JP7267779B2 - Optimal control device, optimal control method and computer program - Google Patents

Description

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

In recent years, extreme value control has attracted attention as one of the methods for realizing real-time control of plants and the like. Extreme value control observes the response of the controlled variable to the manipulated variable that is intentionally changed, and updates the manipulated variable so that the evaluation value related to the controlled variable approaches the optimum value. It is a control method that searches for the quantity, and it is a model-free optimization that can control the manipulated variable of the controlled object without using a complicated model that describes the process of the controlled object (hereinafter referred to as "process to be controlled"). control technology.

On the other hand, intentionally changing the manipulated variable may destabilize the controlled variable. There is a need to suppress fluctuations in Conventionally, various attempts have been made to improve extreme value control in order to solve such problems, but a sufficient suppressing effect has not necessarily been obtained.

JP 2017-033104 A

W,Libin, C,Chen, Z,Hui, A Novel Fast Extremum Seeking Scheme Without Steady-State Oscillation. Proceedings of the 33rd Chinese Control Conference, July 28-30, 2014, Nanjing, China.

A problem to be solved by the present invention is to provide an optimum control device, an optimum control method, and a computer program capable of realizing more stable extreme value control.

The optimum control device of the embodiment has an extremum control section, a dither signal output section, and an amplitude determination section. The extreme value control unit is based on a manipulated variable of a controlled process and an evaluation quantity that is a value based on a controlled variable that changes according to the manipulated variable and is a value to be evaluated regarding optimization of the controlled process. Then, extreme value control is executed to update the manipulated variable so that the evaluated quantity approaches the optimum value. The dither signal output section outputs a dither signal that changes the manipulated variable by acting on the manipulated variable signal in the extreme value control. The amplitude determination unit determines a slope of an evaluation function, which is a function estimated based on measurement results of the operation amount and the evaluation amount and represents a relationship between the operation amount and the evaluation amount, an amplitude of the dither signal, The magnitude of the amplitude of the dither signal is determined based on the amplitude function representing the correspondence relationship between . The amplitude function outputs, in response to the input of the gradient, a value that is determined according to the gradient and is equal to or lower than a preset upper limit value as the magnitude of the amplitude of the dither signal.

FIG. 4 is a diagram showing a first configuration example of a conventional extreme value control controller in the first embodiment; FIG. 5 is a diagram showing a first operation example of a conventional extreme value control controller in the first embodiment; FIG. 5 is a diagram showing a second configuration example of a conventional extreme value control controller in the first embodiment; FIG. 5 is a diagram showing a second operation example of a conventional extreme value control controller in the first embodiment; 4 is a diagram showing a specific example of the functional configuration of the extreme value control controller of the first embodiment; FIG. FIG. 4 is a diagram showing a specific example of an amplitude function in the first embodiment; FIG. 4A and 4B are diagrams showing an operation example of the extreme value control controller according to the first embodiment; FIG. 1 is a diagram showing a configuration example of a water treatment process in a first application example in the first embodiment; FIG. FIG. 5 is a diagram showing a specific example of effects obtained by the return rate control device in the second application example in the first embodiment; The figure which shows the specific example of the functional structure of the extreme value control controller of 2nd Embodiment. FIG. 10 is a diagram showing a specific example of an amplitude function in the second embodiment; FIG. The figure which shows the specific example of the functional structure of the extreme value control controller of 3rd Embodiment. FIG. 11 is a diagram showing a specific example of an amplitude function in the third embodiment; FIG. FIG. 11 is a diagram showing an example of operation of conventional extreme value control that can be improved by the extreme value control controller of the third embodiment; The figure which shows the specific example of the functional structure of the extreme value control controller of 4th Embodiment. The figure which shows the 1st specific example of the amplitude function in 4th Embodiment. The figure which shows the specific example of the evaluation function which has several extreme values in 4th Embodiment. The figure which shows the 2nd specific example of the amplitude function in 4th Embodiment. The figure which shows the specific example of the functional structure of the extreme value control controller of 5th Embodiment. The figure which shows the operation example of the extreme value control controller of 5th Embodiment. The figure which shows the operation example of the extreme value control controller of 5th Embodiment. The figure which shows the operation example of the extreme value control controller of 5th Embodiment. The figure which shows the operation example of the extreme value control controller of 5th Embodiment. The figure which shows the operation example of the extreme value control controller of 5th Embodiment. The figure which shows the operation example of the extreme value control controller of 5th Embodiment.

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

(First embodiment)
[Overview]
FIG. 1 is a diagram showing a first configuration example of a conventional extreme value control controller. The basic concept of extreme value control is to observe the response of the controlled variable when the manipulated variable is intentionally changed, and update the manipulated variable so that the evaluated quantity based on the observed controlled variable approaches the optimum value. It is a control method that searches for the optimum operation amount that gives the optimum value of the evaluation amount. Here, the evaluation amount is a value to be evaluated for optimization in extreme value control, and is a value determined by an evaluation function based on the control amount. In this sense, the evaluation amount may be the control amount itself. In other words, extremum control is a control method in which the control point is brought closer to the extremal point of the evaluation function in which the evaluation amount is optimized by repeating the updating of the manipulated variable and the observation of the evaluation amount. can say there is.

Further, as described above, in extreme value control, a new manipulated variable is determined based on the observed value of the evaluated quantity. More specifically, in extreme value control, an evaluation function is estimated based on observed values of manipulated variables and evaluation variables. Therefore, extreme value control does not necessarily require a control model that indicates the relationship between the manipulated variable and the evaluated variable. This means that even a process whose evaluation function is an unknown function with respect to the manipulated variable can be subject to extreme value control. Therefore, extreme value control has been attracting attention in recent years as a technology that can realize automatic control of all processes. FIG. 1 illustrates the basic configuration of an extreme value control controller 1 that implements such extreme value control.

