WO2021006332A1 - Information processing device, program, and calculation method - Google Patents

Information processing device, program, and calculation method Download PDF

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Publication number
WO2021006332A1
WO2021006332A1 PCT/JP2020/026980 JP2020026980W WO2021006332A1 WO 2021006332 A1 WO2021006332 A1 WO 2021006332A1 JP 2020026980 W JP2020026980 W JP 2020026980W WO 2021006332 A1 WO2021006332 A1 WO 2021006332A1
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series data
parameter
time series
output
controller
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French (fr)
Japanese (ja)
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修一 矢作
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いすゞ自動車株式会社
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators

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  • the present disclosure relates to an information processing device, a program, and a calculation method, and more particularly to a technique for setting control parameters of a closed-loop controller equipped with a disturbance compensator.
  • FRIT Fetitious Reference Iterative Tuning
  • the closed loop system is controlled using the control parameters obtained by data drive control such as FRIT, the system may become unstable.
  • the system tends to become unstable when there is no control parameter that realizes the response of the reference model used in FRIT.
  • the inventor of the present application has found by simulation that the system tends to be unstable even when there is a disturbance compensator for compensating for the disturbance mixed in the input to be controlled in FRIT.
  • an object of the present invention is to provide a technique for evaluating the stability of control in a system having a disturbance compensator in FRIT.
  • a certain aspect of the present disclosure includes a controller, a control target having an output of the control target as an input, and a disturbance compensator for compensating for a disturbance of the input of the control target, and the output of the control target is the said.
  • a control system fed back to the input of a controller it is an information processing device that calculates a first parameter which is a parameter of the controller and a second parameter which is a parameter of the disturbance compensator. This device acquires the first time-series data which is the time-series data obtained by adding the output of the disturbance compensator to the output of the controller and the second time-series data which is the time-series data of the output to be controlled.
  • the third time series data which is a pseudo reference signal of the control system, is calculated from the time series data acquisition unit, the first parameter, the second parameter, the first time series data, and the second time series data.
  • Pseudo-reference signal calculation unit a complementary sensitivity function calculation unit that calculates a complementary sensitivity function for the controller based on the second time series data and the third time series data, and an input signal of the control system. It includes an output calculation unit that calculates fourth time-series data, which is an output when applied to the complementary sensitivity function.
  • the control system may further include a reference model that models the output of the controlled object by using an input signal input to the controlled object as an input, and the information processing apparatus may include the third time series data in the reference model.
  • the model output acquisition unit that acquires the 5th time series data which is the output time series data when is input, and the evaluation function regarding the error between the 4th time series data and the 5th time series data.
  • a parameter update unit for updating the first parameter and the second parameter may be further provided.
  • the evaluation function may be the sum of squares of errors between the fourth time-series data and the fifth time-series data, and the parameter update unit performs iterative processing so that the evaluation value of the evaluation function becomes smaller.
  • the first parameter and the second parameter may be updated by.
  • This program includes a controller, a controlled object having the output of the controller as an input, and a disturbance compensator for compensating for disturbance of the input of the controlled object, and the output of the controlled object is the controller.
  • the output of the disturbance compensator is added to the output of the controller to the computer that calculates the first parameter which is the parameter of the controller and the second parameter which is the parameter of the disturbance compensator.
  • a function of calculating the complementary sensitivity function for the controller and a function of calculating the fourth time series data which is an output when the input signal of the control system is applied to the complementary sensitivity function are realized.
  • Another aspect of the present disclosure is a calculation method. This calculation method includes a controller, a control target whose input is the output of the control target, and a disturbance compensator for compensating for disturbance of the input of the control target, and the output of the control target is the controller.
  • Acquiring the first time-series data which is the time-series data obtained by adding the output of the compensator acquiring the second time-series data which is the time-series data of the output to be controlled, the first parameter, the first.
  • This storage medium includes a controller, a control target having the output of the control target as an input, and a disturbance compensator for compensating for disturbance of the input of the control target, and the output of the control target is the control.
  • a storage medium that stores a computer-readable computer program that calculates a first parameter, which is a parameter of the controller, and a second parameter, which is a parameter of the disturbance compensator, in a control system that feeds back to the input of the device.
  • the computer program when executed by the computer, causes the computer to do the following: first time series data, which is time series data obtained by adding the output of the disturbance compensator to the output of the controller.
  • first time series data which is time series data obtained by adding the output of the disturbance compensator to the output of the controller.
  • second time series data which is the time series data of the output of the control target
  • third time series data which is a pseudo reference signal of the control system
  • complementary sensitivity function for the controller based on the second time series data and the third time series data.
  • fourth time series data which is the output when the input signal of the control system is applied to the complementary sensitivity function.
  • a computer-readable recording medium on which this program is recorded may be provided, or this program may be transmitted over a communication line.
  • Engell et al. The cause of the above problem is the instability of the closed loop system because the unstable poles are canceled when the transfer function of the pseudo error (error between the pseudo reference signal and the plant output) is obtained from the plant output. It indicates that the conversion cannot be detected. Therefore, Engell et al. Proposed to obtain the sensitivity function related to the pseudo-reference input and the pseudo-error from the input / output data, and then apply the target value to the obtained sensitivity function to obtain the error that is the output of the sensitivity function. As a result, the error that is the output of the sensitivity function can be obtained without canceling the unstable poles, and the instability of the closed loop system can be detected.
  • the sensitivity function is identified based on the FIR (Finite Impulse Response) model. Therefore, the structure of the plant model is not required to identify the sensitivity function. Furthermore, since it is calculated in the time domain, it can be expanded to online calculation.
  • FIR Finite Impulse Response
  • an evaluation function is set so that the closed loop system and the reference model set by the designer match.
  • a pseudo-reference input is used to obtain a complementary sensitivity function for the controller to be adjusted. That is, the output of the complementary sensitivity function is a function of the control parameter.
  • the target value that the designer wants to give is applied to the complementary sensitivity function, and the output is obtained.
  • the output of the complementary sensitivity function is the output from the plant. That is, by looking at the output of the complementary sensitivity function, it is possible to evaluate the stability of control using the controller parameters in FRIT.
  • the controller parameter that minimizes the square error between the output obtained from the complementary sensitivity function and the output of the reference model set by the designer is obtained by an optimization method such as particle swarm optimization.
  • an optimization method such as particle swarm optimization.
  • FIG. 1 is a diagram for explaining application of standard FRIT to a control system S which is a closed loop system including a disturbance compensator Dw.
  • the controller C is represented by a function C ( ⁇ ) having a first parameter ⁇ as an argument, which is a parameter used for control.
  • the disturbance compensator Dw is represented by a function Dw ( ⁇ ) having a second parameter ⁇ , which is a parameter used for estimating the disturbance T d , as an argument.
  • the sum of the output u fb of the controller C and the estimated value T'd of the disturbance T d which is the output of the disturbance compensator D w, is the control amount u input to the control target P.
  • the purpose of the control system S shown in FIG. 1 is to match the output y of the controlled object P with the output of the reference model M described later. Specifically, it is an object to specify a first parameter ⁇ and a second parameter ⁇ that output a control amount u to be input to the control target P in order to achieve this object.
  • ⁇ and ⁇ are parameters that can be freely adjusted
  • u, T'd , and y are data that can be acquired by observation.
  • d is a target value of the control system S. The disturbance T d cannot be observed.
  • the FRIT When the FRIT is applied to the control system S provided with the disturbance compensator Dw, the FRIT automatically adjusts the first parameter ⁇ and the second parameter ⁇ from a set of input / output data and the reference model M.
  • a set of closed-loop experiments is performed using the initial first parameter ⁇ 0 and the second parameter ⁇ 0, and the input / output data u and y at that time are sampled and measured. At this time, it is assumed that the control system S is stable.
  • control target P will be described on the premise that the dynamics of the rotating body is the control target.
  • the control target P is represented by the following equation (1).
  • the control target is not limited to the rotating body.
  • J represents inertia
  • B represents the viscous braking coefficient
  • y represents the angular velocity
  • u is a torque
  • the control target P controls, for example, the rotation speed of the engine or the rotation speed of the motor by controlling the torque applied to the rotating body.
  • the disturbance compensator Dw estimates the disturbance based on the following equation (2).
  • ⁇ is the filter time constant used by the disturbance compensator Dw
  • s is the Laplace operator.
  • the inertia J and the time constant ⁇ constitute the second parameter ⁇ , which is a parameter of the disturbance compensator Dw.
  • the method of taking ⁇ is not limited to this.
  • the pseudo reference signal r of the control system S is the following equation using u 0 (k) and y 0 (k) which are time series data of the input / output data u and y measured in advance by the experiment. It can be represented by (5).
  • the first parameter ⁇ and the second parameter ⁇ may be collectively described as the parameter ⁇ .
  • r ( ⁇ , ⁇ , k) is expressed as r ( ⁇ , k).
  • equations (1) to (5) are equations in the Laplace region. When these equations are implemented on a computer using a software program, for example, equations (2) and (5) are discretized.
  • the evaluation function J ⁇ regarding the error between the feedback control response shown in FIG. 1 and the target response obtained from the reference model M (z) and the pseudo reference signal r ( ⁇ , k) is expressed by the following equation (6).
  • the parameter ⁇ that minimizes the evaluation function J ⁇ minimizes the square error between the plant output y (k), which is the output of the controlled object P, and the output M (z) r ( ⁇ , k) of the reference model M. In that sense, it is an optimum parameter of the controller C and the disturbance compensator Dw. In general FRIT, the optimum parameter ⁇ is calculated by offline calculation.
  • the evaluation function is not limited to the form shown in the equation (6), and may be one in consideration of restrictions such as control input.
  • FRIT aims to find the optimum control parameters that match the transfer function of the closed-loop control system S with the reference model. That is, FRIT finds the optimum parameter that minimizes the evaluation function J ⁇ represented by the following equation (7).
  • FRIT is one of the data-driven controls that obtains the optimum control parameters offline using a set of input / output data acquired by experiments without repeating the closed loop test using the pseudo reference signal r ( ⁇ , k). It can be said that.
  • the complementary sensitivity function in the time domain (the complementary sensitivity function of the output y of the controlled object P with respect to the target value d of the control system S) is obtained by using the pseudo reference signal r ( ⁇ , k) and the plant output y 0 .
  • the target value d is applied to the obtained complementary sensitivity function, and the response y * is obtained.
  • the FIR model is used to identify the complementary sensitivity function. As a result, it is not necessary to know the structure of the controlled object P, and the complementary sensitivity function can be identified using only the acquired data.
  • Equation (9) the symbol * represents convolution, and t (k) represents the impulse response of the complementary sensitivity function T to the controller C to be adjusted.
  • the pseudo-reference signal r ( ⁇ , k) and the plant output y 0 are observable, but the impulse response t (k) of the complementary sensitivity function T is unknown.
  • Equation (9) becomes the following equation (10) when expressed using a matrix.
  • the impulse response t (k) of the complementary sensitivity function T is given by the following equation (11). expressed.
  • Equation (11) can be said to be a deconvolution of equation (9).
  • t depends on the parameter ⁇ .
  • Equation (12) becomes the following equation (13) when expressed using a matrix.
