Controller design method

Abstract

To estimate estimated output values regardless of the linearity / non-linearity of a controller and design the optimal control parameters of the controller using the estimated output values in a controller design method that uses estimated output values to design optimal control parameters.SOLUTION: In a closed-loop control system in which a control signal from a controller is input as a control input to a controlled object and an output of the controlled object is fed back to the controller, the controller design method of the present invention comprises: data-driven simulation step (P1) in which an output is simulated based on time-domain calculations using experimental data on the input and output of the controlled object to obtain an estimated output value y; and optimal control parameter design step (P2) in which the estimated output value y obtained in the data-driven simulation step is used for determining optimal control parameters for the controller.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a controller design method for determining optimal control parameters of a controller. [Background technology]

[0002] In conventional control approaches, a control system model is identified, a controller that satisfies predetermined control characteristics is designed based on the identified control system model, and the control characteristics are verified through experiments. However, for actual control systems, there are issues such as the difficulty of identifying the control system model, as it is sometimes impossible to obtain an open-loop response and the long time required for experiments.

[0003] To address these issues, the use of data-driven control, which adjusts controllers directly from experimental data without obtaining a control object model, is being considered. Data-driven control is a type of control that optimizes control parameters so that a closed-loop system approaches a reference model based only on data obtained from a single experiment. Known examples of this type of control include VRFT and FRIT.

[0004] As an alternative to the data-driven control approach, data-driven control simulation has been proposed. Data-driven control simulation provides input data and output data of the controlled object (plant) and the desired control input, and estimates the response output of the controlled object based on this data.

[0005] Known data-driven control simulations include those based on the subspace method (Non-Patent Documents 1 and 2) and those not based on the subspace method (Non-Patent Documents 3, 4, and 5). Simulations based on subspace models require output data from the controlled object (plant) to deal with non-linear control inputs, and the computational cost of matrix inversion becomes excessive. On the other hand, simulations not based on the subspace method cannot take into account the non-linearity of the controller.

[0006] Another simulation-based output estimation method has been proposed, which includes a step of determining the periodic input / output response of the controlled object based on a single trial, and a step of determining the response of the controlled object to a target control signal based on an arithmetic expression. In this output estimation method, the frequency components of the input / output response of the feedback system are determined from the Fourier transform of experimental data and the frequency characteristics of the controller, and the determined frequency components are then subjected to an inverse Fourier transform to determine the virtual time response (Patent Document 1, Non-Patent Document 5). [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Patent Publication No. 2021-43573 [Non-patent literature]

[0008] [Non-Patent Document 1] I. Markovsky, JC Willems, P. Rapisarda, and BLDMoor, “Data driven simulation with applications to system identification,” IFAC Proceedings Volumes, vol.38, no.1 pp.970-9725.2005. [Non-patent document 2] I. Markovsky, and P. Rapisarda, “Data driven simulation and Control,” International Journal f Control, vol. 81, no. 12 pp. 1946-1959, 2008. [Non-patent document 3] O. Kaneko and T. Nakamura, “Data-driven prediction of 2dof control systems with updated feedforward controller,” in 2017 56th Annal Conference of the Society of Instrument and Control Engineers of Japan (SICE), pp. 259-262,20717 [Non-patent document 4] R. Hoogendijk, M. van de Molengraft, A. den Hamer, G. Angelis, and M. Steinbuch, “Computation of transfer function data from frequency response data with application to data-based root-locus,” Control Engineering practice, vol.37.pp.20-31, 2015 [Non-Patent Document 5] M. Kosaka, A. Kosaka, and M. Kosaka, “Virtual time-response base iterative gain evaluation and redesign,” IFAC-PapersOnLine, vol.53, no. 2, pp. 3946-3952,2020 Summary of the Invention [Problem to be solved by the invention]

[0009] Although data-driven control simulations proposed so far have the advantage of not requiring the construction of a controlled object (plant), they have issues related to the nonlinearity of systems that include controllers. For example, there are issues related to nonlinearity, such as the need for output data from the controlled object (plant) to deal with nonlinear control inputs, and the inability to handle nonlinearity in closed-loop systems.

[0010] FIG. 24 shows a system controlled by the V-tiger (Virtual time-response base iterative gain evaluation and redesign) method of Non-Patent Document 5.

[0011] 24A shows a closed loop system 100A in which the V-tiger method can be implemented. The closed loop system 100A converts a control signal of a controller C(z, θ) into an input signal U(z) for a controlled object P(z). in (z), and the output signal Y of the controlled object P(z) out A closed-loop control system is constructed in which (z) is fed back to the controller C(z, θ). In this closed-loop control system, the V-tiger method can be executed, provided that the controller C(z, θ) is linear.

[0012] On the other hand, Fig. 24B shows a closed loop system 100B in which the V-tiger method is not feasible. The closed loop system 100B, like the closed loop system 100A, uses the control signal of the controller C(z, θ) as the input signal U in (z), and the output signal Y of the controlled object P(z) out A closed-loop control system is constructed in which the input signal U(z, θ) is fed back to the controller C(z, θ). However, the controller C(z, θ) has a nonlinear element, and the control object P(z) receives the input signal U(z, θ) which has a nonlinear element. in (z) is input. In the closed loop system 100B having such a nonlinear element, the V-tiger method cannot be applied.

[0013] Furthermore, although the output estimation method of Patent Document 1 does not require a transfer function model of a reference model, the estimated output value y includes the transfer function K of the controller, which poses a problem that it cannot handle cases where the transfer function of the controller has nonlinearity.Furthermore, the output estimation method of Patent Document 1 is a method that handles periodic input / output signals, which also poses a problem that it cannot handle non-periodic signals.

[0014] The present invention aims to solve the above-mentioned problems of output estimation in a controller design method for designing optimal control parameters using estimated output values, to estimate estimated output values ​​regardless of the linearity / non-linearity of the controller, and to design optimal control parameters of the controller using the obtained estimated output values. [Means for solving the problem]

[0015] In a closed-loop control system in which a control signal from a controller is input as a control input to a controlled object and an output from the controlled object is fed back to the controller, the controller design method of the present invention includes the steps of: (P1) a data-driven simulation step of performing a time domain calculation using experimental data of input and output of a control target, simulating an output based on the time domain calculation, and obtaining an estimated output value y; (P2) an optimal control parameter design process for determining optimal control parameters of the controller using the estimated output value y obtained in the data-driven simulation process; Equipped with.

[0016] (P1) Data-driven simulation process In the data-driven simulation process, a first convolution value is obtained by performing a convolution operation in the time domain between an estimated input value u obtained in a simulation of the controlled object and experimental output data y0 obtained in an experiment on the controlled object, and a second convolution value is obtained by performing a convolution operation in the time domain between an estimated output value y obtained in a simulation of the controlled object and experimental input data u0 obtained in an experiment on the controlled object, and an estimated output value (y) of the controlled object at the next sampling time is estimated from the difference between the two convolution values, the first convolution value and the second convolution value.

[0017] In a more detailed data-driven simulation process, An experiment process for collecting and storing sampled values ​​of experimental input data u0 and experimental output data y0 obtained in an experiment to be controlled; a simulation step of inputting a reference value r to the controller to perform a simulation to obtain an output signal of the controller, and calculating and storing the output signal of the simulation as an estimated input value u for the controlled object; a simulation step of an estimated output value to obtain an estimated output value y of the controlled object; The process comprises the following steps.

[0018] The simulation process for the estimated output value is as follows: calculating a first convolution value by performing a convolution operation in the time domain on estimated input values ​​u from sampling times 0 to k−1 obtained in the simulation step of the estimated input values ​​and experimental output data y0 from sampling times k to 1 obtained in the experimental step; calculating a second convolution value by performing a convolution operation in the time domain on the estimated output value y from sampling time 0 to k-1 obtained in the simulation step of the estimated output value and the experimental input data u0 from sampling time k to 1 obtained in the experimental step; The difference between the first convolution calculation value and the second convolution calculation value is calculated, and an estimated output value y(k) of the controlled object at sampling time k is calculated from the calculated difference.

[0019] (P2) Optimal control parameter design process The optimal control parameter design process is based on the following design approach: (p1) Direct optimization approach, (p2) Iterative optimization approach, and (p3) Three types of optimization approaches for single calculation approaches Equipped with.

[0020] (p1) Direct optimization approach The direct optimization approach is an optimization approach that uses an evaluation function suitable for direct application of the estimated output value y obtained in the data-driven simulation process, and applies a heuristic algorithm as an optimization solver to find the control parameters that minimize the evaluation function.

[0021] Evaluation function J for evaluating the response of the controlled object by the controllerDO As (θ), the following equation (1) is used, which is expressed as the 2-norm of the difference between the reference value r(k) and the estimated output value y(k).

