation amounts g, i, and m at three points. Similarly, G ₂ in the equation (12) is a second-order differential value based on the evaluation amounts of the _three manipulated variables h, i, and l, and G _{3 in the} equation (13) is an evaluation of the three points of the manipulated variables g, i, and l. The second-order differential value based on the amount, and G ₄ in the equation (14) represent the second-order differential value based on the evaluation amount measurement values of the three manipulated variables h, i, and m, respectively. That is, the equations (11) to (14) are equations for calculating the second-order differential value based on the evaluation amounts of the selected three points for each different combination of the three points selected from the five evaluation amounts. Then, the expression (15) is the second value of the evaluation function in the observation cycle T, which is the average value of the plurality of second-order differential values (hereinafter, referred to as “second-order differential value G _c ”) calculated for each such combination. It represents that it is a differential value G. Note that the combination of three points selected from g, h, i, l, and m may be a combination different from the combination selected by Expressions (11) to (14). In the case of the example in FIG. 11, since there are ₅ C ₃ (=10) combinations, there are 6 combinations other than the above-described combinations of 3 points.

Returning to the description of FIG. The integration coefficient updating unit 14a calculates the integration coefficient k based on the second-order differential value G calculated by the change rate calculating unit 16, and updates the existing integration coefficient set in the integrator 225 with the calculated integration coefficient k. To do.

The time delay unit 17 delays the evaluation amount input to itself by a time corresponding to the dead time of the process to be controlled and outputs it to the extreme value control unit 11. Due to the delayed input of the evaluation amount, the extreme value control unit 11 determines a new operation amount based on the evaluation amount that responds to the operation amount determined based on the updated integration coefficient k. With such a configuration, the control device 1a can function the extreme value control so that a new manipulated variable is determined in accordance with the change in the process characteristics.

The control device 1a according to the second embodiment configured as described above includes the change rate calculation unit 16 and thus can update the integration coefficient k based on the operation amount and the evaluation amount that are measured in real time. By providing such a configuration, the control device 1a according to the second embodiment adaptively updates the integration coefficient k even for a control target process in which the process characteristics greatly change with a small change in the operation amount. can do.

Hereinafter, modified examples of the control device 1a according to the second embodiment will be described.

<First Modification>
Change rate calculating section 16, among the plurality of second-order differential value G _c, only G _c take positive or negative one value may be calculated second order differential value G of each observation period using. Specifically, when the optimum value of the evaluation amount is the maximum value of the evaluation function, G is calculated using only G _c that takes a negative value, and the optimum value of the evaluation amount is the minimum value of the evaluation function. In that case, G is calculated using only G _c that takes a positive value. This is because the sign of the second derivative is a factor that greatly affects the search for the optimum value. By selecting the second-order differential value G _c as described above, it becomes possible to cause the extreme value control to function more accurately. As a result of such selection, if any G _c was not selected may recalculate G _c on the basis of the measured values of the other combinations.

<Second Modification>
The control information acquisition unit 15 may change the observation period in which the operation amount and the control amount are measured (or the measured operation amount and the evaluated amount are output) according to the tendency of the variation of the second-order differential value. For example, the control information acquisition unit 15 changes the observation cycle to a shorter cycle when a rapid change in the second-order differential value is observed. By changing the observation period in this way, it becomes possible to adapt to more local changes in the process characteristics. Furthermore, if a predetermined threshold value is set for the amount of change in the second-order differential value, it is possible to determine the second-order differential value that shows a sharp change above the threshold value as an abnormal value. In this case, the second-order differential value determined as an abnormal value may not be used for calculating the integration coefficient k. Conversely, the control information acquisition unit 15 may change the observation period to a longer period when a situation in which the second-order differential value hardly changes is observed. By changing the observation cycle in this way, it is possible to reduce the processing load of the control device 1a.