Note that the controlled process TP in FIG. 1 receives a signal (hereinafter referred to as "manipulated amount signal") u indicating an operation amount from the extreme value control controller 1, and a signal indicating an evaluation amount (hereinafter referred to as " ) represents any process acting as an unknown merit function y=f(u) for u that outputs y.

Specifically, the extreme value controller 1 includes a high-pass filter 11 (High-Pass Filter), a dither signal generator 12 (an example of a dither signal output unit), a multiplier 13, a low-pass filter 14 (Low-Pass Filter), It has an integrator 15 , an amplifier 16 and an adder 17 . The high-pass filter 11 filters the evaluation amount signal input from the controlled process TP and outputs the result to the multiplier 13 . Dither signal generator 12 generates a dither signal and outputs it to multiplier 13 and amplifier 16 . Multiplier 13 multiplies the output signal of high-pass filter 11 and the dither signal and outputs the result to low-pass filter 14 . The low-pass filter 14 filters the output signal of the multiplier 13 and outputs the filtered signal to the integrator 15 . Integrator 15 outputs a signal obtained by integrating the output signal of low-pass filter 14 to adder 17 . Amplifier 16 amplifies the dither signal and outputs it to adder 17 . The adder 17 outputs a signal obtained by adding the output signal of the integrator 15 and the output signal of the amplifier 16 to the controlled process TP as the manipulated variable signal u.

In the extreme value controller 1 configured as described above, the high-pass filter 11 has a role of removing a constant bias corresponding to the optimum value from the feedback evaluation quantity signal. Further, the dither signal generator 12 has a role of intentionally changing the operation amount and changing the evaluation amount according to the operation amount. The low-pass filter 14 has the role of extracting low-frequency components from the evaluation quantity signal multiplied by the dither signal. This makes it possible to know whether the evaluation amount has increased or decreased due to the change in the manipulated variable. The integrator 15 integrates the low-frequency component of the evaluation quantity signal extracted by the low-pass filter 14 to determine the direction of the manipulated variable that should be moved in order to bring the evaluation quantity closer to the optimum value of the evaluation function.

FIG. 2 is a diagram showing a first operation example of a conventional extreme value control controller. FIG. 2 is a simulation result of searching for the optimum value of the operation amount with the initial value of the operation amount set to 2 when the operation amount that gives the optimum value of the evaluation amount (hereinafter referred to as the “optimum value of the operation amount”) is 1. indicates From the results in Fig. 2, in the basic extreme value control method, while the value of the manipulated variable converges from the initial value of 2 to the optimum value of 1, oscillation continues even after the manipulated variable converges to the optimum value. I know it continues. This is because the amplitude of the dither signal is always constant in the extremal control of the basic configuration. In this case, even after the operation amount converges to the optimum value, the evaluation amount repeats increase and decrease, which is not preferable.

A method of changing the amplitude of the dither signal according to the state of the process to be controlled has been proposed for extremal value control with such a basic configuration (see, for example, Non-Patent Document 1).

FIG. 3 is a diagram showing a second configuration example of a conventional extreme value control controller. The extreme value controller 2 differs from the conventional extreme value controller 1 according to the first configuration example in that it includes a low-pass filter 21 instead of the low-pass filter 14 and an amplifier 22 instead of the amplifier 16 . The amplification section 22 includes a low-pass filter 221 , an amplitude determination section 222 and a multiplier 223 . In the conventional extreme value controller 2 according to the second configuration example configured in this manner, the amplification unit 22 generates a dither signal such that the amplitude increases as the rate of increase in the evaluation amount (that is, the slope of the evaluation function) increases. By amplifying , it is possible to reduce the amplitude of the manipulated variable in the convergence period.

FIG. 4 is a diagram showing a second operation example of a conventional extreme value control controller. FIG. 4 shows a simulation result of searching for the optimum value of the manipulated variable of the controlled process similar to that in FIG. 2 under the same conditions as in FIG. From the results of FIG. 4, it can be seen that in the conventional extreme value control according to the second configuration example, the swing width of the manipulated variable decreases as the manipulated variable converges to the optimum value. However, on the other hand, the amplitude of the manipulated variables increases during the transitional period from immediately after the start of the search until the manipulated variables converge to some extent. In this case, the evaluation amount also increases or decreases significantly during the transitional period until the operation amount converges, which is not preferable.

On the other hand, the extreme value controller of the first embodiment can suppress the oscillation of the manipulated variable due to the dither signal regardless of the convergence period or the transition period. The extreme value controller of the first embodiment will be described in detail below.

[detail]
FIG. 5 is a diagram showing a specific example of the functional configuration of the extreme value controller 3 of the first embodiment. The extreme value control controller 3 includes a CPU (Central Processing Unit), a memory, an auxiliary storage device, etc., which are connected via a bus, and executes programs. The extreme value controller 3 functions as an optimum control device that controls the controlled process TP by extreme value control by executing a program. Specifically, the extreme value controller 3 is an extreme value controller based on the gradient method. An adder 17 is provided. The extreme value control controller 3 differs from the basic extreme value control configuration in that it includes a low-pass filter 31 instead of the low-pass filter 14 and an amplifier 32 instead of the amplifier 16 . Since the rest of the configuration is the same as that of the basic extremal value control, the same reference numerals as in FIG. 1 are assigned to the same configurations, and the description in FIG. 5 is omitted.

Further, all or part of each function of the extreme value control controller 3 may be realized using hardware such as ASIC (Application Specific Integrated Circuit), PLD (Programmable Logic Device), FPGA (Field Programmable Gate Array), or the like. good. The 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. The program may be transmitted over telecommunications lines.