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[0022] Evaluation function J DO The optimal control parameter θ of the controller that minimizes (θ) * is calculated by the following equation (2) using the reference value r and the estimated output value y estimated in the data-driven simulation process.

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[0023] Evaluation function J DO The optimal control parameter θ of the controller that minimizes (θ) * The Nelder-Mead method can be applied as a heuristic algorithm to obtain

[0024] (p2) Iterative optimization approach In the iterative optimization approach, when the performance index is differentiable with respect to the control parameter θ, the optimal control parameter θ of the controller is * can be found using the gradient method.

[0025] Target output value y for reference value r d is the product of the nominal model M(z) and the reference value r according to the following equation (3):

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[0026] Evaluation function J MR The optimal control parameter θ of the controller that minimizes (θ) * has a partial derivative of 0

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[0027] (p3) Single calculation approach The single calculation approach is an optimization approach that performs the iterative calculations performed in the iterative optimization approach in a single calculation.

[0028] The output in the open loop control system is y O year, Nominal model M in open-loop control systems O (z) and the reference value r (r(k) M O (z)) is the target output value y with respect to the reference value r dO year, Evaluation function J for evaluating the response of the controlled object by the controller O (θ) as the desired output value y dO and the output value y O It is expressed as the 2-norm of the difference between

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[0029] Evaluation function J O The optimal control parameter θ of the controller that minimizes (θ) * teeth,

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[0030] Control parameter θ * is the proportional gain K of the controller, which is set depending on the control method: PID control, PI control, or PI-D control. P , integral gain K I , differential gain K D , feedback gain K L is. [Effects of the Invention]

[0031] As described above, in the controller design method for designing optimal control parameters using estimated output values, the controller design method of the present invention makes it possible to estimate estimated output values ​​regardless of the linearity / non-linearity of the controller, and to design optimal control parameters of the controller using the obtained estimated output values. [Brief explanation of the drawings]

[0032] [Figure 1] 1 is a diagram showing a closed-loop control system 100 to which an output estimation method of the present invention is applied. [Figure 2] 1 is a flowchart illustrating the outline of steps of a controller design method according to the present invention. [Figure 3] 1 is a schematic diagram for explaining an outline of an output estimation method using a data-driven simulation process according to the present invention; [Figure 4] 3 is a flowchart illustrating an output estimation method according to the present invention. [Figure 5]FIG. 1 is a diagram for explaining an experimental process of the present invention. [Figure 6] FIG. 10 is a diagram for explaining an estimated input simulation process. [Figure 7] 10 is a flowchart illustrating an estimated output simulation process for output estimation according to the present invention. [Figure 8] FIG. 2 is a block diagram for explaining an estimated output simulation process of the output estimation of the present invention. [Figure 9] 10 is a flowchart illustrating an estimated output simulation process for output estimation according to the present invention. [Figure 10] FIG. 1 is a block diagram illustrating an estimated output simulation process for output estimation according to the present invention. [Figure 11] 1 is a block diagram illustrating a configuration of an estimated output device according to the present invention. [Figure 12] FIG. 1 is a diagram illustrating an example of a DC-DC converter. [Figure 13] FIG. 10 is a diagram illustrating an example of the configuration of a controller that performs PI control in which an inductor current is added as a minor loop for feedback. [Figure 14] FIG. 2 is a diagram illustrating an example of the configuration of a controller that performs PID control in current mode control. [Figure 15] FIG. 1 is a diagram illustrating an example of the configuration of a controller using PI-D control in current mode control. [Figure 16] 1 is a flowchart illustrating an example of a procedure for obtaining optimal control parameters using a direct optimization approach. [Figure 17] FIG. 2 is a block diagram showing a reference model of a closed-loop control system. [Figure 18] 1 is a flowchart illustrating an example of a procedure for obtaining optimal control parameters by an iterative optimization approach. [Figure 19] 10 is a flowchart illustrating an example of a procedure for obtaining a first-order partial differential in an iterative optimization approach. [Figure 20] 10 is a flowchart illustrating an example of a procedure for obtaining a second-order partial differential in an iterative optimization approach. [Figure 21] 1 shows a reference model of the open-loop control system. [Figure 22] 1 shows a block diagram of an open-loop control system. [Figure 23] 1 is a flowchart illustrating an example of a procedure for determining optimal control parameters using a single-run optimization approach. [Figure 24] FIG. 1 is a block diagram for explaining a conventional V-tiger method. DETAILED DESCRIPTION OF THE INVENTION

[0033] The controller design method of the present invention designs optimal control parameters of a controller provided in a closed-loop control system.

[0034] (closed loop control system) 1 shows a block diagram of a closed-loop control system 100. The present invention is applied to the closed-loop control system 100 to perform output estimation to obtain an estimated output value y, and the obtained estimated output value y is used to design optimal control parameters of a controller provided in the closed-loop control system.

[0035] The closed-loop control system 100 inputs a reference signal r(k) to a controller C(θ), and converts the control signal obtained by the controller C(θ) into an input signal u(k) of the controlled object P(z). in (k), and the output signal y of the controlled object P(z) out (k) is fed back to the controller C(θ) and the control process is performed in discrete time. out (k) corresponds to the plant and plant output.

[0036] The flowchart in Figure 2 shows the outline of the steps of the controller design method of the present invention. In a closed-loop control system in which a control signal from the controller is input as a control input to a controlled object and the output of the controlled object is fed back to the controller, the controller design method of the present invention includes the following steps: (P1) a data-driven simulation process for simulating an output based on time-domain calculations using experimental data of input and output of a controlled object, and obtaining an estimated output value y; (P2) an optimal control parameter design process for determining optimal control parameters of the controller using the estimated output value y obtained in the data-driven simulation process; Equipped with.

[0037] (P1) Data-driven simulation process The data-driven simulation process of the present invention is a data-driven simulation that estimates an output by performing a simulation using experimental data of the input and output of a control object P(z) in a discrete-time closed-loop control system, and performs a convolution operation in the time domain on the experimental output data, experimental input data, and estimated output values ​​and estimated input values ​​obtained by the simulation.

[0038] The convolution operation is performed in the time domain between the input / output experimental data (u0, y0) and the estimated input / output values ​​(u, y). The input / output experimental data (u0, y0) are the experimental input data (u0) and experimental output data (y0) obtained by actually experimenting with the controlled object. The estimated input / output values ​​(u, y) are the estimated input values ​​(u) and estimated output values ​​(y) at each sampling time obtained by simulating the controlled object P(z).

[0039] The estimated output value (y) of the control object P(z) at the next sampling time is estimated by a simulation using a convolution operation.

[0040] In the data-driven simulation of the present invention, the experimental data used in the simulation of the controlled object P(z) are the experimental input data (u0) and experimental output data (y0) obtained in an experiment on the controlled object, and the input / output values ​​used in the simulation are the estimated input values ​​(u) and estimated output values ​​(y) obtained in a simulation of the controlled object (P), and neither the experimental data nor the input / output values ​​used in the calculation are related to the parameter θ of the controller C(θ).

[0041] Therefore, the output estimation method using a data-driven simulation process of the present invention is a simulation that eliminates the involvement of the controller C(θ) and uses only the controlled object P(z). Because the involvement of the controller C(θ) is eliminated, the involvement of linearity / nonlinearity due to the controller C(θ) is eliminated, and even if the controller C(θ) has nonlinearity, it is possible to perform a convolution operation and estimate the output of the controlled object. Furthermore, it is possible to estimate the output of the controlled object regardless of the linearity / nonlinearity of the controller C(θ).

[0042] Furthermore, the time domain convolution calculation used in the output estimation method is expressed as an arithmetic expression that excludes the term of the controlled object P(z). Therefore, the output estimation can be simulated without involving not only the controller C(θ) but also the controlled object P(z).

[0043] FIG. 3 is a schematic diagram for explaining an outline of the output estimation method by the data-driven simulation process of the present invention, in which the output is estimated by a simulation using experimental data of the input and output of the controlled object P(z).

[0044] In the closed-loop control system 100 shown in FIG. 3A, when the controller C(θ) has a nonlinear characteristic, the input signal u input from the controller C(θ) to the controlled object P(z) in (k) is a nonlinear signal. In Figure 3A, the nonlinear characteristics of the controller C(θ) are represented by the nonlinearity φ(u).

[0045] In the output estimation method using a data-driven simulation process of the present invention, only the controlled object P(z) is set as the execution range of output estimation. By excluding the nonlinearity φ(u) of the controller C(θ) from the range of output estimation and leaving only the controlled object P(z), it becomes possible to estimate the output of the controlled object regardless of the linearity / nonlinearity of the controller C(θ).

[0046] In the present invention, in output estimation, the following assumptions are set: a first assumption that the control object P(z) is a linear time-invariant (LTI) system; a second assumption that the state of the control object P(z) before the 0th sampling time k=0 of the experimental data can be ignored; and a third assumption that the first experimental input data u0(0) of the experimental data is a value other than zero.

