Controller parameter calculation method, computer program, and recording medium

Abstract

To provide a technology that makes it possible to optimize controller parameters for general purposes according to FRIT while taking control constraints into account.SOLUTION: A controller parameter calculation method includes: an optimization step S2 for optimizing controller parameters using an evaluation function based on FRIT including time-series data on input and output signals and a preliminary determined reference model; a prediction step S3 for predicting a predictive input signal that is the predictive value of an input signal by a data drive prediction using the controller parameter calculated by the optimization step S2; an evaluation step S4 for evaluating whether the predictive input signal deviates from control constraints; an update step S6 for updating the reference model by a global optimization using a cost function including a value relating to an evaluation function based on FRIT and the amount of violation deviating from the control constraint of the predictive input signal when the predictive input signal deviates from the control constraint; and a step for repeating the reference model update step S6.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The subject matter disclosed in this specification relates to a controller parameter calculation method, a computer program, and a recording medium.

Background Art

[0002] For example, in a process system using heat or fluid, since it is difficult to model the system based on the first principle due to non-linearity, and parameter adjustment based on the behavior of the controlled object is intuitively easy to understand, PID control is widely used as feedback control. However, with a controller using fixed PID parameters, it is often difficult to always obtain good control results, so in many cases, the desired control performance cannot be achieved. Therefore, when using a PID controller, not only adjustment is performed at the time of design, startup, etc., but also readjustment is carried out in accordance with changes in usage conditions and the like.

[0003] In recent years, several methods have been proposed to satisfy the desired control performance without modeling the controlled object. Among them, data-driven control is known as one of the powerful methods. Data-driven control is a method of designing a controller that achieves a target by directly using data without using a model of the controlled object.

[0004] Several variations of data-driven control are known. For example, Non-Patent Document 1 proposes FRIT (Fictitious Reference Iterative Tuning), which is one of the variations. FRIT can adjust the controller parameters based on the experimental data obtained from a single closed-loop system control experiment. Therefore, FRIT is superior in terms of costs such as time and expenses compared to other methods that require repeated experiments.

[0005] However, even when controlling using the control parameters obtained by data-driven control such as FRIT, it may not be possible to obtain the desired control performance. In particular, when there are no control parameters that can realize the response of the reference model used in FRIT, it is known that the control system is likely to become unstable.

[0006] To address such problems, for example, Patent Document 1 proposes obtaining, by an optimization method such as particle swarm optimization, the controller parameters that minimize the squared error between the output obtained from the complementary sensitivity function and the output of the reference model set by the designer. However, when controlling using the controller obtained by FRIT, it is unclear what input signal the controller outputs to the controlled object. For this reason, it is not always guaranteed that the input signal satisfies the control constraints or that the input signal is within the range that the controller can output.

[0007] To address the problems of Patent Document 1 as described above, Non-Patent Document 2 proposes a method of combining FRIT with a method capable of predicting the input signal. In Non-Patent Document 2, the controller parameters are optimized by FRIT using a predefined reference model (target transfer function). Then, by data-driven prediction using the optimized controller parameters, a predicted input signal, which is the predicted value of the input signal, is calculated. If the calculated predicted input signal violates the control constraints, the time constant τ of the reference model (target transfer function) is increased by a predetermined amount, and the controller parameters are updated by FRIT using the updated reference model.

Prior Art Documents

Patent Documents

[0008]

Patent Document 1

Non-Patent Documents

[0009]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0010] However, in the case of the method of increasing the time constant τ of the reference model by a predetermined amount as in Non-Patent Document 2, it is premised that the time constant τ of the initial reference model is smaller than the time constant of the initial experimental data (i.e., the response is faster). Therefore, depending on the results of the initial experiment, it is difficult to optimize the controller parameters. That is, the method of Non-Patent Document 2 has a problem of low versatility in that it depends on the results of the initial experiment.

[0011] An object of the present invention is to provide a technique capable of generally optimizing controller parameters according to FRIT while considering control constraints.