  • the pseudo-reference signal r ( ⁇ , k), which is a function of the parameter ⁇ is adjusted so as to match the acquired plant output y 0 .
  • the parameter ⁇ is adjusted to change the plant output y * so that the plant output y 0 matches the output M (z) d (k) of the reference model M. That is, while the standard FRIT finds the parameter ⁇ so as to match the plant output obtained in advance by the experiment, the method according to the embodiment matches the output M (z) d (k) of the reference model. To find the parameter ⁇ .
  • FIG. 2 is a diagram schematically showing a configuration of FRIT in consideration of stability.
  • the pseudo reference signal r ( ⁇ ) is calculated from the input / output data of the control system S when the first parameter ⁇ is the initial value ⁇ 0 and the initial value of the second parameter ⁇ is ⁇ 0 .
  • the complementary sensitivity function t is obtained by using the calculated pseudo reference input r ( ⁇ ) and the plant output y using the above equation (11), and the target value d, which is the input signal of the control system S, is used as the complementary sensitivity function t. Is entered in.
  • the parameter ⁇ that minimizes the error between the output y * which is the output of the complementary sensitivity function t, and the output M (z) d of the reference model is obtained by the optimization method.
  • FIG. 3 is a diagram schematically showing a functional configuration of the information processing device 1 according to the embodiment.
  • the information processing device 1 includes a storage unit 2 and a control unit 3.
  • the arrows indicate the main data flows, and there may be data flows not shown in FIG.
  • each functional block shows not the configuration of each hardware (device) but the configuration of each function. Therefore, the functional block shown in FIG. 3 may be mounted in a single device, or may be mounted separately in a plurality of devices. Data transfer between functional blocks may be performed via any means such as a data bus, a network, and a portable storage medium.
  • the storage unit 2 includes a ROM (Read Only Memory) that stores the BIOS (Basic Input Output System) of the computer that realizes the information processing device 1, a RAM (Random Access Memory) that serves as a work area of the information processing device 1, and an OS ( It is a large-capacity storage device such as an HDD (Hard Disk Drive) or an SSD (Solid State Drive) that stores various information referred to when the application program is executed, such as an Operating System) or an application program.
  • BIOS Basic Input Output System
  • RAM Random Access Memory
  • OS It is a large-capacity storage device such as an HDD (Hard Disk Drive) or an SSD (Solid State Drive) that stores various information referred to when the application program is executed, such as an Operating System) or an application program.
  • the control unit 3 is a processor such as a CPU (Central Processing Unit) or GPU (Graphics Processing Unit) of the information processing device 1, and the time-series data acquisition unit 30 is simulated by executing a program stored in the storage unit 2. It functions as a reference signal calculation unit 31, a complementary sensitivity function calculation unit 32, an output calculation unit 33, a model output acquisition unit 34, and a parameter update unit 35.
  • a processor such as a CPU (Central Processing Unit) or GPU (Graphics Processing Unit) of the information processing device 1
  • the time-series data acquisition unit 30 is simulated by executing a program stored in the storage unit 2. It functions as a reference signal calculation unit 31, a complementary sensitivity function calculation unit 32, an output calculation unit 33, a model output acquisition unit 34, and a parameter update unit 35.
  • FIG. 3 shows an example in which the information processing device 1 is composed of a single device.
  • the information processing device 1 may be realized by computing resources such as a plurality of processors and memories, such as a cloud computing system.
  • each unit constituting the control unit 3 is realized by executing a program by at least one of a plurality of different processors.
  • the information processing device 1 is a control system S including a controller C, a control target P having an output of the control C as an input, and a disturbance compensator Dw for compensating for a disturbance of the input of the control target P.
  • This is a device for calculating the first parameter ⁇ , which is a parameter of the controller C, and the second parameter ⁇ , which is a parameter of the disturbance compensator Dw.
  • the control system S is a closed loop system in which the output of the controlled object P is fed back to the input of the controller C.
  • the time-series data acquisition unit 30 includes the first time-series data which is the time-series data obtained by adding the output of the disturbance compensator Dw to the output of the controller C and the second time-series data which is the time-series data of the output of the control target P. And get.
  • the first time-series data corresponds to the control amount u to be input to the control target P described above
  • the second time-series data corresponds to the output y of the control target P described above. Therefore, in the present specification, they may be referred to as "first time series data u" and "second time series data y".
  • the pseudo-reference signal calculation unit 31 uses the first parameter ⁇ , the second parameter ⁇ , the first time-series data u, and the second time-series data y from the pseudo-reference of the control system S based on the above equation (5). Estimate the third time series data which is a signal.
  • the complementary sensitivity function calculation unit 32 calculates the complementary sensitivity function t for the controller C using the above equation (11) based on the second time series data y and the third time series data r ( ⁇ ). ..
  • the impulse response t of the complementary sensitivity function T is calculated by the complementary sensitivity function calculation unit 32, but the calculation result of the complementary sensitivity function calculation unit 32 is described as the complementary sensitivity function t for convenience of the following description.
  • the output calculation unit 33 calculates the fourth time series data which is the output when the input signal d of the control system S is applied to the complementary sensitivity function t by using the above equation (12) or equation (13).
  • the fourth time-series data corresponds to the output y * when the input signal d (target value) of the control system S is applied to the complementary sensitivity function T. Therefore, it may be described below as “fourth time series data y * ".
  • the first time series data u which is the control amount to be input to the control target P
  • the second time series data y which is the output of the control target P
  • the input signal d of the control system S are all quantities that can be acquired by observation. Is.
  • the information processing device 1 calculates the output y * when the input signal d is input to the control system S by using the first time series data u, the second time series data y, and the input signal d acquired by observation. can do.
  • the output y * is the output from the control target P.
  • the information processing device 1 analyzes the behavior of the output y * (for example, whether or not it diverges, whether or not it vibrates, whether or not it converges, etc.), thereby controlling the control having the disturbance compensator Dw in FRIT.
  • the stability of control using the first parameter ⁇ and the second parameter ⁇ in the system S can be evaluated.
  • the control system S includes a reference model M that realizes that the output of the control target P with respect to the input signal d is a predetermined output.
  • the reference model M is determined by the designer so that the output of the controlled object P is the output desired by the designer.
  • the model output acquisition unit 34 acquires the fifth time-series data, which is the output time-series data when the input signal d is input to the reference model M.
  • the fifth time series data corresponds to the output M (z) d of the reference model described above.
  • the fifth time-series data may be referred to as a "fifth time-series data y d".
  • the information processing device 1 can evaluate the stability of the control using the first parameter ⁇ and the second parameter ⁇ in the FRIT, the information processing device 1 has a parameter so that the control is stabilized.
  • ⁇ first parameter ⁇ and second parameter ⁇
  • the parameter update unit 35 based on the evaluation value of the evaluation function J * (sigma) regarding the error of the fourth time-series data y * and fifth time-series data y d, updates the parameter sigma To do.
  • the evaluation function J * ( ⁇ ) used by the parameter update unit 35 is the fourth time series data y * and the fifth time series data. It is the sum of squares of the error with y d .
  • the parameter update unit 35 updates the parameter ⁇ by iterative processing so that the evaluation value of the evaluation function J * ( ⁇ ) becomes small. That is, the parameter updating unit 35 is determined by repeating the optimum parameter ⁇ in the sense that the sum of squares of errors between the fourth time-series data y * and fifth time-series data y d becomes smaller.
  • the fourth time series data y * diverges or vibrates, the sum of squares of the errors between the fourth time series data y * and the fifth time series data y d becomes large.
  • the information processing apparatus 1 updates the parameter ⁇ so that the sum of squares of the errors between the fourth time series data y * and the fifth time series data y d becomes smaller by the parameter update unit 35, so that the information processing apparatus 1 uses the first parameter in FRIT. It is possible to stabilize the control of the plant using ⁇ and the second parameter ⁇ .
  • the parameter update unit 35 may use any optimization method as long as the parameter ⁇ can be updated so that the evaluation value of the evaluation function becomes small.
  • the parameter updating unit 35 may update the parameter ⁇ by using a particle swarm optimization method with a predetermined number of repetitions as the upper limit of the number of iterations.
  • FIG. 4 is a flowchart for explaining the flow of information processing executed by the information processing apparatus 1 according to the embodiment. The process in this flowchart starts, for example, when the information processing device 1 is activated.
  • the time-series data acquisition unit 30 acquires the first time-series data u, which is the time-series data obtained by adding the output of the disturbance compensator Dw to the output of the controller C (S2). Further, the time-series data acquisition unit 30 acquires the second time-series data y, which is the time-series data of the output of the control target P (S4).
  • the pseudo-reference signal calculation unit 31 controls from the first parameter ⁇ which is a parameter of the controller C, the second parameter ⁇ which is a parameter of the disturbance compensator Dw, the first time series data u, and the second time series data y.
  • the third time series data r ( ⁇ ), which is a pseudo reference signal of the system S, is estimated (S6).
  • the complementary sensitivity function calculation unit 32 calculates the complementary sensitivity function t for the controller C using the equation (11) based on the second time series data y and the third time series data r ( ⁇ ) (S8). ..
  • the output calculation unit 33 uses the equation (14) to apply the input signal d of the control system S to the complementary sensitivity function t, which is the output of the fourth time series data y * (that is, the control target for the input signal d). Output of P) is calculated (S10).
  • the model output acquisition unit 34 acquires the fifth time series data y d , which is the output time series data when the input signal d is input to the reference model M (S12).
  • Parameter updating unit 35 calculates the evaluation value of the evaluation function J (sigma) regarding the error of the fourth time-series data y * and fifth time-series data y d (S14).
  • the parameter update unit 35 updates the parameter ⁇ (first parameter ⁇ and second parameter ⁇ ) by iterative processing so that the evaluation value of the evaluation function J ( ⁇ ) becomes smaller (S16).
  • the parameter ⁇ which is the parameter of the controller C in the control system S having the disturbance compensator Dw and the parameter of the disturbance compensator Dw.
  • the stability of control using the second parameter ⁇ can be evaluated.
  • the information processing apparatus 1 can also optimize the first parameter ⁇ and the second parameter ⁇ in FRIT so that the control of the closed loop system is stabilized.
  • the information processing apparatus, program, and calculation method of the present disclosure are useful in that the stability of control in a system having a disturbance compensator can be evaluated in FRIT.
  • Control unit 30 Time series data acquisition unit 31 ... Pseudo-reference signal calculation unit 32 ... Complementary sensitivity function calculation unit 33 ... Output calculation unit 34 ... Model output acquisition unit 35 ... Parameter update unit C ... Controller Dw ... Disturbance compensator M ... Reference model P ... Control target S ... Control system

Abstract

Provided is a feature for evaluating, with regard to FRIT, the stability of control in a system having a disturbance compensator.　An information processing device (1) calculates a control parameter in a control system (S) of a closed loop system provided with a disturbance compensator (Dw). A time series data acquisition unit (30) acquires first time series data, which is time series data obtained by adding an output of the disturbance compensator (Dw) to an output of a controller (C), and second time series data, which is time series data of an output of a control subject (P). A pseudo-reference signal calculation unit (31) calculates third time series data, which is a pseudo-reference signal of the control system (S), from a first parameter, a second parameter, the first time series data, and the second time series data. A complementary sensitivity function calculation unit (32) calculates a complementary sensitivity function for the controller (C) on the basis of the second time series data and the third time series data. An output operation unit (33) calculates fourth time series data, which is an output when an input signal of the control system (S) is applied to the complementary sensitivity function.