[0047] The first assumption is that the control object P(z) is a linear time-invariant (LTI) system. A linear time-invariant system is a linear system for which the principle of superposition holds, and the system properties do not change over time. By introducing the assumption of a linear time-invariant system into the control object P(z), the relationship between the control object P(z) and the input and output can be expressed in the form of a product in the frequency domain (z domain).

[0048] The experimental output data Y0(z) obtained by experiment is expressed as the product in the z domain of the controlled object P(z) and the experimental input data U0(z) obtained by experiment, as shown in equation (10). The estimated output value Y(z) simulated in the z domain is expressed as the product in the z domain of the controlled object P(z) and the estimated input value U(z) simulated in the z domain, as shown in equation (11). [Number 10] Y0(z)=P(z)U0(z) (10) [Number 11] Y(z)=P(z)U(z) (11)

[0049] In the equations in the z domain expressed by equations (10) and (11), the experimental input data U0(z) and the experimental output data Y0(z) are obtained during the experiment, and the estimated input value U(z) is input during the simulation, so the estimated output value Y(z) is the only unknown.

[0050] The relationship between equations (10) and (11) can be expressed as equation (12) by canceling the term of the controlled object P(z). [Number 12] Y(z)U0(z)=U(z)Y0(z) ···(12)

[0051] The second and third assumptions are introduced to obtain the estimated output value y(k) in the time domain from the estimated output value Y(z) in the z domain.

[0052] The second assumption, that the state of the controlled plant P(z) before the 0th sampling time k=0 of the experimental data can be ignored, guarantees the causality of the experimental data. This guarantees that the state of the controlled plant P(z) before the sampling time k=0 does not affect the experimental data after the sampling time k=0. Therefore, when the response of the controlled plant P(z) starts from the zero state or steady state, the experimental data obtained in the experiment of the controlled plant P(z) can be used for the estimated output value y(k) in the time domain.

[0053] When the relational expression in the z domain expressed by Equation (12) is converted into a relational expression in the time domain, the following Equation (13) is obtained. [Number 13] y(k)*u0(k)=u(k)*y0(k) ···(13) Equation (13) is converted into the time domain signal of equation (14) below by a convolution operation.

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[0054] When equation (14) is expanded with respect to the estimated output value y(k) at sampling time k, equation (15) is obtained.

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[0055] In equation (15), if the first experimental input data u0(0) is set to a value other than zero according to the third assumption, equation (16) for the estimated output value y(k) in the time domain is obtained.

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[0056] Equation (16) shows that the estimated output value y(k) of the controlled object P(z) at sampling time k can be obtained from the experimental input / output data (u0, y0) of the controlled object P(z) and the estimated output value y(i) up to sampling time k-1.

[0057] The first term on the right side of equation (16) represents the convolution operation between the estimated input value u(i) and the experimental output data y0(k-1), the second term represents the convolution operation between the estimated output value y(i) and the experimental input data u0(k-1), and the third term represents the product of the estimated input value u(k) and the experimental output data y0(0).

[0058] The estimated output value y(k) in equation (16) does not include a term for the controlled object P(z), so a transfer function representing a plant model of the controlled object P(z) is not required. Therefore, setting a plant model for the controlled object P(z) is not required to estimate the estimated output value y(k).

[0059] FIG. 3B shows an outline of a simulation of output estimation by a data-driven simulation process in which only the control object P(z) is set as the execution range.

[0060] In the present invention, the estimated output value y(k) is calculated by simulating only the control object P(z) of the closed-loop control system 100 shown in FIG. 3A, excluding the controller C(z, θ) and the nonlinearity φ(u), in the time domain.

[0061] Simulation 11 of the controlled object P(z) is performed by calculating the estimated output value y(k) expressed by equation (16). Simulation 11 of the controlled object P(z) estimates the estimated output value y(k) of the controlled object P(z) at sampling time k using the experimental input / output data (u0, y0) of the controlled object P(z) obtained in experiment 12, the estimated input value u obtained in simulation 13 of the controller, and the estimated input / output values ​​(u(i), y(i)) up to the previous sampling time k-1 obtained in simulation 11. In the simulation of a feedback system, a reference value r and an estimated output value y are required to calculate the estimated input value u.

[0062] The input / output experimental data (u0, y0) are the experimental input data (u0) and the experimental output data (y0) obtained by actually operating the controlled object. The estimated input / output values ​​(u, y) are the estimated input values ​​(u) and the estimated output values ​​(y) at each sampling time obtained by simulating the controlled object P(z). Note that the input / output data (u 0, The subscript "0" in y0) indicates that this is experimental data.

[0063] The calculation of the estimated output value y(k) expressed by equation (16) includes a convolution operation of the input / output experimental data (u0, y0) and the estimated input / output value (u, y) in the time domain. The simulator 11 estimates the estimated output value (y) of the control object P(z) at the next sampling time by simulating the convolution operation.

[0064] In the present invention, in a data-driven simulation, the experimental data used in the simulation of the controlled object P(z) are experimental input data (u0) and experimental output data (y0) obtained in an experiment on the controlled object, and the input / output values ​​used in the simulation are estimated input values ​​(u) and estimated output values ​​(y) obtained in a simulation of the controlled object (P), and neither the experimental data nor the input / output values ​​used in the calculation are involved with the controller C(θ).

[0065] Therefore, the output estimation method in the data-driven simulation process of the present invention is a simulation that eliminates the involvement of the controller C(θ) and uses only the controlled object P(z). Because the involvement of the controller C(θ) is eliminated, the involvement of linearity / nonlinearity due to the controller C(θ) is eliminated, and even if the controller C(θ) has nonlinearity, it is possible to perform a convolution operation and estimate the output of the controlled object. Therefore, it is possible to estimate the output of the controlled object regardless of the linearity / nonlinearity of the controller C(θ).

[0066] In addition, the time domain convolution calculation used for output estimation is expressed as an arithmetic expression that excludes the term of the controlled object P(z). Therefore, output estimation can be simulated without involving not only the controller C(θ) but also the controlled object P(z).

[0067] The estimated output value y(k) is given by the convergence condition of the experimental output data in the time domain convolution operation as follows: (Case 1) When the value of the experimental output data at sampling time k=0 is y0(0)=0, (Case 2) When the input / output state is steady just before sampling starts, (Case 3) When the experimental output data value beyond sampling time k=N can be considered to converge to the experimental output data value at sampling time k=0, For each case, y a (k), y b (k), and y c The estimated output value y(k) is calculated using each of the equations (k). Below, we show the estimated output value y(k) in each of the following cases: when the experimental output data y0(0) is "0" (Case 1), when the experimental output data y0(0) is a steady value (Case 2), and when the sampling time m is equal to or greater than the number of samplings N-1, the experimental output data y0(m) is a constant value that has sufficiently converged to the initial state (k=0) (Case 3).

[0068] (Case 1) Case 1 is a case where the value of the experimental output data y0(k) of the controlled object P(z) at sampling time k=0 is y0(0)=0. The calculation formula for the estimated output value y(k) in this Case 1 is y a It is expressed as (k).

[0069] Since the third term (u(k)y0(0)) on the right side of the estimated output value y(k) shown in equation (16) is 0, the calculation formula y a (k) is expressed by equation (17) in which the difference between the first convolution calculation value of the first item on the right-hand side and the second convolution calculation value of the second item is divided by the experimental input data u0(0).

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[0070] (Case 2) Case 2 is the case where the state of the control object P(z) is in a steady state at the start of the experiment. In this steady state, the steady values ​​of the experimental input data u0 and the experimental output data y0 of the control object P(z) at sampling time k=0 are the steady values ​​u 0_offset and the steady-state value y 0_offset When this is the case, the formula y(k) for estimating the estimated output value y(k) at sampling time k is b (k) is the difference between the first convolution calculation value of the first item on the right-hand side and the second convolution calculation value of the second item on the right-hand side, calculated using the experimental input data u0 ofs This is expressed as equation (18) divided by (0).

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[0071] Expression y b u0 in (k) ofs (k), y0 ofs (k) is the steady-state value u 0_offset and the steady-state value y 0_offset is the offset compensated value, [Number 19] u0 ofs (k)=u0(k)-u0_offset ···(19) [Number 20] y0 ofs (k)=y0(k)-y 0_offset ···(20) It is expressed as:

[0072] (Case 3) Case 3 is the case where the state of the control target P can be considered to have sufficiently converged to the initial state after the experiment is completed. In equation (14) relating to the convolution operation, the input value u and the output value y are in an equal relationship in terms of which is the start end of the time series i and which is the end end of the convolution operation.