The amplification section 32 includes a low-pass filter 321 , an amplitude determination section 322 and a multiplier 323 . The low-pass filter 321 filters the output signal of the multiplier 13 and outputs the filtered signal to the amplitude determining section 322 . The amplitude determining section 322 has a function of determining the amplitude of the dither signal based on the output signal of the low-pass filter 321 . Specifically, the amplitude determining unit 322 determines the dither signal using a function (hereinafter referred to as “amplitude function”) that indicates the relationship between the rate of increase in the evaluation amount (that is, the gradient η of the evaluation function) and the amplitude A of the dither signal. determines the magnitude of the amplitude of More specifically, when the rate of increase in the evaluation amount is equal to or less than a predetermined value, the amplitude determination unit 322 increases the amplitude as the rate of increase in the evaluation amount increases, and increases the amplitude when the rate of increase in the evaluation amount exceeds the predetermined value. In this case, the magnitude of the amplitude is determined so as to keep the amplitude constant. The multiplier 323 multiplies the output signal of the amplitude determining section 322 by the dither signal, thereby amplifying the dither signal to the amplitude determined by the amplitude determining section 322 .

FIG. 6 is a diagram showing a specific example of the amplitude function in the first embodiment. The horizontal axis of the graph shown in FIG. 6 represents the gradient η of the evaluation function (rate of increase in the evaluation amount), and the vertical axis represents the amplitude A of the dither signal. Here, the gradient η of the evaluation function is given by the output signal of the low-pass filter 321 . In this case, the amplitude determination unit 322 increases or decreases the amplitude A in proportion to the slope η when the slope η is equal to or less than the threshold η _lim , and increases or decreases the amplitude A to the upper limit value when the slope η exceeds the threshold η _lim . A _max is fixed. That is, the amplitude determination unit 322 determines the amplitude of the dither signal by the variable amplitude method when the gradient η is equal to or less than the threshold, and determines the amplitude of the dither signal by the fixed amplitude method when the gradient η exceeds the threshold. do.

FIG. 7 is a diagram showing an operation example of the extreme value controller 3 of the first embodiment. FIG. 7 shows a simulation result of searching for the optimum value of the manipulated variable of the controlled process similar to that in FIG. 2 under the same conditions as in FIG. As is clear from FIG. 7, the extreme value controller 3 of the first embodiment can suppress the vibration of the manipulated variable both during the transition period and the convergence period.

According to the extreme value control controller 3 of the first embodiment configured as described above, when the rate of increase in the evaluation amount is high, the amplitude of the dither signal is prevented from increasing beyond the upper limit value, thereby Vibration of the manipulated variable can be suppressed. On the other hand, when the rate of increase in the evaluation amount is low, the oscillation of the manipulated variable during the convergence period can be suppressed by increasing or decreasing the amplitude of the dither signal as the evaluation amount increases or decreases.

Further, according to the optimum control method of the first embodiment, the range in which the amplitude of the dither signal is variable and the range in which it is fixed can be determined by the threshold value η _lim of the gradient η of the evaluation function. does not require any parameter adjustment. Therefore, it is possible to stably operate the process to be controlled while suppressing complication of the configuration, design, and the like.

In the first embodiment, _the threshold _ηmax to be set for the gradient η of the evaluation function is determined by the amplitude _Amax of the dither signal. The frequency ω, the cutoff frequency ω _l of the low-pass filter, the cutoff frequency ω _h of the high-pass filter, the gain KI of the integrator, etc., hereinafter referred to as “extremum control parameters”) are determined based on the characteristics of the controlled process. As long as it is determined appropriately, it may be determined based on any conventionally proposed guideline (see, for example, Patent Document 1).

An example in which the extreme value controller 3 of the first embodiment is applied to control a water treatment process will be described below.

(First application example)
FIG. 8 is a diagram showing a configuration example of a water treatment process in the first application example. For example, a water treatment system 400 shown in FIG. 8 is an example of a system that realizes a biological wastewater treatment process. It is a system that purifies the water to be treated in the process of sending it.

In the water treatment system 400 , the water to be treated is first sent to the sedimentation tank 41 . In the first sedimentation tank 41, solid-liquid separation of the water to be treated is performed by sedimentation. As a result, solid matter with a large specific gravity is separated from the water to be treated, and the supernatant liquid is sent to the biological reaction tank 42 in the subsequent stage. The sludge that has settled at the bottom of the sedimentation tank 41 is properly drawn out by the sludge drawing pump 411 and sent as excess sludge to the excess sludge storage tank 45 . The excess sludge sent to the excess sludge storage tank 45 is sent to a sludge treatment process (not shown) by the sludge treatment pump 451 and treated.

In the biological reaction tank 42, the action of microorganisms is used to decompose and remove unnecessary substances contained in the water to be treated. More specifically, in the biological reaction tank 42, processes such as decomposition of organic matter, removal of phosphorus, digestion of ammonia, and removal of nitrogen from the water to be treated are performed. In order to promote these treatments, the biological reaction tank 42 is equipped with a blower 421 that supplies air to the water to be treated in the tank, and a part of the surplus sludge in the final sedimentation tank 43 (hereinafter also referred to as "return sludge"). ) to the bioreactor 42 is provided. The air supply from the blower 421 activates the aerobic microorganisms in the water to be treated, and the surplus sludge is returned to maintain the necessary amount of microorganisms in the biological reaction tank 42 . The water to be treated that has been treated in the biological reaction tank 42 is sent to the final sedimentation tank 43 in the latter stage.

In the final sedimentation tank 43, solid-liquid separation of the water to be treated is carried out by sedimentation in the same manner as in the first sedimentation tank 41. As a result, solids such as activated sludge are separated from the water to be treated to some extent, and the supernatant liquid is sent to the filtration basin 44 in the subsequent stage. Further, the final sedimentation tank 43 is provided with an excess sludge pump 431 for appropriately extracting excess sludge and sending it to the excess sludge storage tank 45 .

In the filter basin 44, the water to be treated is filtered using a membrane. As a result, fine solids that could not be separated in the final sedimentation tank 43 are separated from the water to be treated. The filtered water is discharged into a river or the like as treated water (hereinafter referred to as "treated water") that has been purified.