Description

情報処理装置、プログラム、及び算出方法Information processing equipment, programs, and calculation methods
　本開示は情報処理装置、プログラム、及び算出方法に関し、特に、外乱補償器を備える閉ループ系の制御器の制御パラメータを設定する技術に関する。 The present disclosure relates to an information processing device, a program, and a calculation method, and more particularly to a technique for setting control parameters of a closed-loop controller equipped with a disturbance compensator.
　閉ループ系における制御対象のモデルを用いない制御手法が種々提案されている。このようなモデルを用いない制御器パラメータの自動調整手法の一つとしてＦＲＩＴ（Fictitious Reference Iterative Tuning）が知られている（特許文献１参照）。 Various control methods that do not use a model to be controlled in a closed loop system have been proposed. FRIT (Fictitious Reference Iterative Tuning) is known as one of the methods for automatically adjusting controller parameters without using such a model (see Patent Document 1).
日本国特開２０１７－１８２６２４号公報Japanese Patent Application Laid-Open No. 2017-182624
　ＦＲＩＴ等のデータ駆動制御により得られた制御パラメータを用いて閉ループ系を制御すると、系が不安定となる場合がある。特に、ＦＲＩＴで用いられる参照モデルの応答を実現する制御パラメータが存在しない場合に系が不安定となりやすいことが知られている。また、本願の発明者は、ＦＲＩＴにおいて制御対象の入力に混入する外乱を補償する外乱補償器が存在する場合にも、系が不安定となりやすいことをシミュレーションにより見出した。 If the closed loop system is controlled using the control parameters obtained by data drive control such as FRIT, the system may become unstable. In particular, it is known that the system tends to become unstable when there is no control parameter that realizes the response of the reference model used in FRIT. Further, the inventor of the present application has found by simulation that the system tends to be unstable even when there is a disturbance compensator for compensating for the disturbance mixed in the input to be controlled in FRIT.
　本開示はこれらの点に鑑みてなされたものであり、ＦＲＩＴにおいて、外乱補償器を有する系における制御の安定性を評価する技術を提供することを目的とする。 The present disclosure has been made in view of these points, and an object of the present invention is to provide a technique for evaluating the stability of control in a system having a disturbance compensator in FRIT.
　本開示のある態様は、制御器と、前記制御器の出力を入力とする制御対象と、前記制御対象の入力の外乱を補償するための外乱補償器とを備え、前記制御対象の出力が前記制御器の入力にフィードバックされる制御システムにおいて、前記制御器のパラメータである第１パラメータと前記外乱補償器のパラメータである第２パラメータとを算出する情報処理装置である。この装置は、前記制御器の出力に前記外乱補償器の出力を加算した時系列データである第１時系列データと、前記制御対象の出力の時系列データである第２時系列データとを取得する時系列データ取得部と、前記第１パラメータ、前記第２パラメータ、前記第１時系列データ、及び前記第２時系列データから、前記制御システムの擬似参照信号である第３時系列データを算出する擬似参照信号算出部と、前記第２時系列データと前記第３時系列データとに基づいて、前記制御器に対する相補感度関数を算出する相補感度関数算出部と、前記制御システムの入力信号を前記相補感度関数に印加したときの出力である第４時系列データを算出する出力演算部と、を備える。 A certain aspect of the present disclosure includes a controller, a control target having an output of the control target as an input, and a disturbance compensator for compensating for a disturbance of the input of the control target, and the output of the control target is the said. In a control system fed back to the input of a controller, it is an information processing device that calculates a first parameter which is a parameter of the controller and a second parameter which is a parameter of the disturbance compensator. This device acquires the first time-series data which is the time-series data obtained by adding the output of the disturbance compensator to the output of the controller and the second time-series data which is the time-series data of the output to be controlled. The third time series data, which is a pseudo reference signal of the control system, is calculated from the time series data acquisition unit, the first parameter, the second parameter, the first time series data, and the second time series data. Pseudo-reference signal calculation unit, a complementary sensitivity function calculation unit that calculates a complementary sensitivity function for the controller based on the second time series data and the third time series data, and an input signal of the control system. It includes an output calculation unit that calculates fourth time-series data, which is an output when applied to the complementary sensitivity function.
　前記制御システムは、前記制御対象に入力する入力信号を入力として前記制御対象の出力をモデル化する参照モデルをさらに備えてもよく、前記情報処理装置は、前記参照モデルに前記第３時系列データを入力した場合の出力の時系列データである第５時系列データを取得するモデル出力取得部と、前記第４時系列データと前記第５時系列データとの誤差に関する評価関数の評価値に基づいて前記第１パラメータと前記第２パラメータとを更新するパラメータ更新部と、をさらに備えてもよい。 The control system may further include a reference model that models the output of the controlled object by using an input signal input to the controlled object as an input, and the information processing apparatus may include the third time series data in the reference model. Based on the evaluation value of the model output acquisition unit that acquires the 5th time series data which is the output time series data when is input, and the evaluation function regarding the error between the 4th time series data and the 5th time series data. Further, a parameter update unit for updating the first parameter and the second parameter may be further provided.
　前記評価関数は、前記第４時系列データと前記第５時系列データとの誤差の二乗和であってもよく、前記パラメータ更新部は、前記評価関数の評価値が小さくなるように、反復処理によって前記第１パラメータ及び前記第２パラメータを更新してもよい。 The evaluation function may be the sum of squares of errors between the fourth time-series data and the fifth time-series data, and the parameter update unit performs iterative processing so that the evaluation value of the evaluation function becomes smaller. The first parameter and the second parameter may be updated by.
　本開示の別の態様は、プログラムである。このプログラムは、制御器と、前記制御器の出力を入力とする制御対象と、前記制御対象の入力の外乱を補償するための外乱補償器とを備え、前記制御対象の出力が前記制御器の入力にフィードバックされる制御システムにおいて、前記制御器のパラメータである第１パラメータと前記外乱補償器のパラメータである第２パラメータとを算出するコンピュータに、前記制御器の出力に前記外乱補償器の出力を加算した時系列データである第１時系列データを取得する機能と、前記制御対象の出力の時系列データである第２時系列データを取得する機能と、前記第１パラメータ、前記第２パラメータ、前記第１時系列データ、及び前記第２時系列データから、前記制御システムの擬似参照信号である第３時系列データを算出する機能と、前記第２時系列データと前記第３時系列データとに基づいて、前記制御器に対する相補感度関数を算出する機能と、前記制御システムの入力信号を前記相補感度関数に印加したときの出力である第４時系列データを算出する機能と、を実現させる。
　本開示の別の態様は、算出方法である。この算出方法は、制御器と、前記制御器の出力を入力とする制御対象と、前記制御対象の入力の外乱を補償するための外乱補償器とを備え、前記制御対象の出力が前記制御器の入力にフィードバックされる制御システムにおいて、前記制御器のパラメータである第１パラメータと前記外乱補償器のパラメータである第２パラメータとを算出する算出方法であって、前記制御器の出力に前記外乱補償器の出力を加算した時系列データである第１時系列データを取得すること、前記制御対象の出力の時系列データである第２時系列データを取得すること、前記第１パラメータ、前記第２パラメータ、前記第１時系列データ、及び前記第２時系列データから、前記制御システムの擬似参照信号である第３時系列データを算出すること、前記第２時系列データと前記第３時系列データとに基づいて、前記制御器に対する相補感度関数を算出すること、及び前記制御システムの入力信号を前記相補感度関数に印加したときの出力である第４時系列データを算出すること、を含む。
　本開示の別の態様は、記憶媒体である。この記憶媒体は、制御器と、前記制御器の出力を入力とする制御対象と、前記制御対象の入力の外乱を補償するための外乱補償器と、を備え、前記制御対象の出力が前記制御器の入力にフィードバックされる制御システムにおいて、前記制御器のパラメータである第１パラメータと前記外乱補償器のパラメータである第２パラメータとを算出するコンピュータによって読取可能なコンピュータプログラムを記憶する記憶媒体であって、前記コンピュータプログラムは、前記コンピュータにより実行されると、前記コンピュータに以下を実行させる：前記制御器の出力に前記外乱補償器の出力を加算した時系列データである第１時系列データを取得すること、前記制御対象の出力の時系列データである第２時系列データを取得すること、前記第１パラメータ、前記第２パラメータ、前記第１時系列データ、及び前記第２時系列データから、前記制御システムの擬似参照信号である第３時系列データを算出すること、前記第２時系列データと前記第３時系列データとに基づいて、前記制御器に対する相補感度関数を算出すること、及び前記制御システムの入力信号を前記相補感度関数に印加したときの出力である第４時系列データを算出すること。 Another aspect of the disclosure is a program. This program includes a controller, a controlled object having the output of the controller as an input, and a disturbance compensator for compensating for disturbance of the input of the controlled object, and the output of the controlled object is the controller. In the control system fed back to the input, the output of the disturbance compensator is added to the output of the controller to the computer that calculates the first parameter which is the parameter of the controller and the second parameter which is the parameter of the disturbance compensator. The function of acquiring the first time-series data which is the time-series data obtained by adding the above, the function of acquiring the second time-series data which is the time-series data of the output of the control target, the first parameter, and the second parameter. , The function of calculating the third time series data which is a pseudo reference signal of the control system from the first time series data and the second time series data, and the second time series data and the third time series data. Based on the above, a function of calculating the complementary sensitivity function for the controller and a function of calculating the fourth time series data which is an output when the input signal of the control system is applied to the complementary sensitivity function are realized. Let me.
Another aspect of the present disclosure is a calculation method. This calculation method includes a controller, a control target whose input is the output of the control target, and a disturbance compensator for compensating for disturbance of the input of the control target, and the output of the control target is the controller. This is a calculation method for calculating a first parameter which is a parameter of the controller and a second parameter which is a parameter of the disturbance compensator in the control system fed back to the input of the controller, and the disturbance is output to the output of the controller. Acquiring the first time-series data which is the time-series data obtained by adding the output of the compensator, acquiring the second time-series data which is the time-series data of the output to be controlled, the first parameter, the first. To calculate the third time series data which is a pseudo reference signal of the control system from the two parameters, the first time series data, and the second time series data, the second time series data and the third time series. It includes calculating the complementary sensitivity function for the controller based on the data, and calculating the fourth time series data which is the output when the input signal of the control system is applied to the complementary sensitivity function. ..