[0073] Expression y for Case 1 a (k) and the formula y in Case 2 b In (k), when looking at the estimated input / output values ​​(u, y), the first convolution calculation value calculates the estimated input value u(i) values ​​in order from the beginning of the time series i, and the second convolution calculation value calculates the estimated output value y(i) values ​​in order from the beginning of the time series i. When looking at the experimental input / output data (u0, y0), the first convolution calculation value calculates the experimental output data y0(i) values ​​in order from the end of the time series i, and the second convolution calculation value calculates the experimental input data u0(i) values ​​in order from the end of the time series i.

[0074] Case 3 is the same as Case 1, but a (k) and the formula y in Case 2 b The relationship between the start and end of time series i in (k) is reversed. In Case 1 and Case 2, the second assumption is that y0(0) is "0" at the start of the experiment, or that the state of the control object P is in a steady state at the start of the experiment. In Case 3, the relationship between the start and end of time series i is reversed, so the second assumption is that the state of the control object P is in a state that can be considered to have sufficiently converged to its initial state at the end of the experiment.

[0075] In this convergence state, the convergence value at the sampling time k=m≧N-1 (N is the number of samplings of the experimental data) of the experimental input data u0 and the experimental output data y0 of the controlled object P(z) is the steady value u0 ofs (m)=u m_offset , and the steady-state value y0 ofs (m)=y m_offset When k>N-1 (N is the number of samples), the long-term simulation formula y(k) for estimating the estimated output value y(k) at sampling time k is c (k) is shown in equation (21).

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[0076] Expression y c u0 in (k) ofs (m), y0 ofs (m) is the steady-state value u m_offset and the steady-state value y m_offset is a value obtained by offset compensation for the offset of [Number 22] u0 ofs (m)=u m_offset ···(twenty two) [Number 23] y0 ofs (m)=y m_offset ···(twenty three) is.

[0077] Case 3: After the experiment, the steady-state value u m_offset , and the steady-state value y of the experimental output data m_offset If this can be obtained, it is possible to estimate the output by long-term simulation regardless of the number of experimental data samples N. The estimated output value y(k) in this case is calculated by the formula y c (k), and u0 in Eq. (22) and Eq. (23) ofs (m), y0ofs (m).

[0078] (Method for estimating output of data-driven simulation process of the present invention) The output estimation method of the data-driven simulation process of the present invention is a method for estimating the output of a controlled object P(z) in a closed-loop control system in which a control signal of a controller C(θ) is input as a control input to the controlled object P(z) and the output of the controlled object P(z) is fed back to the controller C(θ).

[0079] The output estimation method for a data-driven simulation process of the present invention is a data-driven simulation method that simulates an output using experimental data of the input and output of a controlled object P(z), and obtains a first convolution value obtained by performing a convolution operation in the time domain between an estimated input value u obtained by simulating the controlled object P(z) and experimental output data y0 obtained by an experiment on the controlled object P(z), and a second convolution value obtained by performing a convolution operation in the time domain between an estimated output value (y) obtained by simulating the controlled object P(z) and experimental input data u0 obtained by an experiment on the controlled object P(z), and estimates an estimated output value (y) of the controlled object P(z) at the next sampling time from the difference between the two convolution values.

[0080] The output estimation method using a data-driven simulation step of the present invention includes the steps of (a) an experiment step of experimental data, (b) a simulation step of estimated input values, and (c) a simulation step of estimated output values.

[0081] The output estimation method of the present invention will be described using the flowchart in Fig. 4. The output estimation comprises an experiment step (S1, S2) for acquiring experimental input / output data, an estimated input simulation step (S3, S4) for acquiring estimated input values, and an estimated output simulation step (S5, S6) for acquiring estimated output values.

[0082] (a) Experimental process of experimental data (u0, y0) The experimental step of experimental data is a step of collecting and storing each sampled value of experimental input data u0 and experimental output data y0 obtained by an experiment on the control object P(z).

[0083] An example of a closed-loop system for carrying out an experimental process for experimental data is a closed-loop system that feeds back the output of a controlled object P(z) to a controller C(θ), where the parameter θ of the controller C(θ) is set as the initial parameter θ0, an experiment is carried out on the controller C(θ) and the controlled object P(z) of the actual plant, and sampled values ​​of the experimental input data u0 and the experimental output data y0 are collected.

[0084] An example of an open-loop control system that performs an experimental process for experimental data is a system with only a controlled object P(z), where an experiment is performed on the controlled object P(z) of an actual plant, and each sampled value of the experimental input data u0 and the experimental output data y0 is collected. Generally, it is often difficult to obtain data for an unstable system in an open-loop control system.

[0085] Fig. 5 is a diagram for explaining the experimental process. The closed-loop control system shown in Fig. 5A converts the control signal of the controller C(θ0) into a control input value u in (k), and the output value y of the controlled object P(z) out (k) is fed back to the controller C(θ0).

[0086] The experimental process is as follows: In the closed-loop control system shown in Figure 5A, the reference value r O (k) is input to the controller C(θ0), and the control input value u in (k) is obtained as the experimental input data u0(k). Furthermore, the control input value u in (k) is input to the control object P(z) and the output value y out (k) is obtained as the experimental output data y0(k).

[0087] The experimental process is performed by calculating the reference value r at each sampling time k. O(k) is input to a closed-loop control system, experimental input data u0(k) and experimental output data y0(k) obtained at each sampling time k are acquired, and multiple experimental input / output data (u0(k), y0(k)) are obtained (S1), and the acquired experimental input / output data (u0(k), y0(k)) is stored (S2).

[0088] Figure 5B shows the experimental input data u0(k), and Figure 5C shows the experimental output data y0(k). Note that the experimental input / output data in Figures 5B and 5C are shown schematically for the purpose of explanation and do not represent actual data.

[0089] Of the experimental input data u0(k) shown in Figure 5B, u0(0) at sampling time k = 0 is required to be a value other than "0." Figure 5C shows an example of the experimental output data y0(k), where y0(0) at sampling time k = 0 is "0."

[0090] (b) Simulation process of estimated input value u(k) The process of simulating the estimated input value is a process in which a reference value r(k) and an estimated output value y(k) are input as a feedback signal to the controller C(θ) to perform a simulation to obtain the output value of the controller C(θ), and the result is calculated and stored as an estimated input value u(k) for the control object P(z).

[0091] In the simulation process of the estimated input value u(k), in the simulation system of the controller C(θ), the parameter θ of the controller C(θ) is set to any parameter to be simulated, and the reference value r(k) and the estimated output value y(k) are input to the controller (C) as a feedback signal, and the output signal at each sampling time k obtained is found as the estimated input value u(k) for the controlled object P(z).

[0092] Fig. 6 is a diagram for explaining the estimated input simulation process. When experimental data is acquired, the controller C(θ0) is used as the controller in the closed-loop control system shown in Fig. 5A, but in the estimated input simulation process, any controller C(θ) can be used, not limited to the controller C(θ0) used when acquiring the experimental data.

[0093] In the estimated input simulation step, a reference value r(k) and an estimated output value y(k) are input to a controller C(θ), and the resulting control signal is acquired as an estimated input value u(k) to be input to a controlled object P(z). In the estimated input simulation step, any controller can be set that is calculated using the reference value r(k) and the estimated output value y(k).

[0094] Then, the reference value r(k) and estimated output value y(k) at each sampling time k are input to the controller C(θ), the estimated input value u(k) obtained at each sampling time k is acquired (S3), and the acquired estimated input value u(k) is stored (S4).

[0095] (c) Simulation process of estimated output value y(k) The simulation process of the estimated output value is a process of performing a convolution operation in the time domain using each sampling value of the experimental input data u0 and the experimental output data y0 obtained in the experimental process, the estimated input value u from sampling time 0 to (k-1) obtained in the simulation process of the estimated input value, and the estimated output value y(k) of the controlled object P(z) from sampling time 0 to (k-1) in the simulation of the controlled object P(z), and storing the estimated output value y(k) of the controlled object P(z) at sampling time k.

[0096] The estimated input value u from sampling time 0 to (k-1) obtained in the simulation process of the estimated input value and the experimental output data y0 from sampling time k to 1 obtained in the experimental process are convolved in the time domain to obtain a first convolution value, the estimated output value y(k) from sampling time 0 to (k-1) obtained in the simulation process of the estimated output value and the experimental input data u0 from sampling time k to 1 obtained in the experimental process are convolved in the time domain to obtain a second convolution value, the difference between the first convolution value and the second convolution value is obtained, and the estimated output value y(k) at sampling time k of the controlled object P(z) is obtained from the obtained difference.

[0097] The estimated output value y(k) at sampling time k is obtained by dividing the difference between the first convolution calculation value and the second convolution calculation value by the experimental input data u0(0) when sampling time k is 0. In the estimated output simulation step, the estimated output value is obtained by calculation processing including the convolution calculation (S5) and stored (S6).

[0098] The acquisition of the estimated output value in the estimated output simulation step will be described with reference to the flowcharts of FIGS. 7 and 9 and the block diagrams of FIGS.