In such a biological wastewater treatment process, control is performed by using the aeration air volume of the water to be treated by the blower 421 as an operation amount and the water quality of the treated water (for example, the nitrogen concentration or phosphorus concentration of the treated water) as a control amount. It is common to be In this case, the extreme value control controller 3 of the first embodiment inputs an evaluation amount based on the quality of the treated water, and adjusts the aeration air volume such that the evaluation amount approaches the optimum value (here, the minimum value) of the evaluation function. It can be applied as an aeration air volume control device 5 that outputs as an operation amount.

In this case, the evaluation function can be defined as a function of the nitrogen concentration and phosphorus concentration of the treated water, for example. When searching for the optimum value of the manipulated variable based on such an evaluation function, the evaluation function should have at least one extreme value for the given manipulated variable within the range from the upper limit value to the lower limit value of the aeration air flow rate. Must be set. As an example of how to set such an evaluation function, the total sum of the water quality cost based on the idea of the waste water charge, the power cost of the return sludge pump 422, and the power cost of the blower 421 (hereinafter referred to as "total cost") A method of defining the evaluation quantity is conceivable.

The power cost of the return sludge pump 422 and the blower 421 can be calculated from the flow rate of the return sludge, the rated power of the return sludge pump 422 and the blower 421, and the like. On the other hand, it is known that the nitrogen concentration and phosphorus concentration of the treated water are greatly changed by changing the return flow rate (or return rate) of the return sludge and the aeration air volume by the blower 421 . Therefore, the water quality cost can be expressed by the following equation (1), for example, as the sum of the water quality cost (TN cost) due to all nitrogen in the treated water and the water quality cost (TP cost) due to all phosphorus in the treated water.

If the aeration air volume is increased, the nitrogen removal rate is improved and the TN cost is reduced. Conversely, if the aeration air volume is decreased, the phosphorus removal rate is improved and the TP cost is reduced. In this case, minimizing the power cost does not necessarily lead to maintaining the quality of the water to be treated. Therefore, in such a case, the evaluation function may be defined as a function with the water quality cost as the total cost.

On the other hand, if there is no trade-off relationship between the water quality costs as described above, by searching for the optimum value including the power cost in the total cost, the evaluation function will be in the range from the upper limit value to the lower limit value of the aeration air volume. can be set to have at least one extremum for the manipulated variables given in .

Moreover, the water quality that the treated water should satisfy may be incorporated as a constraint in the evaluation function. For example, the evaluation function may incorporate as a constraint a function that increases the total cost if the treated water quality exceeds a predetermined regulation value. If such an evaluation function is used, the total cost will increase according to the water quality exceeding the regulation value, so it can be expected that the extreme value control will function to keep the water quality below the regulation value. .

As described in Patent Document 1 above, it is desirable that the period of the dither signal (that is, ω/2π) is set sufficiently longer than the time constant of the process to be controlled (here, the water treatment process). . This makes it possible to more accurately capture the change in the evaluation amount caused by the change in the manipulated variable due to the dither signal.

Also, for the sake of simplicity, in FIG. The amount output unit 51 may be configured as part of the aeration air amount control device 5 .

(Second application example)
As another application example, the extreme value controller 3 of the first embodiment can be applied to control the return sludge pump 422 in the water treatment system 400 . As described above, in the water treatment system 400, the TN cost and the TP cost are in a trade-off relationship with respect to the treatment capacity of microorganisms. Therefore, the TN cost and the TP cost also have a trade-off relationship with respect to the amount of return sludge returned from the final sedimentation tank 43 to the biological reactor 42 . Therefore, even when the amount of returned sludge indicated by the amount of water to be treated flowing into the biological reaction tank 42 (hereinafter referred to as "return rate") is used as the manipulated variable, the total cost is reduced as in the first modification. The evaluation function can be defined to take at least one minimum value within the possible range of the manipulated variable.

In this case, the extreme value control controller 3 of the first embodiment inputs an evaluation amount based on the quality of the treated water, and makes the evaluation amount (total cost) closer to the optimum value (here, the minimum value) of the evaluation function. can be applied as a return rate control device (not shown) that outputs a similar return rate as a manipulated variable.

FIG. 9 is a diagram showing a specific example of the effect obtained by the return rate control device in the second application example. FIG. 9A shows an example of the control result obtained by the conventional extreme value control controller according to the second configuration example, and FIG. 9B shows the control result obtained by the extreme value control controller of the present embodiment. An example result is shown. Both cases show examples in which the return rate, which was about 0.9 at the start of control, converged to about 0.2. As can be seen from these operation examples, the return rate control device of the application example is able to suppress excessive fluctuations of the manipulated variable in both the transition period and the convergence period. In particular, in the convergence period, it is possible to achieve a swing width close to zero, and it can be seen that a higher suppressing effect than the conventional extreme value control method can be obtained only by looking at the convergence period.

In the biological wastewater treatment process, the return rate is one of the factors that greatly fluctuates the water quality of the treated water. Therefore, in the conventional extreme value control method in which the swing of the manipulated variable is large in the transition period or the convergence period, it was sometimes difficult to manage the water quality of the treated water by the extreme value control of the return rate. On the other hand, the extreme value controller 3 of the first embodiment can suppress the fluctuation range of the manipulated variable from becoming excessively large in both the transition period and the convergence period. Even when extreme value control is applied, it is possible to operate the biological wastewater treatment process stably.

As described above, as application examples of the first embodiment, the first application example in which the aeration air volume is the manipulated variable and the second application example in which the return rate of excess sludge is the manipulated variable have been described. The manipulated variable in the treatment process is not limited to aeration airflow or return rate. Moreover, the two application examples described do not limit the controlled process to which the extreme value controller 3 of the first embodiment is applied to the biological wastewater treatment process. The extreme value controller 3 of the first embodiment can take any process as a process to be controlled as long as the unknown evaluation function for the manipulated variable has an extreme value within the possible range of the manipulated variable. , any manipulated variable can be the object of manipulation.