Another aspect of the disclosure is a storage medium. This storage medium includes a controller, a control target having the output of the control target as an input, and a disturbance compensator for compensating for disturbance of the input of the control target, and the output of the control target is the control. A storage medium that stores a computer-readable computer program that calculates a first parameter, which is a parameter of the controller, and a second parameter, which is a parameter of the disturbance compensator, in a control system that feeds back to the input of the device. The computer program, when executed by the computer, causes the computer to do the following: first time series data, which is time series data obtained by adding the output of the disturbance compensator to the output of the controller. To acquire, to acquire the second time series data which is the time series data of the output of the control target, from the first parameter, the second parameter, the first time series data, and the second time series data. To calculate the third time series data which is a pseudo reference signal of the control system, and to calculate the complementary sensitivity function for the controller based on the second time series data and the third time series data. And to calculate the fourth time series data which is the output when the input signal of the control system is applied to the complementary sensitivity function.
　このプログラムを提供するため、あるいはプログラムの一部をアップデートするために、このプログラムを記録したコンピュータ読み取り可能な記録媒体が提供されてもよく、また、このプログラムが通信回線で伝送されてもよい。 In order to provide this program or to update a part of the program, a computer-readable recording medium on which this program is recorded may be provided, or this program may be transmitted over a communication line.
　なお、以上の構成要素の任意の組み合わせ、本開示の表現を方法、装置、システム、コンピュータプログラム、データ構造、記録媒体などの間で変換したものもまた、本開示の態様として有効である。 It should be noted that any combination of the above components and the conversion of the expression of the present disclosure between methods, devices, systems, computer programs, data structures, recording media, etc. are also effective as aspects of the present disclosure.
　本開示によれば、ＦＲＩＴにおいて、外乱補償器を有する系における制御の安定性を評価することができる。 According to the present disclosure, it is possible to evaluate the stability of control in a system having a disturbance compensator in FRIT.
外乱補償器を備える閉ループ系である制御システムに標準的なＦＲＩＴを適用することを説明するための図である。It is a figure for demonstrating the application of a standard FRIT to a control system which is a closed loop system equipped with a disturbance compensator. 安定性を考慮したＦＲＩＴの構成を模式的に示す図である。It is a figure which shows typically the structure of FRIT in consideration of stability. 実施の形態に係る情報処理装置の機能構成を模式的に示す図である。It is a figure which shows typically the functional structure of the information processing apparatus which concerns on embodiment. 実施の形態に係る情報処理装置が実行する情報処理の流れを説明するためのフローチャートである。It is a flowchart for demonstrating the flow of the information processing executed by the information processing apparatus which concerns on embodiment.
［１．概略］
　ＦＲＩＴや非反証制御等のデータ駆動制御により得られた制御パラメータを用いて制御を行うと、閉ループ系が不安定化する場合がある。特に、制御器の構造上、参照モデルの応答を実現する制御パラメータが存在しない場合に不安定化が生じやすいことが知られている。この問題はSafonovが提案した擬似参照入力を使用する場合に生じる。 [1. Summary]
If control is performed using control parameters obtained by data-driven control such as FRIT or non-proof control, the closed loop system may become unstable. In particular, it is known that instability is likely to occur when there is no control parameter that realizes the response of the reference model due to the structure of the controller. This problem arises when using the pseudo-reference input proposed by Safonov.
　Engellらは、上記の問題が発生する原因として、プラント出力から擬似誤差（擬似参照信号とプラント出力の誤差）の伝達関数を求める際に不安定極が相殺されてしまうため、閉ループ系の不安定化を検知できないことを示している。そこで、Engellらは、擬似参照入力と擬似誤差に関する感度関数を入出力データから求めた後、得られた感度関数に目標値を印加し感度関数の出力である誤差を求めることを提案した。これにより、不安定極を相殺することなく感度関数の出力である誤差を求めることができ、閉ループ系の不安定化を検知することができる。Engellらの手法において、感度関数はＦＩＲ（Finite Impulse Response）モデルに基づいて同定される。このため、感度関数の同定にプラントモデルの構造は不要である。さらに、時間領域で計算していることからオンライン計算への展開が可能となる。 Engell et al., The cause of the above problem is the instability of the closed loop system because the unstable poles are canceled when the transfer function of the pseudo error (error between the pseudo reference signal and the plant output) is obtained from the plant output. It indicates that the conversion cannot be detected. Therefore, Engell et al. Proposed to obtain the sensitivity function related to the pseudo-reference input and the pseudo-error from the input / output data, and then apply the target value to the obtained sensitivity function to obtain the error that is the output of the sensitivity function. As a result, the error that is the output of the sensitivity function can be obtained without canceling the unstable poles, and the instability of the closed loop system can be detected. In the method of Engell et al., The sensitivity function is identified based on the FIR (Finite Impulse Response) model. Therefore, the structure of the plant model is not required to identify the sensitivity function. Furthermore, since it is calculated in the time domain, it can be expanded to online calculation.
　Engellらは感度関数の出力である誤差を最小にする評価関数を設定した。これに対し、実施の形態に係る手法は、閉ループ系と設計者が設定した参照モデルとが一致するような評価関数を設定する。具体的には、本実施の形態では、まず、擬似参照入力を利用し、調整する制御器に対する相補感度関数を求める。すなわち相補感度関数の出力は制御パラメータの関数となる。次に、設計者が与えたい目標値を相補感度関数に印加しその出力を求める。相補感度関数の出力はプラントからの出力である。すなわち、相補感度関数の出力を見ることにより、ＦＲＩＴにおいて制御器パラメータを用いた制御の安定性を評価することができる。 Engell et al. Set an evaluation function that minimizes the error that is the output of the sensitivity function. On the other hand, in the method according to the embodiment, an evaluation function is set so that the closed loop system and the reference model set by the designer match. Specifically, in the present embodiment, first, a pseudo-reference input is used to obtain a complementary sensitivity function for the controller to be adjusted. That is, the output of the complementary sensitivity function is a function of the control parameter. Next, the target value that the designer wants to give is applied to the complementary sensitivity function, and the output is obtained. The output of the complementary sensitivity function is the output from the plant. That is, by looking at the output of the complementary sensitivity function, it is possible to evaluate the stability of control using the controller parameters in FRIT.
　実施の形態に係る手法では、相補感度関数から得られた出力と設計者が設定した参照モデルの出力の二乗誤差が最小になる制御器パラメータを粒子群最適化等の最適化手法により求める。これにより、標準的なＦＲＩＴでは閉ループ系が不安定になる場合であっても、本実施の形態では安定な制御パラメータが得られる。これより、実施の形態は標準ＦＲＩＴの利点を活かしたまま不安定化を軽減することができる。 In the method according to the embodiment, the controller parameter that minimizes the square error between the output obtained from the complementary sensitivity function and the output of the reference model set by the designer is obtained by an optimization method such as particle swarm optimization. As a result, stable control parameters can be obtained in the present embodiment even when the closed loop system becomes unstable in the standard FRIT. From this, the embodiment can reduce the instability while taking advantage of the standard FRIT.
［２．安定性を考慮したＦＲＩＴの導出］［２．１．標準ＦＲＩＴ］
　図１は、外乱補償器Ｄｗを備える閉ループ系である制御システムＳに標準的なＦＲＩＴを適用することを説明するための図である。図１に示す制御システムＳにおいて、制御器Ｃは制御に用いるパラメータである第１パラメータθを引数とする関数Ｃ（θ）で表現されている。また、外乱補償器Ｄｗは、外乱Ｔｄの推定に用いるパラメータである第２パラメータξを引数とする関数Ｄｗ（ξ）で表現されている。制御器Ｃの出力ｕｆｂと、外乱補償器Ｄｗの出力である外乱Ｔｄの推定値Ｔ’ｄとの和が、制御対象Ｐに入力される制御量ｕとなる。 [2. Derivation of FRIT in consideration of stability] [2.1. Standard FRIT]
FIG. 1 is a diagram for explaining application of standard FRIT to a control system S which is a closed loop system including a disturbance compensator Dw. In the control system S shown in FIG. 1, the controller C is represented by a function C (θ) having a first parameter θ as an argument, which is a parameter used for control. Further, the disturbance compensator Dw is represented by a function Dw (ξ) having a second parameter ξ, which is a parameter used for estimating the disturbance T d , as an argument. The sum of the output u fb of the controller C and the estimated value T'd of the disturbance T d , which is the output of the disturbance compensator D w, is the control amount u input to the control target P.
　図１に示す制御システムＳは、制御対象Ｐの出力ｙと後述する参照モデルＭの出力とを一致させることが目的である。具体的には、この目的を達成するために制御対象Ｐに入力すべき制御量ｕを出力するような第１パラメータθ及び第２パラメータξを特定することが目的である。なお、図１において、θ及びξは自由に調整できるパラメータであり、ｕ、Ｔ’ｄ、及びｙは観測により取得可能なデータである。また、ｄは制御システムＳの目標値である。外乱Ｔｄは観測することができない。 The purpose of the control system S shown in FIG. 1 is to match the output y of the controlled object P with the output of the reference model M described later. Specifically, it is an object to specify a first parameter θ and a second parameter ξ that output a control amount u to be input to the control target P in order to achieve this object. In FIG. 1, θ and ξ are parameters that can be freely adjusted, and u, T'd , and y are data that can be acquired by observation. Further, d is a target value of the control system S. The disturbance T d cannot be observed.
　外乱補償器Ｄｗを備える制御システムＳにＦＲＩＴを適用する場合、ＦＲＩＴは１組の入出力データと参照モデルＭとから、第１パラメータθと第２パラメータξとを自動調整することになる。初期の第１パラメータθ０及び第２パラメータξ０を用いて１組の閉ループ実験を行い、そのときの入出力データｕ及びｙをサンプリングして計測する。このとき、制御システムＳは安定であるとする。 When the FRIT is applied to the control system S provided with the disturbance compensator Dw, the FRIT automatically adjusts the first parameter θ and the second parameter ξ from a set of input / output data and the reference model M. A set of closed-loop experiments is performed using the initial first parameter θ 0 and the second parameter ξ 0, and the input / output data u and y at that time are sampled and measured. At this time, it is assumed that the control system S is stable.
　以下、本明細書では、制御対象Ｐは回転体の動力学を制御対象であることを前提として説明する。この場合、制御対象Ｐは以下の式（１）で表される。しかしながら、制御対象は回転体に限られないことは当業者であれば理解できることである。 Hereinafter, in the present specification, the control target P will be described on the premise that the dynamics of the rotating body is the control target. In this case, the control target P is represented by the following equation (1). However, those skilled in the art can understand that the control target is not limited to the rotating body.
Figure JPOXMLDOC01-appb-M000001
 　式（１）において、Ｊはイナーシャ、Ｂは粘性制動係数を表し、ｙは角速度を表す。この場合、ｕはトルクであり、制御対象Ｐは、回転体に与えるトルクを制御することにより、例えばエンジンの回転数やモータの回転数を制御する。
Figure JPOXMLDOC01-appb-M000001
 In equation (1), J represents inertia, B represents the viscous braking coefficient, and y represents the angular velocity. In this case, u is a torque, and the control target P controls, for example, the rotation speed of the engine or the rotation speed of the motor by controlling the torque applied to the rotating body.
　外乱補償器Ｄｗは、以下の式（２）に基づいて外乱を推定する。 The disturbance compensator Dw estimates the disturbance based on the following equation (2).