[0099] The flowchart in FIG. 7 and the block diagram in FIG. 8 show an overview of the simulation at sampling time k for obtaining the estimated output value.

[0100] First, the experimental input data u0(0), u0(1), u0(2), . . . , u0(k) and the experimental output data y0(1), y0(2), . . . , y0(k) stored in step S2 are read out (S31), the estimated input values ​​u(0), u(1), u(2), . . . , u(k-1) stored in step S4 are read out (S32), and the estimated output values ​​y(0), y(1), y(2), . . . , y(k-1) before the sampling time (k-1) stored in step S6 are read out (S33).

[0101] The read experimental input data u0(0), u0(1), u0(2), , u0(k), experimental output data y0(1), y0(2), , y0(k), estimated input values ​​u(0), u(1), u(2), , u(k-1), and estimated output values ​​y(0), y(1), y(2), , y(k-1) are used to calculate y(k), y a (k),y b (k),y c (k), the estimated output value y(k) at sampling time k is estimated.

[0102] The block diagram in Figure 8 shows the operation formula y(k), y a (k),y b (k),y c The figure shows a schematic diagram of the calculation process of experimental input / output data (u0, y0) and estimated input / output values ​​(u, y) when estimating the estimated output value y(k) at sampling time k by executing (k). Here, the calculation formula y a The simulation for obtaining the estimated output value will be explained using (k) as an example.

[0103] The convolution calculation block 6a in FIG. 8 calculates the equation y a The convolution block 6a selects the estimated input value u(i) and experimental output data y0(k-1) corresponding to each sampling time "i" in the time series from the estimated input values ​​u(0), u(1), u(2), . . . , u(k-1) and the experimental output data y0(1), y0(2), . . . , y0(k), calculates the product, and calculates the sum from i = 0 to i = (k-1).

[0104] On the other hand, the convolution calculation block 6b in FIG. 8 calculates the equation y aThe convolution operation block 6b selects the estimated output value y(i) corresponding to each sampling time "i" in the time series from the estimated output values ​​y(0), y(1), y(2), . . . , y(k-1) and the experimental input data u0(1), u0(2), . . . , u0(k), and calculates the product, and calculates the sum from i = 0 to i = (k-1).

[0105] Addition block 6c in FIG. 8 calculates the difference between the convolution calculation value obtained by convolution calculation block 6a and the convolution calculation value obtained by convolution calculation block 6b, and division block 6d in FIG. 8 divides the difference obtained by addition block 6c by u0(0) to calculate an estimated output value y0(k) at sampling time k.

[0106] When the sampling time k is 3, the calculation of the estimated output value y(3) will be described with reference to the flowchart in FIG. 9 and the block diagram in FIG.

[0107] First, the experimental input data u0(0), u0(1), u0(2), u0(3) and the experimental output data y0(1), y0(2), y0(3) stored in step S2 are read out (S41), then the estimated input values ​​u(0), u(1), u(2) stored in step S4 are read out (S42), and further the estimated output values ​​y(0), y(1), y(2) before sampling time k=2 stored in step S6 are read out (S43).

[0108] The read experimental input data u0(0), u0(1), u0(2), experimental output data y0(1), y0(2), y0(3), estimated input values ​​u(0), u(1), u(2), and estimated output values ​​y(0), y(1), y(2) are used to calculate the equations y(k), y a (k),y b (k),y c By substituting into (k), the estimated output value y(3) at sampling time k=3 is estimated.

[0109] In Case 1, when y0(0)=0, ya (3) is obtained by setting k=3 in equation (17).

number

[0110] The block diagram in Figure 10 shows the operation formula y(k), y a (k),y b (k),y c When estimating the estimated output value y(k) at sampling time k by executing (k), the calculation process of the experimental input / output data (u0, y0) and the estimated input / output value (u, y) is shown schematically with k=3 as an example. Here, the calculation formula y a A simulation for obtaining the estimated output value y(k) will be explained using (k) as an example.

[0111] The convolution calculation block 6a in FIG. 10 calculates the equation y a This corresponds to the first convolution operation on the right side of (k). The convolution operation block 6a selects the estimated input value u(i) and experimental output data y0(k-1) corresponding to each sampling time "i" in the time series from the estimated input values ​​u(0), u(1), u(2) and the experimental output data y0(1), y0(2), y0(3), calculates the product, and calculates the sum from i=0 to i=(k-1).

[0112] On the other hand, the convolution calculation block 6b in FIG. 10 calculates the equation y a This corresponds to the second convolution operation on the right side of (k). Convolution operation block 6b selects the estimated output value y(i) and experimental input data u0(k-1) corresponding to each sampling time "i" in the time series from the estimated output values ​​y(0), y(1), y(2), y(3) and the experimental input data u0(1), u0(2), u0(3), calculates the product, and calculates the sum from i=0 to i=(k-1).

[0113] Addition block 6c in FIG. 10 calculates the difference between the convolution calculation value obtained by convolution calculation block 6a and the convolution calculation value obtained by convolution calculation block 6b, and division block 6d in FIG. 10 divides the difference obtained by addition block 6c by u0(0) to calculate the estimated output value y(k) at sampling time k.

[0114] (Estimated output device) The estimation output device using data-driven simulation of the present invention is a device that estimates the output of a controlled object in a closed-loop control system in which a control signal from a controller is input as a control input to the controlled object and the output of the controlled object is fed back to the controller. The estimation output device constitutes a data-driven simulation device that simulates the output using experimental data of the input and output of the controlled object.

[0115] The estimated output device of the present invention is configured to simulate the controlled object P(z) in the closed-loop control system 100 shown in Figure 3A and estimate the output, and corresponds to the device that executes the simulation 11 of the controlled object P(z) in Figure 3B.

[0116] The configuration of the estimated output device will be explained using the block diagram of Fig. 11. The block diagram shown in Fig. 11 shows the configuration of a calculation block that obtains an estimated output value y(k) by simulation in the data-driven simulation device, and corresponds to the simulation 11 of the controlled object P(z) shown in Fig. 3B.

[0117] The estimated output device 1 includes an experimental data storage unit 2, an estimated output value storage unit 3, an estimated input value calculation unit 4, an estimated input value storage unit 5, and a calculation unit 6.

[0118] The experimental data storage unit 2 stores experimental input data u0 and experimental output data y0 obtained through an experiment on the control object P(z). The experimental input data u0 and experimental output data y0 are acquired through an experiment 12 in FIG. 3B.

[0119] The estimated output value storage unit 3 stores the estimated output value (y) of the controlled object P(z). The estimated output value (y) is y(k-1) calculated by the calculation unit 6 up to the sampling time (k-1).

[0120] The estimated input value calculation unit 4 calculates the estimated input value u(k) obtained by simulating the controller C(θ).

[0121] The estimated input value storage unit 5 stores the estimated input value u(k) calculated by the estimated input value calculation unit 4. The estimated input value u(k) is obtained by a simulation 13 of the controller in FIG. 3B.

[0122] The calculation unit 6 performs a convolution operation in the time domain using experimental input data u0 and experimental output data y0 obtained in an experiment on the controlled object P(z) and estimated input values ​​u and estimated output values ​​y(y) obtained in a simulation of the controlled object P(z), and estimates an estimated output value y(y) at the next sampling time of the controlled object P(z). Each part of the estimation output device shown in the block diagram of Figure 11 can be controlled according to a protocol defined in a program.

[0123] (P2) Optimal control parameter design process The optimal control parameter design step of the present invention is a step of determining optimal control parameters of a controller using the estimated output value y obtained in the data-driven simulation step.

[0124] Below, we will explain the optimal control parameter design process using a DC-DC converter as the controlled object and PI control, PID control, and PI-D control as examples of closed-loop control systems.

[0125] (Control object) Figure 12 shows an example of a DC-DC converter. The DC-DC converter operates on an input voltage V inThe inverter circuit is composed of an LC circuit consisting of a switch SW1 connected in series to a load R, a switch SW2 connected in parallel to the load R, an inductor L connected in series to the load R, and a capacitor C connected in parallel to the load R. The switches SW1 and SW2 are switched by a PWM signal from a controller C.

[0126] The controller inputs input data u to the DC-DC converter to be controlled, and controls the on / off of switches SW1 and SW2 using PWM signals to output the output voltage V c On the other hand, the output data y output from the DC-DC converter is the output voltage V of the capacitor C. c , and the inductor current i of inductor L L The controller feeds back the output data y to form a closed-loop control system.

[0127] (PI control) Figure 13 shows an example of the configuration of a controller that performs PI control by feeding back the inductor current as a minor loop. PI control is performed by controlling the target voltage V r and the capacitor voltage output voltage V c The difference between (e=(V r -V c )) is input to the proportional and integral terms to perform proportional-integral control, and the inductor current i L is entered into the feedback term.

