Controller parameter calculation method, computer program, and recording medium

Abstract

Provided is a technology that enables generalized optimization of controller parameters according to FRIT while taking control constraints into account. This controller parameter calculation method comprises: an optimization step (S2) for optimizing controller parameters using an FRIT-based evaluation function that includes time-series data of an input signal and an output signal and a predetermined reference model; a prediction step (S3) for predicting a predicted input signal, which is a predicted value of the input signal, by data-driven prediction using the controller parameters calculated in the optimization step (S2); an evaluation step (S4) for evaluating whether the predicted input signal deviates from control constraints; an update step (S6) for, if the predicted input signal deviates from the control constraints, updating the reference model by global optimization using a cost function that includes a value related to the FRIT-based evaluation function and a violation amount representing the extent of deviation of the predicted input signal from the control constraints; and a step for repeating the optimization step (S2) to the reference model update step (S6).

Description

Controller parameter calculation method, computer program, and recording medium

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

[0002] For example, in process systems that use heat or fluids, PID control is widely used as a feedback control method because it is difficult to model the system from first principles due to nonlinearity and because parameter adjustment based on the behavior of the controlled object is intuitively easy to understand. However, controllers using fixed PID parameters often fail to achieve the desired control performance because it is difficult to consistently obtain good control results. Therefore, when using a PID controller, adjustments are made not only at the time of design and startup, but also as the operating conditions change.

[0003] In recent years, several methods have been proposed to achieve desired control performance without modeling the controlled object. Data-driven control is one of the most effective methods. Data-driven control is a method for 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, and for example, Non-Patent Document 1 proposes one of these variations, FRIT (Fictitious Reference Iterative Tuning). FRIT allows for adjustment of controller parameters based on experimental data obtained from a single closed-loop control experiment. Therefore, FRIT is advantageous in terms of time and cost compared to other methods that require repeated experiments.

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

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

[0007] In response to the problem of Patent Document 1, Non-Patent Document 2 proposes a method of combining FRIT with a method capable of predicting an input signal. In Non-Patent Document 2, controller parameters are optimized by FRIT using a predefined reference model (target transfer function). Then, a predicted input signal, which is a predicted value of the input signal, is calculated by data-driven prediction using the optimized controller parameters. If the calculated predicted input signal violates the control constraint, 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.

[0008] Japanese Patent Application Laid-Open No. 2021-51462

[0009] Shotaro Soma, Osamu Kaneko, Takao Fujii, A New Approach to Controller Parameter Tuning Using Single Experimental Data - Proposal of Fictitious Reference Iterative Tuning, Transactions of the Institute of Systems, Control and Information Engineers, Vol. 17, No. 12, pp. 528-536, 2004. Miku Ikezawa, Osamu Kaneko, FRIT with Reference Response Update Considering Input Constraints for Cascade Control Systems, 64th Joint Conference on Automatic Control Systems, 1A2-2, pp. 216-220, 2021.

[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 assumed 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 fast). Therefore, it is difficult to optimize the controller parameters depending on the results of the initial experiment. In other words, 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 that can generally optimize controller parameters according to FRIT while taking into account control constraints.

[0012] In order to solve the above-mentioned problems, a first aspect is a controller parameter calculation method for calculating controller parameters of a feedback control system including a controller and a controlled object that receives an output from the controller as an input, the method comprising: a) acquiring, in a real machine, time series data of an input signal input from the controller to the controlled object and an output signal output from the controlled object; b) setting a reference model of the control system; and c) using FRIT (Fictitious Reference Iterative Modeling) including the time series data and the reference model. d) predicting a predicted input signal, which 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 a control constraint; f) if the predicted input signal violates the control constraint in step e), updating the reference model by global optimization using a cost function including a value related to the evaluation function based on the FRIT and an amount of violation of the predicted input signal from the control constraint; and 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 of the first aspect, further including the step of: 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 of the third aspect, wherein the transfer function of the controller is expressed by the formula It is expressed as:

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

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

[0018] A seventh aspect is the controller parameter calculation method according to any one of the first to sixth aspects, wherein the evaluation function based on the FRIT is expressed by the formula It is expressed as:

[0019] An eighth aspect is the controller parameter calculation method according to any one of the first to seventh aspects, wherein the global optimization is Bayesian optimization.

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

[0021] A tenth aspect is the controller parameter calculation method of the ninth aspect, wherein the cost function is an equation designed so that a value relating to the evaluation function based on the FRIT is greater than the violation amount.

[0022] An eleventh aspect is a computer-readable computer program that causes the computer to execute the controller parameter calculation method of any one of the first to tenth aspects.

[0023] A twelfth aspect is a computer-readable recording medium on which the computer program of the eleventh aspect is recorded.

[0024] According to the first to twelfth aspects, when a deviation from a control constraint occurs, the reference model is updated by a global search. Therefore, the reference model can be appropriately updated without relying on initial experimental data, and therefore, controller parameters can be generally optimized.