Figure JPOXMLDOC01-appb-M000002
 　式（２）において、τは外乱補償器Ｄｗが使用するフィルタ時定数であり、ｓはラプラス演算子である。ここでは、一例として、イナーシャＪ及び時定数τが、外乱補償器Ｄｗのパラメータである第２パラメータξを構成する。なお、ξの取り方はこれに限らない。
Figure JPOXMLDOC01-appb-M000002
 In equation (2), τ is the filter time constant used by the disturbance compensator Dw, and s is the Laplace operator. Here, as an example, the inertia J and the time constant τ constitute the second parameter ξ, which is a parameter of the disturbance compensator Dw. The method of taking ξ is not limited to this.
　式（１）、式（２）、及び図１より、以下の式（３）が成り立つ。 From equations (1), (2), and FIG. 1, the following equation (3) holds.
Figure JPOXMLDOC01-appb-M000003
Figure JPOXMLDOC01-appb-M000003
　式（３）を整理すると以下の式（４）を得る。 The following formula (4) is obtained by rearranging the formula (3).
Figure JPOXMLDOC01-appb-M000004
Figure JPOXMLDOC01-appb-M000004
　式（４）より、制御システムＳの擬似参照信号ｒは、実験によりあらかじめ測定した入出力データｕ及びｙの時系列データであるｕ０（ｋ）及びｙ０（ｋ）を用いて以下の式（５）で表せる。 From the equation (4), the pseudo reference signal r of the control system S is the following equation using u 0 (k) and y 0 (k) which are time series data of the input / output data u and y measured in advance by the experiment. It can be represented by (5).
Figure JPOXMLDOC01-appb-M000005
Figure JPOXMLDOC01-appb-M000005
　以下、記載の便宜のため、第１パラメータθと第２パラメータξとをあわせてパラメータσと記載することがある。この場合、ｒ（θ，ξ，ｋ）はｒ（σ，ｋ）と表現される。また、説明の便宜上、上記式（１）から式（５）はラプラス領域における式である。これらの式をソフトウェアプログラムを用いて計算機上で実装する場合には、例えば式（２）や式（５）は離散化することになる。 Hereinafter, for convenience of description, the first parameter θ and the second parameter ξ may be collectively described as the parameter σ. In this case, r (θ, ξ, k) is expressed as r (σ, k). Further, for convenience of explanation, the above equations (1) to (5) are equations in the Laplace region. When these equations are implemented on a computer using a software program, for example, equations (2) and (5) are discretized.
　図１に示すフィードバック制御の応答と、参照モデルＭ（ｚ）及び擬似参照信号ｒ（σ，ｋ）から得られる目標応答との誤差に関する評価関数Ｊσは次式（６）で表される。 The evaluation function J σ regarding the error between the feedback control response shown in FIG. 1 and the target response obtained from the reference model M (z) and the pseudo reference signal r (σ, k) is expressed by the following equation (6).
Figure JPOXMLDOC01-appb-M000006
Figure JPOXMLDOC01-appb-M000006
　この評価関数Ｊσを最小にするパラメータσは、制御対象Ｐの出力であるプラント出力ｙ（ｋ）と参照モデルＭの出力Ｍ（ｚ）ｒ（σ，ｋ）との二乗誤差を最小化するという意味において、制御器Ｃ及び外乱補償器Ｄｗの最適なパラメータである。一般的なＦＲＩＴでは、オフライン計算で最適なパラメータσが計算される。なお、評価関数は式（６）に示す形に限られず、制御入力等の制約を考慮したものであってもよい。 The parameter σ that minimizes the evaluation function J σ minimizes the square error between the plant output y (k), which is the output of the controlled object P, and the output M (z) r (σ, k) of the reference model M. In that sense, it is an optimum parameter of the controller C and the disturbance compensator Dw. In general FRIT, the optimum parameter σ is calculated by offline calculation. The evaluation function is not limited to the form shown in the equation (6), and may be one in consideration of restrictions such as control input.
　式（６）から明らかなように、ＦＲＩＴは閉ループ系の制御システムＳの伝達関数と参照モデルがマッチングする最適な制御器パラメータを求めることを目的としている。すなわち、ＦＲＩＴは、以下の式（７）で表される評価関数Ｊσを最小にする最適パラメータを求める。ＦＲＩＴは擬似参照信号ｒ（σ，ｋ）を利用して、閉ループ試験を繰り返すことなく実験により取得した１組の入出力データを用いてオフラインで最適制御パラメータを求めるデータ駆動制御の１つであるともいえる。 As is clear from equation (6), FRIT aims to find the optimum control parameters that match the transfer function of the closed-loop control system S with the reference model. That is, FRIT finds the optimum parameter that minimizes the evaluation function J σ represented by the following equation (7). FRIT is one of the data-driven controls that obtains the optimum control parameters offline using a set of input / output data acquired by experiments without repeating the closed loop test using the pseudo reference signal r (σ, k). It can be said that.
　ＦＲＩＴの評価関数Ｊσ、及び擬似誤差ｅ（σ，ｋ）は次式で表される。 The evaluation function J σ of FRIT and the pseudo error e (σ, k) are expressed by the following equations.
Figure JPOXMLDOC01-appb-M000007
Figure JPOXMLDOC01-appb-M000007
［２．２．安定性を考慮したＦＲＩＴ］
　擬似参照信号ｒ（σ，ｋ）を用いる場合にはＦＲＩＴの閉ループ系の不安定化を検知できない。そこで、まず、擬似参照信号ｒ（σ，ｋ）とプラント出力ｙ０を用いて時間領域における相補感度関数（制御システムＳの目標値ｄに対する制御対象Ｐの出力ｙの相補感度関数）を求める。求めた相補感度関数に目標値ｄを印加し、その応答ｙ＊を求める。この応答ｙ＊が参照モデルＭの応答Ｍ（ｚ）ｄと一致するようなパラメータσを求める。なお、相補感度関数の同定はＦＩＲモデルを用いる。これにより、制御対象Ｐの構造を知る必要はなく、取得したデータのみを用いて相補感度関数を同定することができる。 [2.2. FRIT considering stability]
When the pseudo reference signal r (σ, k) is used, the instability of the closed loop system of FRIT cannot be detected. Therefore, first, the complementary sensitivity function in the time domain (the complementary sensitivity function of the output y of the controlled object P with respect to the target value d of the control system S) is obtained by using the pseudo reference signal r (σ, k) and the plant output y 0 . The target value d is applied to the obtained complementary sensitivity function, and the response y * is obtained. Find the parameter σ such that this response y * matches the response M (z) d of the reference model M. The FIR model is used to identify the complementary sensitivity function. As a result, it is not necessary to know the structure of the controlled object P, and the complementary sensitivity function can be identified using only the acquired data.
　時間領域における擬似参照信号ｒ（σ，ｋ）とプラント出力ｙ０との関係について説明する。時間領域における擬似参照信号ｒ（σ，ｋ）とプラント出力ｙ０との関係は次式（９）となる。 The relationship between the pseudo reference signal r (σ, k) in the time domain and the plant output y 0 will be described. The relationship between the pseudo reference signal r (σ, k) in the time domain and the plant output y 0 is given by the following equation (9).
Figure JPOXMLDOC01-appb-M000008
 　式（９）において、記号＊は畳み込みを表し、ｔ（ｋ）は調整対象とする制御器Ｃに対する相補感度関数Ｔのインパルス応答を表す。擬似参照信号ｒ（σ，ｋ）とプラント出力ｙ０とは観測可能であるが、相補感度関数Ｔのインパルス応答ｔ（ｋ）は未知である。
Figure JPOXMLDOC01-appb-M000008
 In equation (9), the symbol * represents convolution, and t (k) represents the impulse response of the complementary sensitivity function T to the controller C to be adjusted. The pseudo-reference signal r (σ, k) and the plant output y 0 are observable, but the impulse response t (k) of the complementary sensitivity function T is unknown.
　式（９）は行列を用いて表すと以下の式（１０）となる。 Equation (9) becomes the following equation (10) when expressed using a matrix.
Figure JPOXMLDOC01-appb-M000009
Figure JPOXMLDOC01-appb-M000009
　式（１０）の左辺をベクトルｙ０、右辺第１項を行列Ｒσ、右辺第２項をベクトルｔとすると、相補感度関数Ｔのインパルス応答ｔ（ｋ）は、以下の式（１１）で表される。 Assuming that the left side of the equation (10) is the vector y 0 , the first term on the right side is the matrix R σ , and the second term on the right side is the vector t, the impulse response t (k) of the complementary sensitivity function T is given by the following equation (11). expressed.
Figure JPOXMLDOC01-appb-M000010
 　式（１１）は、式（９）のデコンボリューションともいえる。ｔは、パラメータσに依存する。
Figure JPOXMLDOC01-appb-M000010
 Equation (11) can be said to be a deconvolution of equation (9). t depends on the parameter σ.
　制御システムＳの入力信号ｄ（目標値）を相補感度関数Ｔに印加した場合の出力ｙ＊を時間領域で表すと、次式（１２）となる。 The output y * when the input signal d (target value) of the control system S is applied to the complementary sensitivity function T is expressed in the time domain by the following equation (12).
Figure JPOXMLDOC01-appb-M000011
Figure JPOXMLDOC01-appb-M000011
　式（１２）は行列を用いて表すと以下の式（１３）となる。 Equation (12) becomes the following equation (13) when expressed using a matrix.
Figure JPOXMLDOC01-appb-M000012
Figure JPOXMLDOC01-appb-M000012
　式（１３）の左辺をベクトルｙ＊、右辺第１項を行列Ｄ、右辺第２項をベクトルｔとし、式（１１）を用いてｔを消去すると、式（１３）は式（１４）に変形できる。 When the left side of the equation (13) is the vector y * , the first term on the right side is the matrix D, and the second term on the right side is the vector t, and t is eliminated using the equation (11), the equation (13) becomes the equation (14). Can be transformed.
Figure JPOXMLDOC01-appb-M000013
Figure JPOXMLDOC01-appb-M000013
　式（１４）の右辺は全て観測により取得可能であるから、制御器Ｃ及び外乱補償器Ｄｗを用いたときの目標値ｄを閉ループ系の制御システムＳに印加したときの出力ベクトルｙ＊を演算により取得することができる。この出力ベクトルｙ＊と参照モデルＭの出力ｙｄ（ｋ）＝Ｍ（ｚ）ｄ（ｋ）との誤差ｅ＊の二乗和を、次式（１５）で表される評価関数Ｊ＊（σ）とする。 Since all the right sides of the equation (14) can be obtained by observation, the output vector y * when the target value d when the controller C and the disturbance compensator Dw are applied to the closed loop control system S is calculated. Can be obtained by. The error e * of the sum of squares of the output y d of the output vector y * and the reference model M (k) = M (z ) d (k), evaluation is expressed by the following equation (15) function J * (sigma ).
Figure JPOXMLDOC01-appb-M000014
 　式（１５）において、
　ｅ＊（σ，ｋ）＝ｙ＊（σ，ｋ）－ｙｄ（ｋ）　　（１６）である。
Figure JPOXMLDOC01-appb-M000014
 In equation (15)
e * (σ, k) = y * (σ, k) -y d (k) (16).