[0128] The proportional term, integral term, and feedback term of the controller are controlled by the control parameter θ, which is the proportional gain K P , integral gain K I , and feedback gain K L The outputs of these terms are added together to produce an output that is output as input data u for the controlled object. The input signal u converted into a PWM signal is input to the controlled object of the DC-DC converter, and the switching operation of the switching element of the DC-DC converter is controlled.

[0129] (PID control) Fig. 14 shows an example of the configuration of a controller that performs PID control in current mode control. The proportional term, integral term, differential term, and feedback term of PID control are controlled by the control parameter θ, and the proportional gain K P , integral gain K I , differential gain K D , and feedback gain K L The sum output of these is output as input data u to be controlled.

[0130] Proportional Gain K P is the target voltage V r and the output voltage V c Difference with (V r -V c ) and the integral gain K I is the target voltage V r and the output voltage V c Difference with (V r -V c ) is the gain for the integral value of the differential gain K D is the target voltage V r and the output voltage V c Difference with (V r -V c ) and the feedback gain K L is the inductor current i L is the gain relative to

[0131] PID control is the target voltage V r and the output voltage V c The difference between (e=(V r -V c )) is input to the proportional, integral, and derivative terms to perform proportional-integral-derivative control, and the inductor current i L The feedback signal is input to the feedback term.

[0132] (PI-D control) Figure 15 shows an example of the configuration of a controller using PI-D control in current mode control. PI-D control is a method for controlling the target voltage V r and the output voltage V c The difference between (e=(Vr -V c )) is input to the proportional and integral terms to perform proportional-integral control, and the output voltage V c is input to the differential term to perform differential control, and the inductor current i L is entered into the feedback term.

[0133] The proportional, integral, derivative, and feedback terms of the controller are controlled by the control parameters θ, and the proportional gain K P , integral gain K I , differential gain K D , and feedback gain K L The sum output of these is output as input data u to be controlled.

[0134] Proportional Gain K P is the target voltage V r and the output voltage V c Difference with (V r -V c ) and the integral gain K I is the target voltage V r and the output voltage V c Difference with (V r -V c ) is the gain for the integral value of the differential gain K D is the output voltage V c is the gain for the differential value of L is the inductor current i L is the gain relative to

[0135] Three types of optimization approaches can be applied to the optimal control parameter design process: (P2a) direct optimization approach, (P2b) iterative optimization approach, and (P2c) single calculation approach. Each optimization approach designs the optimal control parameters of the controller using the estimated output value y obtained in the data-driven simulation process.

[0136] (P2a) Direct Optimization Approach The direct optimization approach is an optimization approach that uses an evaluation function to directly optimize the control parameter θ of the controller. It uses the estimated output value y obtained in the data-driven simulation process and applies a heuristic algorithm as an optimization solver to find the control parameter that minimizes the evaluation function.

[0137] Evaluation function J for evaluating the response of the controlled object by the controller DO As (θ), the following equation (25) is used, which is expressed as the 2-norm of the difference between the target reference value r(k) and the estimated output value y(k).

number

[0138] Evaluation function J DO The optimal control parameter θ of the controller that minimizes (θ) * is calculated by the following equation (26) using the reference value r(k) and the estimated output value y(k) estimated in the data-driven simulation process.

number

[0139] In equation (26), argmin θ J DO (θ) is the evaluation function J DO (θ) is the set of control parameters θ that minimizes the proportional gain K P , integral gain K I , differential gain K D , feedback gain K L When each gain of the controller is * is the set of optimal values ​​for each gain.

[0140] Evaluation function J DO The optimal control parameter θ of the controller that minimizes (θ) *To directly find this, heuristic algorithms such as the Nelder-Mead method can be applied. The Nelder-Mead method, also known as the simplex method or the amoeba method, is a nonlinear optimization method that searches for the minimum value of a multidimensional nonlinear function by expanding, contracting, and moving a polygonal search area.

[0141] The flowchart in FIG. 16 shows an example of a procedure for finding the optimal control parameters by the direct optimization approach.

[0142] In the design of optimal control parameters using the direct optimization approach, the initial values ​​of the control parameters are first set. In the direct optimization approach using the Nelder-Mead method, the target function is minimized using (n+1) initial value vectors for the n design variables.

[0143] When performing PI control, the controller uses the control parameter θ as the proportional gain K P , integral gain K I , and feedback gain K L In the Nelder-Mead method, four initial values ​​θ1(K P1 ,K I1 ,K L1 ),θ2(K P2 ,K I2 ,K L2 ),θ3(K P3 ,K I3 ,K L3 ), and θ4(K P4 ,K I4 ,K L4 ) (SD1).

[0144] Next, the estimated output value y(k) is calculated using the data-driven simulation method of the present invention for the initial values ​​θ1 to θ4 of the control parameters set in step SD1 (SD2). Subsequently, the estimated output value y(k) calculated in step SD2 and the reference value r(k) are used to calculate the evaluation function J by equation (25). DOFind (θ) (SD3).

[0145] By changing the control parameter θ using the Nelder-Mead method (SD5), the SD2 and SD3 steps are repeated in a loop to obtain the evaluation function J DO This is continued until (θ) is minimized (SD4) to find the optimal control parameter θ. Then, the control parameter θ obtained by optimization is called the optimal control parameter θ * (K P * ,K I * ,K L * ) (SD6).

[0146] (P2b) Iterative Approach When the evaluation function is differentiable with respect to the control parameter θ, the optimal control parameter θ can be obtained by applying an iterative optimization approach. * In the iterative optimization approach, the optimal control parameter θ in Eq. (26) can be calculated more efficiently. * is calculated using the gradient method.

[0147] Figure 17 shows a reference model of a closed-loop control system. The difference (r(k) - y(k;θ)) between the reference value r(k) and the fed-back estimated output value y(k;θ) is input to controller C, and the control signal obtained by controller C is input as an input signal for the controlled object P(z), which outputs the estimated output value y(k;θ).

[0148] The nominal model M(z) represents the characteristics of the closed loop system. The nominal model M(z) represents the desired target output value y for an arbitrarily given reference value r(k). d (k) is output. The desired output value y d (k) is expressed by the following equation (27).

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[0149] When the transfer function of the controller C(z;θ) has linear separability with respect to the control parameter θ, the transfer function of C(z;θ) is the control operation C0 T It is expressed as the product of (z) and the control parameter θ.

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[0150] In data-driven simulation, the evaluation function J is used to evaluate the response of the controlled object to the controller. MR (θ) is the target output value y for the reference value r(k) d (k) and the estimated output value y(k;θ), the 2-norm of the difference is expressed by the following equation (29).

number

[0151] Evaluation function J MR The partial differential value obtained by partially differentiating (θ) with respect to the control parameter θ is expressed by the following equation (30).

number

[0152] The partial differential value of the estimated output value y(k;θ) with respect to θ in equation (30) is expressed by the following equation (31).

number

[0153] Here, since the value of the initial estimated output value y(0;θ) at k=0 is a constant that does not depend on θ, the partial differential value of the estimated output value y(k;θ) at k=0 with respect to θ is given by the following equation (32).

number

[0154] Also, the evaluation function J MR The optimal control parameter θ of the controller that minimizes (θ) * Candidate θ m teeth,

number

[0155] The optimal control parameter θ that satisfies equation (33) * Candidate θ m+1 can be obtained using the gradient method, and is obtained by repeating the calculation of the following equation (34).

number

[0156] In equation (34), H(θ) is a Hessian matrix, and is expressed by the following equation (35).

number

[0157] The second partial differential of the estimated output value y(k;θ) in equation (35) with respect to θ is expressed by the following equation (36).

number

[0158] The first partial differential of the estimated output value y(k;θ) contained in equation (31) and the second partial differential of the estimated output value y(k;θ) contained in equations (35) and (36) are expressed as y in equation (17) of the output estimation method using the data-driven simulation process. a (k), y in equation (18) b (k), y in equation (21) cIt can be obtained using the estimated output value y(i;θ) expressed by (k).

[0159] The control parameter θ is K P ,K I ,K L In the case of C0 T (z) and θ are expressed by equations (37) and (38), respectively.

number

number

[0160] C0 T The matrix (z) sets the feedback variables for each control parameter θ, as well as the proportional, integral, and differential control methods. T (z) is the proportional gain K for voltage feedback P , integral gain for voltage feedback K I , proportional gain K for current feedback L The variables set for each are shown.