Means for Solving the Problems

[0012] To solve the above problems, a first aspect is a controller parameter calculation method for calculating controller parameters in a feedback control system including a controller and a control target that takes the output from the controller as an input, the method comprising: a) in an actual machine, obtaining time series data of an input signal input from the controller to the control target and an output signal output from the control target; b) setting a reference model of the control system; c) optimizing the controller parameters using an evaluation function based on FRIT (Fictitious Reference Iterative Tuning) including the time series data and the reference model; d) predicting a predicted input signal that is a predicted value of the input signal by data-driven prediction using the controller parameters calculated in step b); e) evaluating whether the predicted input signal violates control constraints; f) when, according to step e), the predicted input signal violates the control constraints, updating the reference model by global optimization using a cost function including a value related to the evaluation function based on FRIT and the amount of violation of the control constraints by the predicted input signal; g) optimizing the controller parameters using the evaluation function including the time series data and the reference model updated in step f).

[0013] A second aspect is the controller parameter calculation method according to the first aspect, further comprising: h) repeating steps d) to g) a specified number of times.

[0014] A third aspect is the controller parameter calculation method according to the first or second aspect, wherein the controller is a PID controller.

[0015] A fourth aspect is the controller parameter calculation method according to the third aspect, wherein the transfer function of the controller is represented by the formula

Equation

[0016] The fifth aspect is the controller parameter calculation method of the third aspect, wherein the reference model includes at least a time constant, an order, and a dead time as parameters.

[0017] The sixth aspect is the controller parameter calculation method of the fifth aspect, wherein the reference model is expressed by the formula

Number

[0018] The seventh aspect is the controller parameter calculation method of the first aspect or the second aspect, wherein the evaluation function based on the FRIT is expressed by the formula

Number

Number

Number

[0019] The eighth aspect is the controller parameter calculation method of the first aspect or the second aspect, wherein the global optimization is Bayesian optimization.

[0020] The ninth aspect is the controller parameter calculation method of the eighth aspect, wherein the cost function is the sum of the value related to the evaluation function based on the FRIT and the value related to the violation amount of the predicted input signal deviating from the control constraint.

[0021] The tenth aspect is the controller parameter calculation method of the ninth aspect, wherein the cost function is designed such that the value related to the evaluation function based on the FRIT is greater than the violation amount.

[0022] The eleventh aspect is a computer-readable computer program that causes the computer to execute the controller parameter calculation method of the first aspect or the second aspect.

[0023] A 12th aspect is a computer-readable recording medium on which the computer program of the 11th aspect is recorded.

Advantages of the Invention

[0024] According to the 1st to 12th aspects, when deviating from control constraints, the reference model is updated by global search. Therefore, since the reference model can be appropriately updated without depending on initial experimental data, the controller parameters can be optimized in a general-purpose manner.

Brief Description of the Drawings

[0025]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Modes for Carrying Out the Invention

[0026] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. Note that the components described in this embodiment are merely examples and are not intended to limit the scope of the present invention thereto. In the drawings, for ease of understanding, the dimensions and numbers of each part may be exaggerated or simplified as necessary.

[0027] <1. Embodiment> FIG. 1 is a block diagram showing the hardware configuration of an information processing apparatus 1 according to an embodiment. The information processing apparatus 1 is configured by a general-purpose computer installed with a dedicated computer program P. The information processing apparatus 1 includes a processor 11, a memory 12, a storage 13, an operation device 15, a display 16, and an input / output interface 17.

[0028] The processor 11 includes, for example, a CPU. The memory 12 includes, for example, a RAM which is a semiconductor memory. The storage device 13 is an auxiliary storage device and includes, for example, a hard disk drive (HDD) or a solid state drive (SSD). The storage device 13 stores the computer program P and various data.

[0029] The processor 11 executes processing according to the computer program stored in the storage device 13. The memory 12 is used as a working area for the processor 11. The operation device 15 inputs a user's operation input to the processor 11. The operation device 15 includes, for example, a keyboard or a pointing device. The display 16 displays various information based on the control of the processor 11. The display 16 is, for example, a liquid crystal display.

[0030] The input / output interface 17 is an interface for inputting data from the outside into the information processing apparatus 1 and for outputting data from the information processing apparatus 1 to the outside. The input / output interface 17 is, for example, a USB interface or the like.