[0025] Fig. 1 is a block diagram showing a hardware configuration of an information processing device according to an embodiment; Fig. 2 is a block diagram showing a feedback control system; Fig. 3 is a flow chart showing a process in which an information processing device calculates a controller parameter ρ; Fig. 4 is a diagram showing a flow waveform obtained by an initial experimental data acquisition step S1; Fig. 5 is a diagram showing a flow waveform obtained after optimizing the controller parameter ρ;

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

[0027] 1 is a block diagram showing the hardware configuration of an information processing device 1 according to an embodiment. The information processing device 1 is configured by a general-purpose computer on which a dedicated computer program P is installed. The information processing device 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 a computer program P and various data.

[0029] The processor 11 executes processing in accordance with a computer program stored in the storage device 13. The memory 12 is used as a work area for the processor 11. The operation device 15 inputs user 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 device 1 and for outputting data from the information processing device 1 to the outside. The input / output interface 17 is, for example, a USB interface.

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

[0032] 2 is a block diagram showing a feedback control system 100. The feedback control system 100 includes a subtractor 20, a controller 30, and a controlled object 40. The subtractor 20 inputs the 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 corresponding to the deviation E in accordance with 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 subtractor 20.

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

[0034] In the above formula (1), γ is a constant (for example, 10).

[0035] The information processing device 1 executes a process for calculating a controller parameter p of the controller 30 in the feedback control system 100. Fig. 3 is a flowchart showing the process for calculating the controller parameter p by the information processing device 1.

[0036] In the following explanation, the controlled object 40 is an electric needle valve capable of adjusting the flow rate of a fluid, and the controller 30 performs PID control of the flow rate. The opening of the electric needle valve 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 zero.

[0037] 3, the information processing device 1 first performs an initial experimental data acquisition step S1. In the initial experimental data acquisition step S1, an appropriate controller 30 (C ＰＩＤ (ρ ０ )) is used to perform flow control based on the target value r (target flow rate time series data). This allows a set of time series data to be obtained, which is a combination of the input signal u and the output signal y (flow rate). Hereinafter, the time series data of the input signal u obtained by this initial experiment will be referred to as u ０ (t), the time series data of the output signal y is ０ (t). Note that u ０ (t), y ０ The information processing device 1 may receive the input u from a recording medium such as a USB memory or via a network. ０ (t), y ０ (t) may be stored in memory 12 or storage device 13 .

[0038] Subsequently, the information processing device 1 uses the u obtained in the initial experiment data acquisition step S1 ０ (t), y ０ (t) is used to optimize the controller parameter ρ of the controller 30 (optimization step S2). In the optimization step S2, the evaluation function J defined based on the FRIT algorithm is used. ＦＲＩＴ (ρ) is used. ＦＲＩＴ(ρ) is expressed by the following equation, for example.

[0039]

[0040] T(s) shown in equation (4) is a reference model of the entire closed-loop system shown in Figure 1, and is a transfer function from the target value r to the output signal y. The reference model T(s) includes a time constant τ, an order n, and a 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 device 1 calculates the evaluation function J by a nonlinear programming optimization method. ＦＲＩＴ The controller parameter ρ that minimizes (ρ) ＊ Calculate.

[0042] Next, the information processing device 1 optimizes the controller parameter ρ ＊ is applied to the transfer function C(ρ ＊ ) to obtain a predicted input signal u, which is a predicted value of the input signal u. ｐ (Prediction step S3). Data-driven prediction is a method for adjusting controller parameters based on input / output data of a controlled object. Specifically, the method described in Non-Patent Document 2 can be applied as data-driven prediction.

[0043] In data-driven prediction, the evaluation function J FRIT The parameter θ of the reference model T(s) that minimizes (ρ) ＊ Then, the predicted input signal u is calculated using the obtained parameter θ*. ｐ According to Non-Patent Document 2, the predicted input signal u ｐ is calculated by the following formula:

[0044]

[0045] Next, the information processing device 1 evaluates whether or not the control constraints of the controlled object 40 are satisfied (control characteristic evaluation step S4). Specifically, the control constraints of the electric needle valve include, for example, an upper limit of the valve opening (u ｍａｘ) and the lower bound (u ｍｉｎ ) and the rotation speed limit of the stepping motor (Δu ｌｉｍ The upper limit of the valve opening u ｍａｘ and the lower bound u ｍｉｎ For the predicted input signal u ｐ The maximum value of max(u ｐ ) and the minimum value min(u ｐ ) is the upper limit u ｍａｘ and the lower bound u ｍｉｎ The rotation speed limit of the stepping motor is evaluated based on whether it is within the range of the predicted input signal u ｐ One step deviation Δu ｐ (=u(t+1)-u(t)) maximum value max(Δu ｐ ) is the rotation speed limit Δu ｌｉｍ It will be evaluated based on whether it meets the following criteria.