<Third Modification>
The change rate calculation unit 16 may calculate the second-order differential value of the entire period represented by these observation periods, based on the representative values of a plurality of continuous observation periods. FIG. 12 is a diagram showing a specific example of calculating the second-order differential value according to the third modification. FIG. 12(A) shows a specific example of the operation amount and the evaluation amount measured by the control information acquisition unit 15, and FIG. 12(B) is measured at a certain continuous observation cycle T ₁ , T ₂ and T ₃ . The operation amount and the evaluation amount are expanded. FIG. 12B shows a result in which the measured values in each observation cycle are averaged by the representative value. A curve 401 in FIG. 12B shows the evaluation amount before averaging, and a curve 402 shows the evaluation amount after averaging. Further, g, h, and i represent the median value of the manipulated variables in each observation cycle. In this case, for example, the rate-of-change calculating unit 16 calculates one second-order differential value G for the entire observation period T _{1 to} T ₃ based on the following equation (16). Note that J″(U) in Expression (16) represents the evaluation amount measured for the operation amount U.

That is, Expression (16) represents that the second-order differential value G is calculated based on the value obtained by averaging the measurement values acquired in each observation cycle. In this respect, the expression (16) is different from the expression (15) that calculates the second-order differential value G by averaging the second-order differential value G _c of each observation cycle.

By calculating the second-order differential value G by such a method, the control device 1a adapts an appropriate integration coefficient k even for a control target process in which the evaluation amount repeats minute fluctuations, as shown in FIG. Can be updated.

Note that, although FIG. 12 shows an example in which the second-order differential value G is calculated based on the representative values of the three observation cycles, the control device 1a uses the second-order differential value G based on the representative values of three or more observation cycles. May be calculated. In this case, any three representative values may be selected from the averaged representative values of the observation periods to calculate the second-order differential value G, or the second-order differential value G _c may be calculated for each of the selectable combinations. However, the average value thereof may be used as the second-order differential value G. Further, the representative value is not limited to the average value, and other statistical values such as the median value, the maximum value or the minimum value may be used.

According to at least one embodiment described above, the evaluation amount correction unit that corrects the evaluation amount by a predetermined correction function, or calculates the change rate corresponding to the second-order differential value of the evaluation function based on the operation amount and the evaluation amount. By having the change rate calculation unit, it is possible to set appropriate control parameters according to changes in the process characteristics.

While some 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. The embodiments and their modifications are included in the scope of the invention and the scope thereof, as well as in the invention described in the claims and the scope of equivalents thereof.

1, 1a... Control device, 11... Extreme value control unit, 12... Evaluation function estimation unit, 13... Evaluation amount correction unit, 14, 14a... Integral coefficient update unit, 15... Control information acquisition unit, 16... Change rate calculation unit , 17... Time delay unit, 100... Control target process, 200... Control system, 210... Evaluation amount calculation unit, 220... Extreme value control unit, 221... High pass filter, 222, 222-1, 222-2... Dither signal output 223... Multiplier, 224... Low-pass filter, 225... Integrator, 226... Adder, 300... Water treatment plant, 310... First settling basin, 311... Sludge extraction pump, 320... Biological reaction tank, 321... Blower, 330... Final sedimentation tank, 331... Excess sludge pump, 332... Return sludge pump, 340... Filtration tank, 350... Excess sludge storage tank, 351... Sludge treatment pump, 401... Curve showing evaluation amount before averaging, 402... Curve showing the evaluation amount after averaging

Claims (14)