[0161] Next, the control parameter θ is proportional to the proportional gain K P Equations (37) and (38) are expressed as follows: P In this case, the voltage feedback is C0 T =[1,0] T At this time, the estimated output value y(k;K P )K P The first-order partial differential of is expressed by the following equation (39) from equation (31).

number

[0162] Estimated output value y(k;K P )K PThe second-order partial differential of is expressed by the following equation (40) from equation (36).

number

[0163] The control parameter θ is the integral gain K I , and the proportional gain for the current feedback, K L In the case of C0 T =[T / (z-1),0] T , C0 T =[0,1] T The first and second partial differential values ​​can be calculated in the same way. In addition, the proportional gain K P , and integral gain K I , and the proportional gain K for the current feedback L In addition to when the control parameters θ are used individually, the first-order partial differential value and the second-order partial differential value can be similarly calculated using the matrix of the control parameters even when the control parameters θ are used in any combination.

[0164] Therefore, the optimal control parameter θ in Eq. (34) * Candidate θ m+1 can be calculated by the gradient method using the Hessian matrix H(θ) of equation (35), the first partial differential with respect to θ of the estimated output value y(k;θ) of equation (31), and the second partial differential with respect to θ of the estimated output value y(k;θ) of equation (36), and further using equations (39) and (40) to calculate these first and second partial differential values.

[0165] The flowcharts in FIGS. 18, 19, and 20 show an example of a procedure for finding the optimal control parameters by an iterative optimization approach.

[0166] In the design of the optimal control parameters by the iterative optimization approach, the optimal control parameter θ *To obtain the iterative calculation, first, set the initial value θ1 of the control parameter. If the controller performs PI control, for example, set the proportional gain K P , integral gain K I , and feedback gain K L The three gain values ​​[K P ,K I ,K L ] (SI1).

[0167] Next, we set the transfer function C0 of the controller C in equation (36). In the case of PI control, the gain [K P ,K I ,K L ] transfer function C0 T is expressed by the following equation (41) (SI2).

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[0168] Next, set m = 1 (SI3), and repeat steps SI4 to SI8 to find the optimal control parameter θ * Next, the partial differential value ∂y(k;θ) / ∂θ of the estimated output value y(k;θ) with respect to θ is calculated using equation (31), and the evaluation function J MR Partial differential value of (θ) ∂J MR Calculate (θ) / ∂θ (SI4).

[0169] The flowchart in Figure 19 shows the procedure for ∂y(k;θ) in equation (31) using the estimated output value y(k;θ) in SI4. The first-order partial differential value ∂y(k;θ) / ∂θ of the estimated output value y(k;θ) with respect to θ is θ=K P In this case, it is expressed by equation (39) using equation (31). Here, in PI control, θ is [K P ,K I ,K L ].

[0170] Next, the value of i is increased (s3) in order from i = 0 (s1), and the calculation (s2) of equation (39) is repeated (s4) up to i = k-1. This results in the k partial differential values ​​[∂y(0;θ) / ∂θ, ∂y(1;θ) / ∂θ, , ∂y(k-1;θ) / ∂θ] being calculated (s5).

[0171] Using k first-order partial differential values ​​[∂y(0;θ) / ∂θ, ∂y(1;θ) / ∂θ, , ∂y(k-1;θ) / ∂θ], the evaluation function J MR Partial differential value of (θ) ∂J MR (θ) / ∂θ is calculated (SI4). Then, the second partial differential value ∂ of the estimated output value y(k;θ) with respect to θ is calculated. 2 Calculate y(k;θ) / ∂θ using equation (36) (SI5).

[0172] The flowchart in FIG. 20 uses the estimated output value y(k;θ) in SI5 to calculate ∂ 2 The procedure for calculating y(i;θ) is shown below. The second partial differential value ∂ of the estimated output value y(k;θ) with respect to θ is 2 y(k;θ) / ∂θ T ∂θ is θ=K P In this case, it is expressed by equation (40) using equation (36). Here, in the PI control, θ is [K P ,K I ,K L ].

[0173] Next, the value of i is increased (s13) in order from i=0 (s11), and the calculation (s12) of equation (40) is repeated (s14) up to i=k-1. As a result, k partial differential values ​​[∂ 2 y(0;θ) / ∂θ T ∂θ,∂ 2 y(1;θ) / ∂θ T ∂θ, , ∂ 2 y(k-1;θ) / ∂θ T ∂θ] is found (s15).

[0174] The k first-order partial differential values ​​[∂y(0;θ) / ∂θ, ∂y(1;θ) / ∂θ, ∂y(k-1;θ) / ∂θ] obtained in step SI4 and the k second-order partial differential values ​​[∂2 y(0;θ) / ∂θ T ∂θ,∂ 2 y(1;θ) / ∂θ T ∂θ, , ∂ 2 y(k-1;θ) / ∂θ T ∂θ] to find the Hessian matrix H(θ) in equation (35).

[0175] Next, the evaluation function J obtained in the SI4 step MR Partial differential value of (θ) ∂J MR (θ) / ∂θ and the Hessian matrix H(θ) obtained in step SI5 are substituted into equation (34) to obtain the candidate control parameter θ m+1 Update (SI6).

[0176] Next, the variable m is updated (SI8) and the candidate control parameter θ m+1 It is determined whether the termination condition is satisfied (SI9). If the termination condition is not satisfied, SI4 to SI8 are repeated. If the termination condition is satisfied, the control parameter θm updated in SI6 is used as the optimal control parameter θ * (SI10) As an example of the termination condition, the evaluation function J MR Partial differential value of (θ) ∂J MR It may be possible to use the fact that (θ) / ∂θ has converged within a preset tolerance range.

[0177] (P2c) Single-computation approach: Non-Iterative Approach The single calculation approach is an optimization approach that performs the iterative calculations performed in the iterative optimization approach in a single calculation.

[0178] Figure 21 shows a reference model of an open-loop control system. In the open-loop control system, a reference value r(k) is input to a controller C, and a control signal obtained by the controller C is used as an input signal to a controlled object P(z), and an estimated output value y O (k;θ) is output. On the other hand, the nominal model M O From (z) the target output value y dO (k) is output.

[0179] Nominal Model M O (z) represents the input / output characteristics of the open-loop control system. The nominal model M of the open-loop control system O (z) is the desired output value y for an arbitrarily given reference value r(k). dO (k) where the subscript “ O " indicates an open-loop control system, and the subscript " d " indicates the target value.

[0180] Nominal model M in open-loop control systems O (z) is expressed by the following equation (42) using the nominal model M(z) in the closed loop system.

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[0181] Estimated output value y of the open-loop control system O (k;θ) is y in the closed loop system equation (17). a (k), and in equation (18) y b (k), and in equation (21) y c It can be obtained using the estimated output value y(k;θ) expressed by each equation (k).

[0182] Hereafter, the estimated output value y b (k) will be used as an example. The estimated output value y of the open-loop control system O (k;θ) is the estimated output value y b (k) is transformed and expressed as the convolution operation of the following equation (43).

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[0183] Equation (43) is the estimated output value y O This shows that (k;θ) is separated into a term of the control parameter θ and a term that does not include the control parameter θ. The term that does not include the control parameter θ is called y O0sepT (k) is expressed as the following equation (44).

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[0184] y in equation (44) O0 sepT (i) is the matrix y O0 sep (i) is the transpose matrix, y ofs (ki) is the output data in the closed loop system, r(i) is the input value, C0 T (z) is the transpose matrix of the matrix (equation (28)) that linearly separates the control parameter θ from the controller, and y O0 T is the transpose matrix of the experimental output data in the open loop system, u0 ofs (k-1) is the input data, u0 ofs (0) is the first input data.

[0185] Evaluation function J for evaluating the response of the controlled object by the controller O (θ) is the desired output value y dO and the estimated output value y O It is expressed by the following equation (45) using the 2-norm of the difference between

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[0186] The evaluation function J expressed by equation (45) O (θ) partial derivative ∂J with respect to the control parameter θ o (θ) / ∂θ is expressed by the following equation (46).

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[0187] Evaluation function J O The optimal control parameter θ of the controller that minimizes (θ) * is the partial differential ∂J of the following equation (47) oThis is the value that makes (θ) / ∂θ 0.

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[0188] where y O Since (k;θ) is a linear equation related to θ, the optimal control parameter θ * is expressed by the following equation (48).

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[0189] According to equation (48), the optimal control parameter θ * is the data y obtained by linearly separating the control parameter θ from the estimated output of the open-loop control system. O0 sep Transpose matrix y of (k) O0 sepT (k) and the desired output data y d0 It is calculated by (k).

[0190] The operating point of the data-driven control simulation may deviate from the experimental data, which may affect the accuracy of the simulation. In addition, the controller does not support control systems in which the output of the controlled object is subjected to minor feedback.

[0191] As a means to solve this problem, the optimal control parameter θ * is rewritten as equation (50). This rewriting is performed by setting the reference value r(i) as M(z) in equation (49) below, since there is no restriction on the reference value r(i) for the output data y0(i) in the open-loop control system of the experimental output data or estimated output value.