[0031] The computer program P may be stored in a non-transitory recording medium such as a semiconductor memory such as a USB memory, or an optical or magnetic medium. Then, the computer program P on the recording medium may be provided to the information processing apparatus 1 via the input / output interface 17. Also, the computer program P may be provided to the information processing apparatus 1 via a network such as the Internet.

[0032] FIG. 2 is a block diagram showing a feedback control system 100. The feedback control system 100 includes a subtracter 20, a controller 30, and a controlled object 40. The subtracter 20 inputs a deviation E (= r - y) between a target value r and an output signal y to the controller 30. The controller 30 outputs an input signal u (= C(ρ)·E) to the controlled object 40 with respect to the deviation E according to a transfer function C(ρ) having a controller parameter ρ. The output signal y from the controlled object 40 is measured by a measuring instrument (not shown) and input to the subtracter 20.

[0033] The controller 30 is a feedback controller, for example, a PID controller. The transfer function C(ρ) of the controller 30 is represented by, for example, the following equation.

[0034]

Equation

[0035] The information processing apparatus 1 executes a process of calculating the controller parameter ρ of the controller 30 in the feedback control system 100. FIG. 3 is a flowchart showing the process in which the information processing apparatus 1 calculates the controller parameter ρ.

[0036] In the following description, a case where the controlled object 40 is an electric needle valve whose fluid flow rate can be adjusted and the controller 30 performs PID control on the flow rate will be described. The electric needle valve has a valve opening that can be controlled by a stepping motor, and the controller 30 adjusts the opening so that the deviation between the flow rate, which is the output signal y, and the target flow rate, which is the target value r, becomes 0.

[0037] As shown in FIG. 3, the information processing apparatus 1 first performs an initial experiment data acquisition step S1. In the initial experiment data acquisition step S1, in an actual machine, an appropriate controller 30 (C represented by the above formula (1)) PIDUsing (ρ0), flow rate control is implemented based on the target value r (target flow rate time series data). As a result, a set of time series data that is a combination of the input signal u and the output signal y (flow rate) is acquired. Hereinafter, the time series data of the input signal u obtained by this initial experiment is denoted as u0(t), and the time series data of the output signal y is denoted as y0(t). Note that u0(t) and y0(t) may be input to the information processing apparatus 1 via a recording medium such as a USB memory or a network. Then, the processor 11 of the information processing apparatus 1 may store the input u0(t) and y0(t) in the memory 12 or the storage device 13.

[0038] Subsequently, the information processing apparatus 1 optimizes the controller parameter ρ of the controller 30 using u0(t) and y0(t) obtained in the initial experiment data acquisition step S1 (optimization step S2). In the optimization step S2, an evaluation function J FRIT (ρ) defined based on the FRIT algorithm is used. The evaluation function J FRIT (ρ) is represented by, for example, the following formula.

[0039]

Equation

Equation

Equation

[0040] T(s) shown in Equation (4) is the reference model of the entire closed-loop system shown in FIG. 1, and is the transfer function from the target value r to the output signal y. The reference model T(s) includes the time constant τ, the order n, and the dead time L.

[0041] As shown in Equation (2), the evaluation function J FRIT (ρ) is a function of the control parameter ρ. Therefore, in the optimization step S2, the information processing apparatus 1 uses a non-linear programming optimization method to minimize the evaluation function J FRIT (ρ) of the controller parameter ρ* Calculate it.

[0042] Next, the information processing apparatus 1 uses the controller parameter ρ calculated in the optimization step S2 * and predicts the predicted input signal u, which is the predicted value of the input signal u, by data-driven prediction using the transfer function C(ρ * ). (Prediction step S3). Data-driven prediction is a method of adjusting controller parameters based on the input-output data of the controlled object. Specifically, the method described in Non-Patent Document 2 can be applied as the data-driven prediction. p In data-driven prediction, the parameter θ of the reference model T(s) that minimizes the evaluation function J

[0043] FRIT (ρ) is obtained. Then, using the obtained parameter θ*, the predicted input signal u (ρ) is calculated. According to Non-Patent Document 2, the predicted input signal u * is obtained by the following equation. p According to Non-Patent Document 2, the predicted input signal u p is obtained by the following equation.