An extreme value control that searches for an optimum value of the operation amount based on the operation amount of the control target process and an evaluation amount that indicates an index related to optimization of the control target process based on the control amount that changes according to the operation amount. An extreme value control unit for executing
An evaluation amount correction unit for correcting the evaluation amount by a predetermined correction function,
An integral coefficient updating unit for updating an integral coefficient, which is a control parameter for the extreme value control, based on the corrected evaluation amount;
Equipped with
The extreme value control unit executes the extreme value control based on the corrected evaluation amount,
Control device. The correction function is a function that corrects the evaluation function indicating the relationship between the operation amount and the evaluation amount into a function such that the variance of the second derivative becomes smaller.
The control device according to claim 1. The correction function is a function obtained by multiplying a function that is an evaluation function after correction and an inverse function of the evaluation function before correction,
The evaluation amount correction unit corrects the evaluation function by performing variable conversion of the evaluation function with the correction function, and corrects the evaluation amount based on the corrected evaluation function,
The control device according to claim 1. The evaluation amount correction unit corrects the evaluation function with a correction function according to each section for an arbitrary section of the evaluation function,
The control device according to claim 3. The evaluation amount correction unit corrects a part or all of the evaluation function by the correction function,
The control device according to claim 3 or 4. An extreme value control that searches for an optimum value of the operation amount based on the operation amount of the control target process and an evaluation amount that indicates an index related to optimization of the control target process based on the control amount that changes according to the operation amount. An extreme value control step for executing
An evaluation amount correction step of correcting the evaluation amount by a predetermined correction function,
An integral constant updating step of updating an integral coefficient, which is a control parameter of the extreme value control, based on the corrected evaluation amount;
Have
In the extreme value control step, the extreme value control is executed based on the evaluation amount after correction,
Control method. An extreme value control that searches for an optimum value of the operation amount based on the operation amount of the control target process and an evaluation amount that indicates an index related to optimization of the control target process based on the control amount that changes according to the operation amount. To the computer running
An evaluation amount correction step of correcting the evaluation amount by a predetermined correction function,
An integral coefficient updating step of updating an integral coefficient, which is a control parameter of the extreme value control, based on the corrected evaluation amount;
An extreme value control step of executing the extreme value control based on the corrected evaluation amount;
A computer program for executing. An extreme value control that searches for an optimum value of the operation amount based on the operation amount of the control target process and an evaluation amount that indicates an index related to optimization of the control target process based on the control amount that changes according to the operation amount. An extreme value control unit for executing
Based on the operation amount and the evaluation amount, a change rate calculation unit that calculates a change rate corresponding to the second-order differential value of the evaluation function indicating the relationship between the operation amount and the evaluation amount,
An integral coefficient updating unit that calculates an integral coefficient that is a control parameter for the extreme value control based on the change rate, and updates an existing integral coefficient with the calculated integral coefficient,
A control device including. The change rate calculation unit calculates a plurality of the change rates based on a plurality of operation amounts and evaluation amounts acquired in a certain period, and uses a representative value of the calculated plurality of change rates as a change rate of the period. calculate,
The control device according to claim 8. The change rate calculation unit calculates a representative value of the evaluation amount for each of a plurality of consecutive periods, and based on the calculated representative value of the plurality of evaluation amounts, calculates the change rate of the entire plurality of periods,
The control device according to claim 8. The change rate calculation unit changes the length of the period according to the tendency of increase or decrease of the change rate,
The control device according to claim 9 or 10. The change rate calculation unit removes an abnormal value from the evaluation amount acquired in the period, and calculates the change rate based on the evaluation amount from which the abnormal value is removed,
The control device according to any one of claims 9 to 11. An extreme value control that searches for an optimum value of the operation amount based on the operation amount of the control target process and an evaluation amount that indicates an index related to optimization of the control target process based on the control amount that changes according to the operation amount. An extreme value control step for executing
Based on the operation amount and the evaluation amount, a change rate calculation step of calculating a change rate corresponding to the second-order differential value of the evaluation function indicating the relationship between the operation amount and the evaluation amount,
An integral coefficient updating step of calculating an integral coefficient which is a control parameter of the extreme value control based on the change rate, and updating an existing integral coefficient with the calculated integral coefficient,
And a control method. An extreme value control that searches for an optimum value of the operation amount based on the operation amount of the control target process and an evaluation amount that indicates an index related to optimization of the control target process based on the control amount that changes according to the operation amount. An extreme value control step for executing
Based on the operation amount and the evaluation amount, a change rate calculation step of calculating a change rate corresponding to the second-order differential value of the evaluation function indicating the relationship between the operation amount and the evaluation amount,
An integral coefficient updating step of calculating an integral coefficient which is a control parameter of the extreme value control based on the change rate, and updating an existing integral coefficient with the calculated integral coefficient,
A computer program that causes a computer to execute.

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