(Second embodiment)
FIG. 10 is a diagram showing a specific example of the functional configuration of the extreme value controller 3a of the second embodiment. The extreme value controller 3a differs from the extreme value controller 3 of the first embodiment in that an amplifier 32a is provided instead of the amplifier 32. FIG. Further, the amplifying section 32a differs from the amplifying section 32 in the first embodiment in that it includes an amplitude determining section 322a instead of the amplitude determining section 322. FIG. Since other configurations are the same as those of the extreme value controller 3 of the first embodiment, similar configurations are denoted by the same reference numerals as those in FIG. 5, and description thereof with reference to FIG. 10 is omitted.

The amplitude determining unit 322a in the first embodiment sets the amplitude of the dither signal to a fixed value (upper limit) for gradients η exceeding a predetermined value, while for gradients η less than a predetermined value. On the other hand, the amplitude of the dither signal is set to a variable value proportional to the gradient _η . 1 differs from the amplitude determination unit 322 in the first embodiment. It should be noted that the upper limit of the saturation function may be any value equal to or lower than the upper limit A _max , and the upper limit of the upper limit A _max is not necessarily the upper limit.

FIG. 11 is a diagram showing a specific example of the amplitude function in the second embodiment. For example, the saturation function F(η) shown in FIG. 11 is a sigmoid function having an upper bound on A=A _lim and is expressed by the following equation (2). where A represents the amplitude of the dither signal.

By using such a sigmoid function, it is possible to greatly vary the amplitude of the dither signal when η is small, and to maintain the amplitude of the dither signal close to the upper limit A _lim when η is large.

Also, by defining the saturation function as shown in Equation (3) below, the absolute value of the gradient η can be applied to Equation (2), so the amplitude of the dither signal can always be kept positive. becomes. As a result, it is possible to prevent the search direction from being changed when the amplitude of the dither signal becomes a negative value, and to prevent the control from becoming unstable.

According to the extreme value control controller 3a of the second embodiment configured as described above, in addition to being able to suppress the vibration of the manipulated variable in both the transition period and the convergence period, the manipulated variable in the transition period, the convergence period, and near the boundary can be expected to be further suppressed than in the first embodiment.

This effect is due to the amplitude determining section 322a determining the amplitude of the dither signal using a saturation function that smoothly changes according to the gradient η. In that sense, the saturation function has an upper limit of the amplitude A _lim , and the smaller the rate of increase in the evaluation amount (that is, the slope η of the evaluation function), the larger the slope. It is not necessarily a sigmoid function as long as it is a function that approaches zero (that is, asymptotically approaches an upper bound) and determines an amplitude A that changes smoothly with respect to the gradient η. For example, the saturation function may be a function that joins multiple functions smoothly and satisfies the above conditions.

(Third embodiment)
FIG. 12 is a diagram showing a specific example of the functional configuration of the extreme value controller 3b of the third embodiment. The extreme value controller 3b differs from the extreme value controller 3 of the first embodiment in that it includes an amplifier 32b instead of the amplifier 32. FIG. Further, the amplifying section 32b differs from the amplifying section 32 in the first embodiment in that it includes an amplitude determining section 322b instead of the amplitude determining section 322. FIG. Since other configurations are the same as those of the extreme value controller 3 of the first embodiment, similar configurations are denoted by the same reference numerals as in FIG. 5, and descriptions thereof with reference to FIG. 12 are omitted.

When the rate of increase in the evaluation amount (gradient η of the evaluation function) is equal to or less than a predetermined value, the amplitude determination unit 322b increases the amplitude as the rate of increase in the evaluation amount increases, and determines that the rate of increase in the evaluation amount exceeds the predetermined value. When the amplitude exceeds a predetermined value, the amplitude determination unit 322 determines the magnitude of the amplitude so as to keep the amplitude constant. is different from the amplitude determining section 322 in the first embodiment in that the amplitude of the dither signal can be determined using a monotonically increasing function of . Specifically, the amplitude determination unit 322b includes a first determination unit 3221 that determines the magnitude of the amplitude for the gradient η that is less than or equal to a predetermined value, and a second determination unit that determines the magnitude of the amplitude for the gradient η that exceeds the predetermined value. 3222;

FIG. 13 is a diagram showing a specific example of the amplitude function in the third embodiment. For example, the amplitude function in the third embodiment is given as a junction function F(η) between an nth-order function (n>0) and a zeroth-order function as shown in FIG. This amplitude function F(η) is represented, for example, by the following equation (4). Equation (4) is obtained by joining a P-order function F1 defined by a power exponent P (>0) and a coefficient r (>0) and a 0-order function F2 at η=1. FIG. 13 shows an example in which the values of P are 1, P1, and P2. Here, P1>1 and 0<P2<1.

The amplitude function F(η) defined in this way becomes the amplitude function similar to that of the first embodiment when P=1, while the variable region (0≤η ≤η _lim ), and when P>1, the amplitude in the variable region increases exponentially. Therefore, when 0<P<1, the amplitude in the variable region is larger than when P=1, and when P>1, it is smaller than when P=1.

In this case, the first determining unit 3221 determines the amplitude of the dither signal for η in the range of 0≦η≦η _lim and the second determining unit 3222 determines the amplitude of the dither signal for η in the range of η _lim <η. , the amplitude determination unit 322b functions as a whole to determine one magnitude of the amplitude of the dither signal for any value of η.

FIG. 14 is a diagram showing an operation example of conventional extreme value control that can be improved by the extreme value control controller 3b of the third embodiment. In the first embodiment or the second embodiment, by determining the amplitude of the dither signal using the amplitude functions shown in FIGS. 6 and 11, the oscillation of the manipulated variable is can be suppressed, but depending on the settings of the extreme value control parameters, the state of the controlled process, etc., the oscillation of the manipulated variable may not always be sufficiently suppressed. Such a situation is considered to occur because the speed at which the amplitude of the dither signal changes and the speed at which the evaluation quantity converges to the optimum value (hereinafter referred to as "convergence speed") are not balanced.