[0044]

Equation

[0045] Subsequently, the information processing apparatus 1 evaluates whether or not the control constraints of the controlled object 40 are satisfied (control characteristic evaluation step S4). Specifically, as the control constraints of the electric needle valve, for example, the upper limit (u max ) and the lower limit (u min ) of the valve opening and the rotation speed limit (Δu lim ) of the stepping motor can be mentioned. Regarding the upper limit u max and the lower limit u min of the valve opening, it is evaluated whether the maximum value max(u p ) and the minimum value min(u p ) of the predicted input signal u p are within the upper limit u max and the lower limit u min . Also, regarding the rotation speed limit of the stepping motor, the predicted input signal u pOne-step deviation Δu p (=u(t + 1)-u(t)), the maximum value max(Δu p ) is evaluated based on whether it is within the rotational speed limit Δu lim as follows.

[0046] Based on the result of the control characteristic evaluation step S4, the information processing apparatus 1 determines whether the predicted input signal u p satisfies the control constraints (determination step S5). If the predicted input signal u p satisfies the control constraints, the information processing apparatus 1 ends the process. On the other hand, if the predicted input signal U p does not satisfy the control constraints, the information processing apparatus 1 executes the next reference model update step S6.

[0047] In the reference model update step S6, the information processing apparatus 1 updates the reference model T(s) by global optimization. For global optimization, for example, Bayesian optimization can be used. The optimization targets of the reference model T(s) are the time constant τ, the order n, and the dead time L. For Bayesian optimization, for example, the cost function J expressed by the following equation can be used.

[0048]

Equation

Equation

Equation

[0049] In equations (6) to (8), J FRIT is the J FRIT in the above equation (2), J * obtained by substituting the optimized controller parameter ρ FRIT (ρ * ) multiplied by a constant α. J u is a value indicating the amount of violation of the control constraints of the predicted input signal u p . If the predicted input signal u p satisfies the control constraints, Ju is designed to be zero.

[0050] α and β are constants that are appropriately determined by the user. α is a coefficient multiplied by J FRIT to align the scales of J u and J FRIT . β is designed such that when the predicted input signal u p does not satisfy the control constraints, the value of J u becomes larger than J FRIT . In this example, J FRIT is designed such that its maximum value is β. And, as shown in Equation (8), when the predicted input signal u u does not satisfy the control constraints, β is added so that the violation amount J p is always larger than J FRIT .

[0051] The information processing device 1 stores the number of executions of the reference model update step S6 in the memory 12 or the storage device 13. Then, after executing the reference model update step S6, the information processing device 1 determines whether the number of executions of the reference model update step S6 exceeds a preset default number (determination step S7). In the determination step S7, if the number of executions exceeds the default number, the information processing device 1 terminates the process.

[0052] In the determination step S7, if the number of executions does not exceed the default number, the information processing device 1 executes the optimization step S2 again. That is, the information processing device 1 updates the reference model a default number of times as long as the predicted input signal u p does not satisfy the control constraints. Thereby, the information processing device 1 can calculate the controller parameter ρ * considering the control constraints. Note that the information processing device 1 may store the controller parameter ρ * calculated using the reference model with the lowest cost value in the memory 12 or the storage device 13 as the optimized controller parameter of the controller 30. Thereby, a controller parameter with desirable control performance can be obtained.

[0053] FIG. 4 is a diagram showing a flow rate waveform W21 obtained by the initial experimental data acquisition step S1. FIG. 5 is a diagram showing a flow rate waveform W22 obtained after optimizing the controller parameter ρ. In FIGS. 4 and 5, the horizontal axis represents time (seconds), and the vertical axis represents flow rate (ml / min). Also, in FIGS. 4 and 5, the waveforms W11 and W12 represent the outputs of the reference model, and the dashed line represents the target flow rate.

[0054] As is clear from FIGS. 4 and 5, the controller parameter ρ having desired control performance can be calculated by the flow shown in FIG. 3. In particular, in the section where the flow rate rises from 0 seconds to 2 seconds, desired control performance can be obtained.