　標準的なＦＲＩＴでは、取得したプラント出力ｙ０に一致するようにパラメータσの関数である擬似参照信号ｒ（σ，ｋ）を調整する。これに対し、実施の形態に係る手法では、参照モデルＭの出力Ｍ（ｚ）ｄ（ｋ）にプラント出力ｙ０が一致するように、パラメータσを調整してプラント出力ｙ＊を変更する。すなわち、標準的なＦＲＩＴは実験によりあらかじめ取得したプラント出力に合うようにパラメータσを求めているのに対し、実施の形態に係る手法は参照モデルの出力Ｍ（ｚ）ｄ（ｋ）に合うように、パラメータσを求める。 In standard FRIT, the pseudo-reference signal r (σ, k), which is a function of the parameter σ, is adjusted so as to match the acquired plant output y 0 . On the other hand, in the method according to the embodiment, the parameter σ is adjusted to change the plant output y * so that the plant output y 0 matches the output M (z) d (k) of the reference model M. That is, while the standard FRIT finds the parameter σ so as to match the plant output obtained in advance by the experiment, the method according to the embodiment matches the output M (z) d (k) of the reference model. To find the parameter σ.
［２．３．安定性を考慮したＦＲＩＴの構成］
　図２は、安定性を考慮したＦＲＩＴの構成を模式的に示す図である。まず、第１パラメータθが初期値θ０であり第２パラメータξの初期値がξ０ときの制御システムＳの入出力データから擬似参照信号ｒ（σ）が算出される。算出された擬似参照入力ｒ（σ）とプラント出力ｙとを用いて相補感度関数ｔが上記式（１１）を用いて求められ、制御システムＳの入力信号である目標値ｄを相補感度関数ｔに入力される。相補感度関数ｔの出力である出力ｙ＊と、参照モデルの出力Ｍ（ｚ）ｄとの誤差を最小にするパラメータσが、最適化手法により求められる。 [2.3. Configuration of FRIT considering stability]
FIG. 2 is a diagram schematically showing a configuration of FRIT in consideration of stability. First, the pseudo reference signal r (σ) is calculated from the input / output data of the control system S when the first parameter θ is the initial value θ 0 and the initial value of the second parameter ξ is ξ 0 . The complementary sensitivity function t is obtained by using the calculated pseudo reference input r (σ) and the plant output y using the above equation (11), and the target value d, which is the input signal of the control system S, is used as the complementary sensitivity function t. Is entered in. The parameter σ that minimizes the error between the output y * , which is the output of the complementary sensitivity function t, and the output M (z) d of the reference model is obtained by the optimization method.
［３．参考文献］（ＦＲＩＴ）・相馬 将太郎, 金子 修, 藤井 隆雄, 一回の実験データに基づく制御器パラメータチューニングの新しいアプローチ  Fictitious Reference Iterative Tuning の提案, システム制御情報学会論文誌, Vol. 17, No.12 (2004), pp. 528-536・奥谷 明大, 金子 修, 山本 茂, ＦＲＩＴを用いた多入出力むだ時間系に対するスミス補償器のチューニング, システム制御情報学会論文誌, Vol. 28, No 2 (2015), pp. 58-65
・データを直接用いた制御器のパラメータチューニング, 金子修, 計測と制御, Vol.43, No.11 (2008), pp903-908 [3. References] (FRIT) ・ Shotaro Soma, Osamu Kaneko, Takao Fujii, A new approach to controller parameter tuning based on one-time experimental data Proposal of Fictitious Reference Iterative Tuning, Journal of the Society of Systems Control and Information Science, Vol. 17, No .12 (2004), pp. 528-536 ・ Akihiro Okutani, Osamu Kaneko, Shigeru Yamamoto, Tuning Smith Compensator for Multi-Input Waste Time System Using FRIT, Journal of the Society of System Control and Information Science, Vol. 28, No 2 (2015), pp. 58-65
・ Parameter tuning of controllers using data directly, Osamu Kaneko, Measurement and control, Vol.43, No.11 (2008), pp903-908
（非反証制御）・M. G. Safonov and T. C. Tsao, The unfalsified control, concept and learning, IEEE Trans. on Automat.Contr., Vol. 42, No. 6, pp. 843-847 (1997) (Non-proof control) ・ M. G. Safonov and T. C. Tsao, The unfalsified control, concept and learning, IEEE Trans. On Automat. Contr., Vol. 42, No. 6, pp. 843-847 (1997) )
（安定性の考慮）・弓場井 一裕, 藤井 宏樹, 平井 淳之, パラメータ更新時の閉ループシステムの安定性を考慮したFCbTの提案, 電気学会論文誌Ｄ（産業応用部門誌）, Vol.132, No.6 (2011),pp. 607-615・Kazuhiro Yubai, Hiroki Fujii, Junji Hirai, Fictitious Correlation-based Tuning Integrating the Data-Based Stability Test at Each Parameter Update, Electrical Power Systems and Computers, LNEE 99, pp. 511-518. (Consideration of stability) ・ Kazuhiro Yubai, Hiroki Fujii, Atsuyuki Hirai, Proposal of FCbT considering the stability of closed loop system at the time of parameter update, IEEJ Journal D (Industrial Application Division), Vol.132, No.6 (2011), pp. 607-615 ・ Kazuhiro Yubai, Hiroki Fujii, Junji Hirai, Fictitious Correlation-based Tuning Integration the Data-Based Stability Test at Each Parameter Update, Electrical Power Systems and Computer 511-518.
（擬似参照信号の問題と安定性）・S. Engell, T. Tometzki and T. Wonghong, A New Approach to Adaptive Unfalsified Control. In Proc. European Control Conf., Kos, 2007, 1328-1333.・T. Wonghong and S. Engell, Application of a New Scheme for Adaptive Unfalsified Control to a CSTR. Proc. IFAC World Congress, Korea, 13247-13252, 2008. (Problems and stability of pseudo-reference signal) ・ S. Engell, T. Tometzki and T. Wonghong, A New Approach to Adaptive Unfalsified Control. In Proc. European Control Conf., Kos, 2007, 1328-1333. ・ T. Wonghong and S. Engell, Application of a New Scheme for Adaptive Unfalsified Control to a CSTR. Proc. IFAC World Congress, Korea, 13247-13252, 2008.
［４．実施の形態］
　以上を踏まえ、本開示の実施の形態について説明する。 [4. Embodiment]
Based on the above, embodiments of the present disclosure will be described.
　図３は、実施の形態に係る情報処理装置１の機能構成を模式的に示す図である。情報処理装置１は、記憶部２と制御部３とを備える。図３において、矢印は主なデータの流れを示しており、図３に示していないデータの流れがあってもよい。図３において、各機能ブロックはハードウェア（装置）単位の構成ではなく、機能単位の構成を示している。そのため、図３に示す機能ブロックは単一の装置内に実装されてもよく、あるいは複数の装置内に分かれて実装されてもよい。機能ブロック間のデータの授受は、データバス、ネットワーク、可搬記憶媒体等、任意の手段を介して行われてもよい。 FIG. 3 is a diagram schematically showing a functional configuration of the information processing device 1 according to the embodiment. The information processing device 1 includes a storage unit 2 and a control unit 3. In FIG. 3, the arrows indicate the main data flows, and there may be data flows not shown in FIG. In FIG. 3, each functional block shows not the configuration of each hardware (device) but the configuration of each function. Therefore, the functional block shown in FIG. 3 may be mounted in a single device, or may be mounted separately in a plurality of devices. Data transfer between functional blocks may be performed via any means such as a data bus, a network, and a portable storage medium.
　記憶部２は、情報処理装置１を実現するコンピュータのＢＩＯＳ（Basic Input Output System）等を格納するＲＯＭ（Read Only Memory）や情報処理装置１の作業領域となるＲＡＭ（Random Access Memory）、ＯＳ（Operating System）やアプリケーションプログラム、当該アプリケーションプログラムの実行時に参照される種々の情報を格納するＨＤＤ（Hard Disk Drive）やＳＳＤ（Solid State Drive）等の大容量記憶装置である。 The storage unit 2 includes a ROM (Read Only Memory) that stores the BIOS (Basic Input Output System) of the computer that realizes the information processing device 1, a RAM (Random Access Memory) that serves as a work area of the information processing device 1, and an OS ( It is a large-capacity storage device such as an HDD (Hard Disk Drive) or an SSD (Solid State Drive) that stores various information referred to when the application program is executed, such as an Operating System) or an application program.
　制御部３は、情報処理装置１のＣＰＵ（Central Processing Unit）やＧＰＵ（Graphics Processing Unit）等のプロセッサであり、記憶部２に記憶されたプログラムを実行することによって時系列データ取得部３０、擬似参照信号算出部３１、相補感度関数算出部３２、出力演算部３３、モデル出力取得部３４、及びパラメータ更新部３５として機能する。 The control unit 3 is a processor such as a CPU (Central Processing Unit) or GPU (Graphics Processing Unit) of the information processing device 1, and the time-series data acquisition unit 30 is simulated by executing a program stored in the storage unit 2. It functions as a reference signal calculation unit 31, a complementary sensitivity function calculation unit 32, an output calculation unit 33, a model output acquisition unit 34, and a parameter update unit 35.
　なお、図３は、情報処理装置１が単一の装置で構成されている場合の例を示している。しかしながら、情報処理装置１は、例えばクラウドコンピューティングシステムのように複数のプロセッサやメモリ等の計算リソースによって実現されてもよい。この場合、制御部３を構成する各部は、複数の異なるプロセッサの中の少なくともいずれかのプロセッサがプログラムを実行することによって実現される。 Note that FIG. 3 shows an example in which the information processing device 1 is composed of a single device. However, the information processing device 1 may be realized by computing resources such as a plurality of processors and memories, such as a cloud computing system. In this case, each unit constituting the control unit 3 is realized by executing a program by at least one of a plurality of different processors.
　情報処理装置１は、制御器Ｃと、制御器Ｃの出力を入力とする制御対象Ｐと、制御対象Ｐの入力の外乱を補償するための外乱補償器Ｄｗと、を備える制御システムＳにおいて、制御器Ｃのパラメータである第１パラメータθと外乱補償器Ｄｗのパラメータである第２パラメータξとを算出するための装置である。図３に示すように、制御システムＳは、制御対象Ｐの出力が制御器Ｃの入力にフィードバックされる閉ループ系である。 The information processing device 1 is a control system S including a controller C, a control target P having an output of the control C as an input, and a disturbance compensator Dw for compensating for a disturbance of the input of the control target P. This is a device for calculating the first parameter θ, which is a parameter of the controller C, and the second parameter ξ, which is a parameter of the disturbance compensator Dw. As shown in FIG. 3, the control system S is a closed loop system in which the output of the controlled object P is fed back to the input of the controller C.
　時系列データ取得部３０は制御器Ｃの出力に外乱補償器Ｄｗの出力を加算した時系列データである第１時系列データと、制御対象Ｐの出力の時系列データである第２時系列データとを取得する。ここで、第１時系列データは上述した制御対象Ｐに入力すべき制御量ｕに対応し、第２時系列データは上述した制御対象Ｐの出力ｙに対応する。したがって、以下本明細書において、「第１時系列データｕ」、「第２時系列データｙ」と記載することがある。 The time-series data acquisition unit 30 includes the first time-series data which is the time-series data obtained by adding the output of the disturbance compensator Dw to the output of the controller C and the second time-series data which is the time-series data of the output of the control target P. And get. Here, the first time-series data corresponds to the control amount u to be input to the control target P described above, and the second time-series data corresponds to the output y of the control target P described above. Therefore, in the present specification, they may be referred to as "first time series data u" and "second time series data y".