[Case 1]
For example, as shown in FIG. 14A, the magnitude of the amplitude becomes close to zero before the manipulated variable converges to the optimum value (here, 1), and the search for the optimum value does not proceed any further. Situations may arise. Such a situation is considered to occur because the speed at which the amplitude of the dither signal is reduced (hereinafter referred to as "amplitude reduction speed") is too fast for the convergence speed of the evaluation amount.

Therefore, in such a case, by slowing down the amplitude reduction speed in a region away from the convergence point (that is, η=0) (for example, the region of η _lim /2<η<η _lim ), dithering in the variable amplitude region can be achieved. The amplitude function can be changed to make the signal amplitude larger. For example, if _this problem occurs with the amplitude function shown in FIG. By changing to a convex P-order function (0<P<1), the amplitude of the dither signal can be increased.

[Case 2]
On the other hand, as shown in FIG. 14B, a situation may occur in which the operation amount remains vibrated even though the operation amount has converged to the optimum value. Contrary to the case of FIG. 14A, such a situation is considered to occur because the amplitude reduction speed of the dither signal is too slow with respect to the convergence speed of the evaluation amount. Therefore, in such a case, by increasing the speed of amplitude reduction in a region away from the convergence point (for example, η _lim /2<η<η _lim ), the amplitude of the dither signal in the variable amplitude region should be made smaller. , the amplitude function should be changed to For example, if _this problem occurs with the amplitude function shown in FIG. By changing to a convex P-order function (1<P), the amplitude of the dither signal can be reduced.

Here, the amplitude function in the first embodiment is defined as a P-th order function of P=1 as shown in Equation (4), and the amplitude function is changed by changing the power exponent P. , the changed amplitude function may be replaced with any other function as long as it satisfies the following conditions for the variable amplitude region.

[Case 1]
・It is an upwardly convex function (in other words, a function whose second derivative value is a negative value).
・It is a function that monotonically increases below the upper limit of amplitude.
[Case 2]
・It is a downwardly convex function (in other words, a function whose second-order differential value is a positive value).
・It is a function that monotonically increases below the upper limit of amplitude.

The extreme value controller 3b of the third embodiment configured in this manner is configured to be able to change the amplitude function used when determining the magnitude of the amplitude of the dither signal. According to such an extreme value control controller 3b, the operation manager of the process to be controlled can change the amplitude of the dither signal by switching the amplitude function according to the search condition of the optimum value, the oscillation condition of the manipulated variable, and the like. Since it is possible to adjust the balance between the speed of convergence and the convergence speed of the evaluation quantity, it is possible to improve the searchability of extremal control and more effectively suppress the oscillation of the manipulated variable due to the dither signal. becomes.

In addition, when extreme value control does not function properly as in cases 1 and 2 above, the operation manager of the controlled process must find appropriate control conditions through trial and error. There is also Such work involves redesigning and testing the extreme value control parameters, and thus becomes a very heavy work load. On the other hand, the extreme value controller 3b of the third embodiment can finely adjust the behavior of the extreme value control only by changing the amplitude function without changing the extreme value control parameters. . Therefore, according to the extreme value control controller 3b of the third embodiment, it is also possible to reduce the labor involved in the operation management of the controlled process, the design of the extreme value control, and the like.

In the third embodiment, the method of changing the amplitude function (see FIG. 6) in the first embodiment was taken as an example. Any function may be defined as long as it does not hinder the convergence of the value search and the suppression of the oscillation of the manipulated variable. For example, the amplitude function before modification may be defined as the saturation function (see equation (2) and FIG. 11) in the second embodiment. In this case, the amplitude function can be changed, for example, by changing the parameter value of the sigmoid function (for example, the coefficient of the variable x), and the amplitude reduction speed before and after the change can be made different.

Also, if the amplitude function is defined as a function including a power term as in Equation (4), extreme value control may become unstable depending on the values of the power exponent P and the gradient η. For example, if the slope η is given as a negative value for an amplitude function in which P is not an integer, the amplitude A cannot be calculated as a real value. Also, for an amplitude function in which P is an odd number equal to or greater than 1, the amplitude A can be calculated as a real value even when the slope η is given as a negative value. value. To avoid such a situation, the amplitude function should be defined as a function that inputs the absolute value |η| of the gradient η. However, when the value of the amplitude A is always a real and positive value, such as when P is an even number of 2 or more, the amplitude function is defined as a function that inputs the actual value of the slope η instead of the absolute value. good too.

(Fourth embodiment)
FIG. 15 is a block diagram showing a specific example of the functional configuration of the extreme value controller 3c of the fourth embodiment. The extreme value controller 3c differs from the extreme value controller 3 of the first embodiment in that an amplifier 32c is provided instead of the amplifier 32. FIG. Further, the amplifying section 32c differs from the amplifying section 32 in the first embodiment in that it includes an amplitude determining section 322c instead of the amplitude determining section 322. FIG. Since other configurations are the same as those of the extreme value controller 3 of the first embodiment, similar configurations are denoted by the same reference numerals as those in FIG. 5, and description thereof with reference to FIG. 15 is omitted.

The amplitude determination unit 322c determines the magnitude of the amplitude of the dither signal using a variable amplitude method when the rate of increase in the evaluation amount (slope η of the evaluation function) is equal to or less than a predetermined value, and the rate of increase in the evaluation amount is determined by the predetermined value. is the same as the amplitude determination unit 322 in the first embodiment in that the magnitude of the dither signal amplitude is determined by a fixed amplitude method when exceeding a predetermined value. It differs from the amplitude determining section 322 in the first embodiment in that it has an amplitude region. Specifically, the amplitude determination unit 322c includes a switch 3223 that switches the output destination of the gradient η according to the magnitude of the gradient η, and a plurality of determination units 3224 that output the magnitude of the amplitude according to the value of the gradient η. , provided. FIG. 15 shows first to N-th (N is an integer equal to or greater than 2) determination units 3224-1 to 3224-N as an example of the plurality of determination units 3224. FIG.