[0055] When Bayesian optimization is applied in the case of multiple evaluation indicators, it is empirically known that the optimization becomes stable by exploring the parameter space in stages. In this embodiment, J FRIT and the violation amount J u are used as two indicators for applying Bayesian optimization. Also, in the case of the cost function J, since the cost value of the controller parameter that does not satisfy the control constraint is high, the priority of the search tends to decrease. Therefore, a parameter that satisfies the control constraint is found in the initial stage (small number of epochs) of Bayesian optimization, and it becomes possible to perform a search that satisfies the desired control performance among the parameters that satisfy the control constraint in the later stage. Therefore, stable controller parameter optimization can be performed.

[0056] <2. Modification Example> As described above, the embodiments have been described, but the present invention is not limited to the above, and various modifications are possible.

[0057] For example, in the reference model update step S6 of the above embodiment, Bayesian optimization is used as the global optimization, but other algorithms may be adopted. As the global optimization, for example, a genetic algorithm or an annealing method, which is a metaheuristic method, may be used.

[0058] Also, the controlled object 40 of the feedback control system 100 is not limited to an electric needle valve.

[0059] Although the present invention has been described in detail, the above description is illustrative in all aspects and the present invention is not limited thereto. Innumerable modifications that are not illustrated can be assumed without departing from the scope of the present invention. Each configuration described in each of the above embodiments and each modification can be appropriately combined or omitted as long as they do not conflict with each other.

Description of Reference Numerals

[0060] 10: Information processing device 30: Controller 40: Controlled object 100: Feedback control system

Claims

1. In a feedback control system including a controller and a control target that receives the output from the controller as an input, a method for calculating controller parameters of the controller, comprising: a) obtaining time series data of an input signal input from the controller to the control target and an output signal output from the control target in an actual machine; b) setting a reference model of the control system; c) optimizing the controller parameters using an evaluation function based on FRIT (Fictitious Reference Iterative Tuning) including the time series data and the reference model; d) predicting a predicted input signal that is a predicted value of the input signal by data-driven prediction using the controller parameters calculated in step b); e) evaluating whether the predicted input signal violates control constraints; f) when, according to step e), the predicted input signal violates the control constraints, updating the reference model by global optimization using a cost function including a value related to the evaluation function based on FRIT and a violation amount by which the predicted input signal violates the control constraints; g) optimizing the controller parameters using the evaluation function including the time series data and the reference model updated in step f); A method for calculating controller parameters, including the above steps.

2. The method for calculating controller parameters according to claim 1, further comprising: h) repeating steps d) to g) a specified number of times. A method for calculating controller parameters, further including the above step.

3. The method for calculating controller parameters according to claim 1 or claim 2, wherein the controller is a PID controller.

4. The method for calculating controller parameters according to claim 3, wherein the transfer function of the controller is represented by the formula 【Number 1】 A method for calculating controller parameters, represented by the above formula.

5. The method for calculating controller parameters according to claim 3, wherein the reference model includes at least a time constant, an order, and a dead time as parameters.

6. The method for calculating controller parameters according to claim 5, wherein the reference model is represented by the formula 【Number 2】 A method for calculating controller parameters, represented by the above formula.

7. The method for calculating controller parameters according to claim 1 or claim 2, wherein The evaluation function based on the FRIT is expressed by the formula 【Number 3】 【Number 4】 【Number 2】 A controller parameter calculation method represented by. **Claim 8** A controller parameter calculation method according to claim 1 or claim 2, wherein The global optimization is Bayesian optimization, a controller parameter calculation method. **Claim 9** A controller parameter calculation method according to claim 8, wherein The cost function is a sum of a value related to the evaluation function based on the FRIT and a value related to the amount of violation in which the predicted input signal deviates from the control constraint, a controller parameter calculation method. **Claim 10** A controller parameter calculation method according to claim 9, wherein The cost function is an equation designed such that a value related to the evaluation function based on the FRIT is larger than the amount of violation, a controller parameter calculation method. **Claim 11** A computer-readable computer program that causes the computer to execute the controller parameter calculation method according to claim 1 or claim 2. **Claim 12** A computer-readable recording medium, A recording medium on which the computer program according to claim 11 is recorded.

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