[0046] The information processing device 1 calculates a predicted input signal u based on the result of the control characteristic evaluation step S4. ｐ It is determined whether the predicted input signal u satisfies the control constraint (determination step S5). ｐ satisfies the control constraint, the information processing device 1 ends the process. ｐ does not satisfy the control constraint, the information processing device 1 executes the next reference model updating step S6.

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

[0048]

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

[0050] α and β are constants that are appropriately determined by the user. ＦＲＩＴ and J ｕ In order to align the scale of ＦＲＩＴ β is the coefficient by which the predicted input signal u ｐ does not satisfy the control constraints, ｕ The value of J ＦＲＩＴ In this example, J ＦＲＩＴ is designed so that the maximum value is β. As shown in equation (8), the violation amount J ｕ is the predicted input signal u ｐ does not satisfy the control constraints, J ＦＲＩＴ It is designed so that β is added so that the value is larger than

[0051] The information processing device 1 stores the number of times the reference model updating step S6 has been executed in the memory 12 or the storage device 13. After executing the reference model updating step S6, the information processing device 1 determines whether the number of times the reference model updating step S6 has been executed exceeds a preset number of times (determination step S7). If the number of times exceeds the preset number of times in the determination step S7, the information processing device 1 ends the processing.

[0052] In the determination step S7, if the number of executions does not exceed the predetermined number, the information processing device 1 executes the optimization step S2 again. ｐ does not satisfy the control constraints. ＊ The information processing device 1 can calculate the controller parameter ρ calculated using the reference model with the lowest cost value. ＊may be stored in the memory 12 or the storage device 13 as optimized controller parameters of the controller 30. This makes it possible to obtain controller parameters with desirable control performance.

[0053] Fig. 4 shows a flow waveform W21 obtained by the initial experimental data acquisition step S1. Fig. 5 shows a flow 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). In Figs. 4 and 5, waveforms W11 and W12 represent the output of the reference model, and the dashed line represents the target flow rate.

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

[0055] It is empirically known that when Bayesian optimization is applied to a case where there are multiple evaluation indices, the optimization is stabilized by searching the parameter space in stages. ＦＲＩＴ and the violation amount J ｕ Bayesian optimization is applied using these two indices. Furthermore, in the case of cost function J, controller parameters that do not satisfy the control constraints have a high cost value, and therefore tend to be lower in search priority. Therefore, it is possible to find parameters that satisfy the control constraints in the early stages of Bayesian optimization (small number of epochs), and then search for parameters that satisfy the control constraints in later stages to achieve the desired control performance. Therefore, stable controller parameter optimization can be performed.

[0056] 2. Modifications Although the embodiments have been described above, the present invention is not limited to the above and various modifications are possible.

[0057] For example, in the reference model updating step S6 of the above embodiment, Bayesian optimization is used as the global optimization, but other algorithms may be adopted. For example, metaheuristic methods such as a genetic algorithm or simulated annealing may be used as the global optimization.

[0058] Furthermore, 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 merely illustrative in all respects and does not limit the present invention. It is understood that countless variations not illustrated can be envisioned without departing from the scope of the present invention. The configurations described in the above embodiments and variations can be combined or omitted as appropriate as long as they are not mutually inconsistent.

[0060] 10: Information processing device 30: Controller 40: Control target 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, a controller parameter calculation method for calculating the 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; 4. The controller parameter calculation method according to claim 3, wherein the transfer function of the controller is expressed by the formula The controller parameter calculation method represented by 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; 6. The controller parameter calculation method according to claim 5, wherein the reference model is represented by the formula The controller parameter calculation method represented by 7. The controller parameter calculation method according to any one of claims 1 to 6, wherein the evaluation function based on the FRIT is represented by the formula A controller parameter calculation method represented by 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 the predicted input signal violates the control constraints in step e), 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 deviating from the control constraints of 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).

2. The controller parameter calculation method according to claim 1, further comprising: h) repeating steps d) to g) a specified number of times.

3. The controller parameter calculation method according to claim 1 or 2, wherein the controller is a PID controller.

5. The controller parameter calculation method according to claim 3 or 4, wherein the reference model includes at least a time constant, an order, and a dead time as parameters.

8. The controller parameter calculation method according to any one of claims 1 to 7, wherein the global optimization is Bayesian optimization.

9. A method for calculating controller parameters according to claim 8, wherein the cost function is the 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.

10. A method for calculating controller parameters according to claim 9, wherein the cost function is an equation designed such that the value related to the evaluation function based on the FRIT is larger than the amount of violation.

11. A computer-readable computer program that causes the computer to execute the method for calculating controller parameters according to any one of claims 1 to 10.

12. A computer-readable recording medium on which the computer program according to claim 11 is recorded.

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