FIG. 16 is a diagram showing a first specific example of the amplitude function in the fourth embodiment. For example, the amplitude function F(η) in the first specific example is a first fixed value that sets the amplitude of the dither signal to a first upper limit value A _max1 in a region where the gradient η of the evaluation function exceeds η _lim . It is expressed as a function having an amplitude region and a second fixed amplitude region with a second upper limit _Amax2 .

For example, in this case, if the value of the gradient η of the evaluation function input from the low-pass filter 321 is in the range of 0≦η≦η _lim1 , the switch 3223 outputs the value to the first determination unit 3224-1. , if the value of the gradient η is in the range of η _lim1 ≦η≦η _{lim2 ,} the value is output to the second determining unit 3224-2; 3 determination unit 3224-3.

In this case, the first determining unit 3224-1 is configured to output the value of αη as the magnitude of the amplitude of the dither signal in response to the input of the value of the gradient η. Also, in this case, the second determining unit 3224-2 is configured to always output the value of _Amax1 as the magnitude of the amplitude of the dither signal regardless of the value of the gradient η. Similarly, the third determining unit 3224-3 is configured to always output the value of _Amax2 as the magnitude of the amplitude of the dither signal regardless of the value of the gradient η. With such a configuration, the amplitude determination unit 322c as a whole functions to determine one amplitude of the dither signal for any value of η.

The extreme value controller 3c of the fourth embodiment configured in this way evaluates the magnitude of the amplitude of the dither signal when the rate of increase in the evaluation amount (slope η of the evaluation function) exceeds a predetermined value. It can be a fixed value depending on the rate of increase of the amount. With such a configuration, the extreme value controller 3c of the fourth embodiment can search for a more appropriate optimum value even when the evaluation function has a plurality of optimum values.

FIG. 17 is a diagram showing a specific example of an evaluation function having multiple extreme values. The evaluation function shown in FIG _. 17 is a function that takes a minimum value _y1 at the manipulated variable _u1 and a minimum value _y2 that is smaller than the minimum value y1 at the manipulated variable _u2 . In this case, the optimal value of the evaluation quantity is _y2 . For such an unknown evaluation function, when the search for the optimum value is started from the right side of the manipulated variable u ₂ , the minimum value y ₂ is searched by the method described in the first to third embodiments. However, if the search for _the optimum value starts from the left side _of the manipulated variable _u1 , the search ends when the manipulated variable reaches _u1 . unable to reach.

In such a case, it may be possible to cause the manipulated variable to exceed _u1 and converge to _u2 , which gives the optimum value _y2 , by oscillating the manipulated variable more greatly. For example, for the evaluation function shown in FIG. 17, it is assumed that the operation amount converges to _u1 after the search for the optimum value based on the amplitude function (see, for example, FIG. 6) in the first embodiment is started from point P1. . In this case, if it is assumed that the evaluation function has a minimum value _y2 different from the evaluation value _y1 , the amplitude of the dither signal at the start of the search is set to an upper limit value larger than the upper limit value _Amax1 in FIG. By setting the value to A _max2 , the manipulated variable can be brought closer to another optimum value (here, u ₂ ) before the extreme value control starts to converge.

On the other hand, it is also possible to bring the manipulated variable closer to another optimum value (here, u ₂ ) after the extreme value control begins to converge. FIG. 18 is a diagram showing a second specific example of the amplitude function in the fourth embodiment. The amplitude function F(η) in the second specific example is obtained by changing part of the variable amplitude region of the amplitude function (eg, see FIG. 6) in the first embodiment to a fixed amplitude region. When such an amplitude function is used, after starting the search for the optimum value from the point P1, the amplitude of the dither signal becomes variable once in the process in which the evaluation amount approaches the minimum value _y1 , and then is fixed again. It will be returned to amplitude. As a result, the manipulated variable can be prevented from converging to u ₁ and brought closer to the optimum value (here, u ₂ ).

According to the extreme value control controller 3c of the fourth embodiment configured as described above, even when it is assumed that the evaluation function has a plurality of extreme values, the evaluation amount is reduced while suppressing the vibration of the operation amount. It is possible to adjust the amplitude of the dither signal to converge to other optimal values.

In the fourth embodiment, two fixed amplitude regions with different upper limits are defined in the amplitude function, but the number of fixed amplitude regions defined in the amplitude function and the magnitude of the fixed amplitude It may be changed as appropriate according to the assumed shape of the evaluation function, the number of extreme values, the starting point of the extreme value search, and the like.

(Fifth embodiment)
FIG. 19 is a diagram showing a specific example of the functional configuration of the extreme value controller 3d of the fifth embodiment. The extreme value controller 3d of the fifth embodiment is obtained by applying the amplifier 32 similar to that of the first embodiment to the extreme value controller based on Newton's method. Specifically, the extreme value controller 3d includes an extreme value controller 33 based on Newton's method, a dither signal generator 12 that outputs a dither signal to act on the manipulated variable signal output by the extreme value controller 33, and a dither and an amplifier 32 that amplifies the signal in the same manner as in the first embodiment.

On the other hand, as described above, the extreme value controller 3 of the first embodiment includes the high-pass filter 11, the multiplier 13, the low-pass filter 31, the integrator 15, and the adder 17 as the extreme value controller 30 based on the gradient method. Prepare. That is, the extremum controller 33 based on the Newton's method further includes multipliers 331 and 332, low-pass filters 333 and 334, and a signal adder 335, and includes an integrator 15d in place of the integrator 15. It is different from the extremum control part based on

20 to 25 are diagrams showing operation examples of the extreme value controller 3d of the fifth embodiment. FIG. 20 shows an example of operation when a quadratic function is assumed as the evaluation function, and FIG. 21 shows an example of operation when a quintic function is assumed as the evaluation function. Further, FIG. 22 shows an example of operation when the optimum value fluctuates in the evaluation function assuming a quintic function, and FIG. 23 shows an example of operation when the optimum value fluctuates in the evaluation function assuming a 0.5-order function. show. FIG. 24 shows an example of operation when a sign-inverted normal distribution function is assumed as the evaluation function, and FIG. 25 shows an example of operation when an asymmetric nonlinear function is assumed as the evaluation function.