　擬似参照信号算出部３１は、第１パラメータθ、第２パラメータξ、第１時系列データｕ、及び第２時系列データｙから、上述した式（５）に基づいて、制御システムＳの擬似参照信号である第３時系列データを推定する。第３時系列データは、上述した擬似参照信号ｒ（θ，ξ、ｋ）＝ｒ（σ，ｋ）に対応する。したがって、以下、「第３時系列データｒ（σ）」と記載することがある。 The pseudo-reference signal calculation unit 31 uses the first parameter θ, the second parameter ξ, the first time-series data u, and the second time-series data y from the pseudo-reference of the control system S based on the above equation (5). Estimate the third time series data which is a signal. The third time series data corresponds to the above-mentioned pseudo reference signal r (θ, ξ, k) = r (σ, k). Therefore, it may be described below as "third time series data r (σ)".
　相補感度関数算出部３２は、第２時系列データｙと第３時系列データｒ（σ）とに基づいて、上述した式（１１）を用いて、制御器Ｃに対する相補感度関数ｔを算出する。なお、相補感度関数算出部３２が算出するものは相補感度関数Ｔのインパルス応答ｔであるが、以下説明の便宜上、相補感度関数算出部３２の算出結果を相補感度関数ｔと記載する。 The complementary sensitivity function calculation unit 32 calculates the complementary sensitivity function t for the controller C using the above equation (11) based on the second time series data y and the third time series data r (σ). .. The impulse response t of the complementary sensitivity function T is calculated by the complementary sensitivity function calculation unit 32, but the calculation result of the complementary sensitivity function calculation unit 32 is described as the complementary sensitivity function t for convenience of the following description.
　出力演算部３３は、上述した式（１２）又は式（１３）を用いて、制御システムＳの入力信号ｄを相補感度関数ｔに印加したときの出力である第４時系列データを算出する。第４時系列データは、制御システムＳの入力信号ｄ（目標値）を相補感度関数Ｔに印加した場合の出力ｙ＊に対応する。したがって、以下、「第４時系列データｙ＊」と記載することがある。 The output calculation unit 33 calculates the fourth time series data which is the output when the input signal d of the control system S is applied to the complementary sensitivity function t by using the above equation (12) or equation (13). The fourth time-series data corresponds to the output y * when the input signal d (target value) of the control system S is applied to the complementary sensitivity function T. Therefore, it may be described below as "fourth time series data y * ".
　制御対象Ｐに入力すべき制御量である第１時系列データｕ、制御対象Ｐの出力である第２時系列データｙ、及び制御システムＳの入力信号ｄは、いずれも観測により取得可能な量である。情報処理装置１は、観測により取得した第１時系列データｕ、第２時系列データｙ、及び入力信号ｄを用いることで、制御システムＳに入力信号ｄを入力したときの出力ｙ＊を算出することができる。出力ｙ＊は、制御対象Ｐからの出力である。情報処理装置１は、この出力ｙ＊の振る舞い（例えば、発散するか否か、振動するか否か、収束するか否か等）を解析することで、ＦＲＩＴにおいて、外乱補償器Ｄｗを有する制御システムＳにおける第１パラメータθ及第２パラメータξを用いた制御の安定性を評価することができる。 The first time series data u, which is the control amount to be input to the control target P, the second time series data y, which is the output of the control target P, and the input signal d of the control system S are all quantities that can be acquired by observation. Is. The information processing device 1 calculates the output y * when the input signal d is input to the control system S by using the first time series data u, the second time series data y, and the input signal d acquired by observation. can do. The output y * is the output from the control target P. The information processing device 1 analyzes the behavior of the output y * (for example, whether or not it diverges, whether or not it vibrates, whether or not it converges, etc.), thereby controlling the control having the disturbance compensator Dw in FRIT. The stability of control using the first parameter θ and the second parameter ξ in the system S can be evaluated.
　図２及び図３に示すように、制御システムＳは制御対象Ｐの入力信号ｄに対する出力を所定の出力とすることを実現する参照モデルＭを備えている。なお、参照モデルＭは、制御対象Ｐの出力が設計者が希望する出力となるように、設計者が決定する。モデル出力取得部３４は、参照モデルＭに入力信号ｄを入力した場合の出力の時系列データである第５時系列データを取得する。第５時系列データは、上述した参照モデルの出力Ｍ（ｚ）ｄに対応する。以下、第５時系列データを「第５時系列データｙｄ」と記載することがある。 As shown in FIGS. 2 and 3, the control system S includes a reference model M that realizes that the output of the control target P with respect to the input signal d is a predetermined output. The reference model M is determined by the designer so that the output of the controlled object P is the output desired by the designer. The model output acquisition unit 34 acquires the fifth time-series data, which is the output time-series data when the input signal d is input to the reference model M. The fifth time series data corresponds to the output M (z) d of the reference model described above. Hereinafter, the fifth time-series data may be referred to as a "fifth time-series data y d".
　ここで、情報処理装置１がＦＲＩＴにおける第１パラメータθ及び第２パラメータξを用いた制御の安定性を評価することができるのであれば、情報処理装置１は、制御が安定化するようにパラメータσ（第１パラメータθ及び第２パラメータξ）を最適化することもできる。これを実現するために、パラメータ更新部３５は、第４時系列データｙ＊と第５時系列データｙｄとの誤差に関する評価関数Ｊ＊（σ）の評価値に基づいて、パラメータσを更新する。 Here, if the information processing device 1 can evaluate the stability of the control using the first parameter θ and the second parameter ξ in the FRIT, the information processing device 1 has a parameter so that the control is stabilized. σ (first parameter θ and second parameter ξ) can also be optimized. To achieve this, the parameter update unit 35, based on the evaluation value of the evaluation function J * (sigma) regarding the error of the fourth time-series data y * and fifth time-series data y d, updates the parameter sigma To do.
　より具体的には、上述した式（１５）及び式（１６）に示すように、パラメータ更新部３５が用いる評価関数Ｊ＊（σ）は、第４時系列データｙ＊と第５時系列データｙｄとの誤差の二乗和である。パラメータ更新部３５は、評価関数Ｊ＊（σ）の評価値が小さくなるように、反復処理によってパラメータσを更新する。すなわち、パラメータ更新部３５は、第４時系列データｙ＊と第５時系列データｙｄとの誤差の二乗和が小さくなるという意味において最適なパラメータσを反復によって求める。 More specifically, as shown in the above equations (15) and (16), the evaluation function J * (σ) used by the parameter update unit 35 is the fourth time series data y * and the fifth time series data. It is the sum of squares of the error with y d . The parameter update unit 35 updates the parameter σ by iterative processing so that the evaluation value of the evaluation function J * (σ) becomes small. That is, the parameter updating unit 35 is determined by repeating the optimum parameter σ in the sense that the sum of squares of errors between the fourth time-series data y * and fifth time-series data y d becomes smaller.
　一般に、第４時系列データｙ＊が発散したり振動したりすると、第４時系列データｙ＊と第５時系列データｙｄとの誤差の二乗和は大きくなる。パラメータ更新部３５が第４時系列データｙ＊と第５時系列データｙｄとの誤差の二乗和が小さくなるようにパラメータσを更新することにより、情報処理装置１は、ＦＲＩＴにおいて第１パラメータθ及び第２パラメータξを用いたプラントの制御を安定化させることができる。 In general, when the fourth time series data y * diverges or vibrates, the sum of squares of the errors between the fourth time series data y * and the fifth time series data y d becomes large. The information processing apparatus 1 updates the parameter σ so that the sum of squares of the errors between the fourth time series data y * and the fifth time series data y d becomes smaller by the parameter update unit 35, so that the information processing apparatus 1 uses the first parameter in FRIT. It is possible to stabilize the control of the plant using θ and the second parameter ξ.
　なお、パラメータ更新部３５は、評価関数の評価値が小さくなるようにパラメータσを更新できるのであればどのような最適化手法を用いてもよい。一例としてパラメータ更新部３５は、あらかじめ定められた所定の回数を反復回数の上限として、粒子群最適化の手法を用いてパラメータσを更新してもよい。 The parameter update unit 35 may use any optimization method as long as the parameter σ can be updated so that the evaluation value of the evaluation function becomes small. As an example, the parameter updating unit 35 may update the parameter σ by using a particle swarm optimization method with a predetermined number of repetitions as the upper limit of the number of iterations.
＜情報処理装置１が実行する情報処理方法の処理フロー＞
　図４は、実施の形態に係る情報処理装置１が実行する情報処理の流れを説明するためのフローチャートである。本フローチャートにおける処理は、例えば情報処理装置１が起動したときに開始する。 <Processing flow of information processing method executed by information processing device 1>
FIG. 4 is a flowchart for explaining the flow of information processing executed by the information processing apparatus 1 according to the embodiment. The process in this flowchart starts, for example, when the information processing device 1 is activated.
　時系列データ取得部３０は、制御器Ｃの出力に外乱補償器Ｄｗの出力を加算した時系列データである第１時系列データｕを取得する（Ｓ２）。また、時系列データ取得部３０は、制御対象Ｐの出力の時系列データである第２時系列データｙを取得する（Ｓ４）。 The time-series data acquisition unit 30 acquires the first time-series data u, which is the time-series data obtained by adding the output of the disturbance compensator Dw to the output of the controller C (S2). Further, the time-series data acquisition unit 30 acquires the second time-series data y, which is the time-series data of the output of the control target P (S4).
　擬似参照信号算出部３１は、制御器Ｃのパラメータである第１パラメータθ、外乱補償器Ｄｗのパラメータである第２パラメータξ、第１時系列データｕ、及び第２時系列データｙから、制御システムＳの擬似参照信号である第３時系列データｒ（σ）を推定する（Ｓ６）。 The pseudo-reference signal calculation unit 31 controls from the first parameter θ which is a parameter of the controller C, the second parameter ξ which is a parameter of the disturbance compensator Dw, the first time series data u, and the second time series data y. The third time series data r (σ), which is a pseudo reference signal of the system S, is estimated (S6).
　相補感度関数算出部３２は、第２時系列データｙと第３時系列データｒ（θ）とに基づいて、式（１１）を用いて制御器Ｃに対する相補感度関数ｔを算出する（Ｓ８）。出力演算部３３は、式（１４）を用いて、制御システムＳの入力信号ｄを相補感度関数ｔに印加したときの出力である第４時系列データｙ＊（すなわち、入力信号ｄに対する制御対象Ｐの出力）を算出する（Ｓ１０）。 The complementary sensitivity function calculation unit 32 calculates the complementary sensitivity function t for the controller C using the equation (11) based on the second time series data y and the third time series data r (θ) (S8). .. The output calculation unit 33 uses the equation (14) to apply the input signal d of the control system S to the complementary sensitivity function t, which is the output of the fourth time series data y * (that is, the control target for the input signal d). Output of P) is calculated (S10).