[0192] Assuming that the controller has been properly tuned, the operating point of the data-driven control simulation is assumed to be near M(z)y0(i), and the difference between the output data y0(i) and the minor feedback term of the controller M(z)y0(i) (y0(i)-M(z)y0(i)) approaches 0. This suppresses deviation of the operating point of the data-driven control simulation from the experimental data, and enables compatibility with minor feedback control systems.

[0193] The reference value r(i) is set to the following equation (49) based on the above difference (y0(i)-M(z)y0(i)).

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[0194] This results in the optimal control parameter θ * is expressed by the following equation (50).

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[0195] In equations (48) and (50), y O0 sep and y O0 sepT indicates a matrix and a transpose matrix of data obtained by linearly separating the control parameter θ from the estimated output value yo in the open-loop control system.

[0196] Figure 22 shows a block diagram of an open-loop control system when r(i) of equation (49) is introduced. The reference value r(i) = (1 - M(z)) y0(i) rewritten in equation (49) is input to the controller C(z;θ), and the output y of the controlled object P(z) obtained by the data-driven control simulation is O (k;θ) is output. On the other hand, the output data y0(k) is input to the nominal model M O (z)y obtained by inputting O (k) represents the feedback term.

[0197] In the block diagram of the open loop control system in Figure 22, y O (k;θ) denotes the output term, and assuming ideal tuning is achieved, the minor loop term is M(z)y O (i), the inverse matrix term in equation (50) corresponds to the variance of the output data of the open-loop control system, and the numerator term in equation (50) corresponds to the covariance between the output data of the open-loop control system and the feedback term. Therefore, the optimal control parameter θ obtained by equation (50) is * corresponds to the solution by the least-squares (LS) method, and the optimal control parameters can be obtained by one calculation. O0 sep (k) is data obtained by linearly separating the control parameter θ from the estimated output in the open-loop control system.

[0198] The control system of the present invention can be applied to PID control, PI control, and PI-D control systems, and the optimal control parameter θ * is set according to the control method: PID control, PI control, or PI-D control. For example, in the case of PI control, the control parameter θ of the controller is the proportional gain K P , integral gain K I , differential gain K D , feedback gain K L is.

[0199] The flowchart in FIG. 23 shows an example of a procedure for finding the optimal control parameters using a single-calculation optimization approach.

[0200] The optimal control parameter θ expressed by equation (50) * is a matrix of data obtained by linearly separating the control parameters θ from the estimated output in the open-loop control system, and the transposed matrix y O0 sep (k), y O0 sepT (k), output data y O (k), as well as the nominal model M(z).

[0201] Therefore, the optimal control parameter θ expressed by equation (50) * In order to calculate the output data y O (k) is obtained (SN2). Next, the estimated output value y O (k; θ) is calculated by equation (43). In the calculation of equation (43), the input data u0(0) at k=0 and the input data u0 after offset compensation are ofs (i) Output data y0 after offset compensation ofs (i), the reference value r(i), the matrix C0(z) obtained by linearly separating the control parameter θ from the controller, and the data obtained by linearly separating the control parameter θ from the estimated output are used (SN3). The optimal control parameter θ is calculated using equation (50). * (SN4).

[0202] In addition, y O0 sep (k) is the offset-compensated first input data u0 ofs (0), the offset-compensated output data y0 of the closed loop system ofs (i), input value r(i), controller C0 T (z), the transposed matrix y of the experimental output data in the open loop system O0 T , offset compensated input data u0 ofs (i) is obtained by equation (44). [Industrial Applicability]

[0203] The controller design method of the present invention can be applied to the design of a control parameter θ of a high frequency power source (RF generator) as a controlled object (plant). [Explanation of symbols]

[0204] 1 Estimation output device 2 Experimental data storage section 3 Estimated output value storage section 4. Estimated input value calculation section 5 Estimated input value storage section 6 Arithmetic section 6a Convolution block 6b Convolution block 6c Addition Blocks 6d division block 11 Simulation 12 Experiments 13 Simulation 100 Closed-loop control system 100A closed loop system 100B Closed Loop System C Controller C0,C0 T Transfer Function H Hessian matrix J DO Evaluation Function J MR Evaluation Function K transfer function K D Differential Gain K I Integral Gain K L ,K iC Feedback Gain K P Proportional Gain M,M O Nominal Model N sampling number P(z) Control target SW1 and SW2 switches U in Input signal U(z) Estimated input value U0(z) experimental input data V c Output Voltage V in Input voltage V r Target Voltage Y out Output Signal Y(z) Estimated output value Y0(z) experimental output data i C Capacitor Current i L Inductor Current k,m sampling time r(k) reference value uin Input signal u0(k) experimental input data u0 ofs (k) Offset-compensated experimental input data u(k) Estimated input value y out Output Signal y0(k) experimental output data y0 ofs (k) Offset-compensated experimental output data y(k) Estimated output value y,y O Estimated Output Value y O0 (k) Experimental output data of the open-loop control system y O0 sep Data obtained by linearly separating the control parameter θ from the estimated output value of the open-loop control system y dO Desired Output Value u 0_offset ,u m_offset Steady-state value y 0_offset ,y m_offset Steady-state value y a ,y b ,y c Arithmetic expression θ control parameter θ * Optimal Control Parameters θ0 initial parameter φ(u) nonlinearity

Claims

1. In a closed-loop control system in which a control signal from a controller is input as a control input to a controlled object and an output of the controlled object is fed back to the controller, a data-driven simulation step of simulating an output based on a time domain calculation using experimental data of input and output of the controlled object to obtain an estimated output value; an optimal control parameter design step of determining optimal control parameters of the controller using the estimated output values ​​acquired in the data-driven simulation step; Equipped with The data-driven simulation step includes: The estimated input value u obtained by simulating the controlled object and the experimental output data y obtained by experimenting the controlled object ０ a first convolution value obtained by convolving the first and second values ​​in the time domain; and a second convolution calculation value obtained by performing a convolution calculation in the time domain on the estimated output value obtained by the simulation of the controlled object and experimental input data obtained by an experiment on the controlled object; Seeking An estimated output value of the controlled object at the next sampling time is estimated from the difference between the two convolution calculation values. How to design a controller.

2. The data-driven simulation step includes: an experimental data experiment step of collecting and storing sampled values ​​of experimental input data and experimental output data obtained in an experiment on the controlled object; a simulation step of an estimated input value in which a reference value is input to the controller to perform a simulation to obtain an output signal of the controller, and the output signal of the simulation is calculated as an estimated input value for the controlled object and stored; a simulation step of simulating an estimated output value to obtain an estimated output value of a controlled object; Each process is carried out as follows: The step of simulating the estimated output value includes: calculating a first convolution value by performing a convolution operation in the time domain on the estimated input values ​​from sampling times 0 to k−1 obtained in the simulation step of the estimated input values ​​and on experimental output data from sampling times k to 1 obtained in the experimental step; calculating a second convolution value by performing a convolution operation in the time domain on the estimated output values ​​from sampling times 0 to k−1 obtained in the simulation step of the estimated output values ​​and the experimental input data from sampling times k to 1 obtained in the experimental step; calculating a difference between the first convolution calculation value and the second convolution calculation value, and calculating an estimated output value of the controlled object at sampling time k from the difference; The method for designing a controller according to claim 1 .

3. The optimal control parameter design step includes: An evaluation function J for evaluating the response of the controlled object by the controller ＤＯ (θ) is expressed as the 2-norm of the difference between the reference value r and the estimated output value y. Equipped with The evaluation function J ＤＯ The optimal control parameter θ of the controller that minimizes (θ) * of is obtained by a direct optimization approach. The method for designing a controller according to claim 1 or 2.

4. The optimal control parameter θ * is calculated using the Nelder-Mead method. The method for designing a controller according to claim 3 .

5. The optimal control parameter design step includes: The product of the nominal model M(z) and the reference value r is the target output value y for the reference value r. ｄ year, is expressed as An evaluation function J for evaluating the response of the controlled object by the controller ＭＲ (θ) is the target output value y with respect to the reference value r. ｄ and the estimated output value y. year, The evaluation function J ＭＲ The optimal control parameter θ of the controller that minimizes (θ) * of is calculated by an iterative optimization approach of The method for designing a controller according to claim 1 or 2.

6. The optimal control parameter design step includes: The estimated output value in the open loop system is y Ｏ year, The product of the nominal model M(z) and the reference value r in the open loop system is the target output value y for the reference value r. ｄＯ year, An evaluation function J for evaluating the response of the controlled object by the controller Ｏ (θ) as the target output value y ｄＯ and the estimated output value y Ｏ It is expressed as the 2-norm of the difference between year, The data obtained by linearly separating the control parameters from the estimated output in the open-loop control system is called y Ｏ０ ｓｅｐ (k) is the evaluation function J Ｏ The optimal control parameter θ of the controller that minimizes (θ) * of or A single calculation approach is used to find The method for designing a controller according to claim 1 or 2.

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