In any of FIGS. 20 to 25, the left figure shows the control result of the conventional variable amplitude method, and the right figure shows the control result by the extreme value controller 3d of the fifth embodiment. . As can be seen from the operation examples of FIGS. 20 to 25, the method of determining the amplitude of the dither signal by selectively using the variable amplitude method and the fixed amplitude method according to the gradient η of the evaluation function is extremal value control based on the gradient method. It was confirmed that it is effective not only for the methods (for example, the first to fourth embodiments) but also for the extremum control method (for example, the fifth embodiment) based on Newton's method.

The extreme value controller 3d of the fifth embodiment configured as described above can suppress the oscillation of the manipulated variable in the transition period and the convergence period even in the extreme value control method based on Newton's method.

According to at least one embodiment described above, the slope of the evaluation function, which is a function estimated based on the measurement results of the manipulated variable and the evaluated quantity and represents the relationship between the manipulated variable and the evaluated quantity, and the amplitude of the dither signal More stable extreme value control can be achieved by having an amplitude determination unit that determines the magnitude of the amplitude of the dither signal based on the amplitude function representing the correspondence between .

(Modification)
In the extreme value control controller of each of the above-described embodiments, the amplitude determining section may be implemented by hardware or by software. Further, when the amplitude determination unit is realized by software, the extreme value controller stores the setting information of the amplitude function in a storage device such as a magnetic hard disk device or a semiconductor storage device, and the amplitude determination unit receives the setting information from the storage device. may be configured to obtain Further, in this case, the extreme value controller may be configured to include an input unit that receives an operation to change the amplitude function, and a setting update unit that updates the setting information of the amplitude function according to the input. Furthermore, in this case, the extreme value controller may be configured to include a display section for displaying the content of the setting information.

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.

Reference Signs List 1 conventional extremum control controller 11 high-pass filter 12 dither signal generator 13 multiplier 14 low-pass filter 15, 15d integrator 16 amplifier 17 adder 2 Extremum controller of conventional example 21 Low-pass filter 22 Amplifier 221 Low-pass filter 222 Amplitude determining unit 223 Multiplier 3, 3a, 3b, 3c, 3d Extremum controller 30 ... extreme value control unit based on the gradient method, 31 ... low-pass filter, 32, 32a, 32b, 32c ... amplification section, 321 ... low-pass filter, 322, 322a, 322b, 322c ... amplitude determination section, 3221 ... first determination section, 3222 Second decision unit 323 Multiplier 33 Extremum control unit based on Newton's method 331, 332 Multiplier 333, 334 Low-pass filter 335 Signal adder 400 Water treatment system 41 ... primary sedimentation basin, 411 ... sludge extraction pump, 42 ... biological reaction tank, 421 ... blower, 422 ... return sludge pump, 43 ... final sedimentation basin, 431 ... excess sludge pump to send, 44 ... filtration basin, 45 ... excess sludge storage Tank 451 Sludge treatment pump 5 Aeration air volume control device 51 Evaluation amount output unit

Claims (6)

The evaluation amount is based on a manipulated variable of a controlled process and an evaluation amount that is a value based on a controlled variable that changes according to the manipulated variable and is a value to be evaluated regarding optimization of the controlled process. an extreme value control unit that executes extreme value control to update the manipulated variable so as to approach an optimum value;
a dither signal output unit that outputs a dither signal that changes the manipulated variable by acting on the manipulated variable signal in the extreme value control;
Represents a correspondence relationship between a slope of an evaluation function, which is a function estimated based on the measurement results of the operation amount and the evaluation amount and represents the relationship between the operation amount and the evaluation amount, and the amplitude of the dither signal. an amplitude determination unit that determines the magnitude of the amplitude of the dither signal based on an amplitude function;
with
The amplitude function outputs an output value that is determined according to the gradient and that is equal to or lower than a preset upper limit value as the magnitude of the amplitude of the dither signal, with respect to the input of the gradient.
optimum controller. The amplitude function is represented by a function that monotonically increases the magnitude of the amplitude up to a gradient value that gives the upper limit, and that after the gradient value, the magnitude of the amplitude is the upper limit.
2. The optimal control device according to claim 1. The amplitude function has a plurality of gradient ranges for outputting the magnitude of the amplitude of the dither signal as a constant value equal to or lower than the upper limit value.
3. The optimum control device according to claim 1 or 2. an input unit that receives input of an operation to change the amplitude function;
a setting update unit that updates setting information of the amplitude function according to the input;
4. The optimal controller of any one of claims 1-3, further comprising: the computer
The evaluation amount is based on a manipulated variable of a controlled process and an evaluation amount that is a value based on a controlled variable that changes according to the manipulated variable and is a value to be evaluated regarding optimization of the controlled process. an extreme value control step of executing extreme value control to update the manipulated variable so as to approach an optimum value;
a dither signal output step of outputting a dither signal that changes the manipulated variable by acting on the manipulated variable signal in the extreme value control;
Represents a correspondence relationship between a slope of an evaluation function, which is a function estimated based on the measurement results of the operation amount and the evaluation amount and represents the relationship between the operation amount and the evaluation amount, and the amplitude of the dither signal. an amplitude determining step of determining the amplitude magnitude of the dither signal based on an amplitude function;
An optimal control method for executing
The amplitude function outputs an output value that is determined according to the gradient and that is equal to or lower than a preset upper limit value as the magnitude of the amplitude of the dither signal, with respect to the input of the gradient.
Optimal control method. A computer program for causing a computer to function as the optimum control device according to any one of claims 1 to 4.

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