　モデル出力取得部３４は、参照モデルＭに入力信号ｄを入力した場合の出力の時系列データである第５時系列データｙｄを取得する（Ｓ１２）。パラメータ更新部３５は、式（１５）及び式（１６）を用いて、第４時系列データｙ＊と第５時系列データｙｄとの誤差に関する評価関数Ｊ（σ）の評価値を算出する（Ｓ１４）。パラメータ更新部３５は、評価関数Ｊ（σ）の評価値が小さくなるように、反復処理によってパラメータσ（第１パラメータθ及び第２パラメータξ）を更新する（Ｓ１６）。 The model output acquisition unit 34 acquires the fifth time series data y d , which is the output time series data when the input signal d is input to the reference model M (S12). Parameter updating unit 35, the formula (15) and using equation (16) calculates the evaluation value of the evaluation function J (sigma) regarding the error of the fourth time-series data y * and fifth time-series data y d (S14). The parameter update unit 35 updates the parameter σ (first parameter θ and second parameter ξ) by iterative processing so that the evaluation value of the evaluation function J (σ) becomes smaller (S16).
　パラメータ更新部３５がパラメータσを更新すると、本フローチャートにおける処理は終了する。情報処理装置１は、上記の処理をオンラインで繰り返すことにより、パラメータσの更新を継続する。 When the parameter update unit 35 updates the parameter σ, the process in this flowchart ends. The information processing apparatus 1 continues to update the parameter σ by repeating the above processing online.
＜実施の形態に係る情報処理装置１が奏する効果＞
　以上説明したように、実施の形態に係る情報処理装置１によれば、ＦＲＩＴにおいて、外乱補償器Ｄｗを有する制御システムＳにおける制御器Ｃのパラメータであるパラメータθ及び外乱補償器Ｄｗのパラメータである第２パラメータξを用いた制御の安定性を評価することができる。また、情報処理装置１は、閉ループ系の制御が安定化するようにＦＲＩＴにおける第１パラメータθ及び第２パラメータξを最適化することもできる。 <Effects of the information processing device 1 according to the embodiment>
As described above, according to the information processing apparatus 1 according to the embodiment, in the FRIT, the parameter θ which is the parameter of the controller C in the control system S having the disturbance compensator Dw and the parameter of the disturbance compensator Dw. The stability of control using the second parameter ξ can be evaluated. Further, the information processing apparatus 1 can also optimize the first parameter θ and the second parameter ξ in FRIT so that the control of the closed loop system is stabilized.
　以上、本開示を実施の形態を用いて説明したが、本開示の技術的範囲は上記実施の形態に記載の範囲には限定されず、その要旨の範囲内で種々の変形及び変更が可能である。例えば、装置の全部又は一部は、任意の単位で機能的又は物理的に分散・統合して構成することができる。また、複数の実施の形態の任意の組み合わせによって生じる新たな実施の形態も、本開示の実施の形態に含まれる。組み合わせによって生じる新たな実施の形態の効果は、もとの実施の形態の効果を併せ持つ。 Although the present disclosure has been described above using the embodiments, the technical scope of the present disclosure is not limited to the scope described in the above embodiments, and various modifications and changes can be made within the scope of the gist. is there. For example, all or a part of the device can be functionally or physically distributed / integrated in any unit. Also included in the embodiments of the present disclosure are new embodiments resulting from any combination of the plurality of embodiments. The effect of the new embodiment produced by the combination has the effect of the original embodiment.
　本出願は、2019年7月11日付で出願された日本国特許出願（特願2019-129028）に基づくものであり、その内容はここに参照として取り込まれる。 This application is based on a Japanese patent application (Japanese Patent Application No. 2019-129028) filed on July 11, 2019, the contents of which are incorporated herein by reference.
　本開示の情報処理装置、及びプログラム、及び算出方法は、ＦＲＩＴにおいて、外乱補償器を有する系における制御の安定性を評価することができる点において有用である。 The information processing apparatus, program, and calculation method of the present disclosure are useful in that the stability of control in a system having a disturbance compensator can be evaluated in FRIT.
１・・・情報処理装置
２・・・記憶部
３・・・制御部
３０・・・時系列データ取得部
３１・・・擬似参照信号算出部
３２・・・相補感度関数算出部
３３・・・出力演算部
３４・・・モデル出力取得部
３５・・・パラメータ更新部
Ｃ・・・制御器
Ｄｗ・・・外乱補償器
Ｍ・・・参照モデル
Ｐ・・・制御対象
Ｓ・・・制御システム 1 ... Information processing device 2 ... Storage unit 3 ... Control unit 30 ... Time series data acquisition unit 31 ... Pseudo-reference signal calculation unit 32 ... Complementary sensitivity function calculation unit 33 ... Output calculation unit 34 ... Model output acquisition unit 35 ... Parameter update unit C ... Controller Dw ... Disturbance compensator M ... Reference model P ... Control target S ... Control system

Claims (5)

  1. 　制御器と、前記制御器の出力を入力とする制御対象と、前記制御対象の入力の外乱を補償するための外乱補償器とを備え、前記制御対象の出力が前記制御器の入力にフィードバックされる制御システムにおいて、前記制御器のパラメータである第１パラメータと前記外乱補償器のパラメータである第２パラメータとを算出する情報処理装置であって、
    　前記制御器の出力に前記外乱補償器の出力を加算した時系列データである第１時系列データと、前記制御対象の出力の時系列データである第２時系列データとを取得する時系列データ取得部と、
    　前記第１パラメータ、前記第２パラメータ、前記第１時系列データ、及び前記第２時系列データから、前記制御システムの擬似参照信号である第３時系列データを算出する擬似参照信号算出部と、
    　前記第２時系列データと前記第３時系列データとに基づいて、前記制御器に対する相補感度関数を算出する相補感度関数算出部と、
    　前記制御システムの入力信号を前記相補感度関数に印加したときの出力である第４時系列データを算出する出力演算部と、
    　を備える情報処理装置。     A controller, a control target having an output of the control target as an input, and a disturbance compensator for compensating for a disturbance of the input of the control target are provided, and the output of the control target is fed back to the input of the controller. An information processing device that calculates a first parameter that is a parameter of the controller and a second parameter that is a parameter of the disturbance compensator in the control system.
    Time-series data for acquiring the first time-series data which is the time-series data obtained by adding the output of the disturbance compensator to the output of the controller and the second time-series data which is the time-series data of the output to be controlled. Acquisition department and
    A pseudo reference signal calculation unit that calculates a third time series data, which is a pseudo reference signal of the control system, from the first parameter, the second parameter, the first time series data, and the second time series data.
    A complementary sensitivity function calculation unit that calculates a complementary sensitivity function for the controller based on the second time series data and the third time series data.
    An output calculation unit that calculates the fourth time series data, which is the output when the input signal of the control system is applied to the complementary sensitivity function.
    Information processing device equipped with.
  2. 　前記制御システムは、前記制御対象に入力する入力信号を入力として前記制御対象の出力をモデル化する参照モデルをさらに備えており、
    　前記情報処理装置は、
    　　前記参照モデルに前記第３時系列データを入力した場合の出力の時系列データである第５時系列データを取得するモデル出力取得部と、
    　　前記第４時系列データと前記第５時系列データとの誤差に関する評価関数の評価値に基づいて前記第１パラメータと前記第２パラメータとを更新するパラメータ更新部と、
    　をさらに備える請求項１に記載の情報処理装置。     The control system further includes a reference model that models the output of the controlled object by using an input signal input to the controlled object as an input.
    The information processing device
    A model output acquisition unit that acquires the fifth time series data, which is the output time series data when the third time series data is input to the reference model.
    A parameter update unit that updates the first parameter and the second parameter based on the evaluation value of the evaluation function regarding the error between the fourth time series data and the fifth time series data.
    The information processing apparatus according to claim 1, further comprising.
  3. 　前記評価関数は、前記第４時系列データと前記第５時系列データとの誤差の二乗和であり、
    　前記パラメータ更新部は、前記評価関数の評価値が小さくなるように、反復処理によって前記第１パラメータ及び前記第２パラメータを更新する、
    　請求項２に記載の情報処理装置。     The evaluation function is the sum of squares of errors between the fourth time series data and the fifth time series data.
    The parameter update unit updates the first parameter and the second parameter by iterative processing so that the evaluation value of the evaluation function becomes smaller.
    The information processing device according to claim 2.
  4. 　制御器と、前記制御器の出力を入力とする制御対象と、前記制御対象の入力の外乱を補償するための外乱補償器とを備え、前記制御対象の出力が前記制御器の入力にフィードバックされる制御システムにおいて、前記制御器のパラメータである第１パラメータと前記外乱補償器のパラメータである第２パラメータとを算出するコンピュータに、
    　前記制御器の出力に前記外乱補償器の出力を加算した時系列データである第１時系列データを取得する機能と、
    　前記制御対象の出力の時系列データである第２時系列データを取得する機能と、
    　前記第１パラメータ、前記第２パラメータ、前記第１時系列データ、及び前記第２時系列データから、前記制御システムの擬似参照信号である第３時系列データを算出する機能と、
    　前記第２時系列データと前記第３時系列データとに基づいて、前記制御器に対する相補感度関数を算出する機能と、
    　前記制御システムの入力信号を前記相補感度関数に印加したときの出力である第４時系列データを算出する機能と、
    　を実現させるプログラム。     A controller, a control target having an output of the control target as an input, and a disturbance compensator for compensating for a disturbance of the input of the control target are provided, and the output of the control target is fed back to the input of the controller. In a control system, a computer that calculates a first parameter that is a parameter of the controller and a second parameter that is a parameter of the disturbance compensator
    A function to acquire first time-series data, which is time-series data obtained by adding the output of the disturbance compensator to the output of the controller, and
    A function to acquire the second time series data which is the time series data of the output to be controlled, and
    A function of calculating a third time series data, which is a pseudo reference signal of the control system, from the first parameter, the second parameter, the first time series data, and the second time series data.
    A function of calculating a complementary sensitivity function for the controller based on the second time series data and the third time series data, and
    A function to calculate the fourth time series data which is an output when the input signal of the control system is applied to the complementary sensitivity function, and
    A program that realizes.
  5. 　制御器と、前記制御器の出力を入力とする制御対象と、前記制御対象の入力の外乱を補償するための外乱補償器とを備え、前記制御対象の出力が前記制御器の入力にフィードバックされる制御システムにおいて、前記制御器のパラメータである第１パラメータと前記外乱補償器のパラメータである第２パラメータとを算出する算出方法であって、
    　前記制御器の出力に前記外乱補償器の出力を加算した時系列データである第１時系列データを取得すること、
    　前記制御対象の出力の時系列データである第２時系列データを取得すること、
    　前記第１パラメータ、前記第２パラメータ、前記第１時系列データ、及び前記第２時系列データから、前記制御システムの擬似参照信号である第３時系列データを算出すること、
    　前記第２時系列データと前記第３時系列データとに基づいて、前記制御器に対する相補感度関数を算出すること、及び
    　前記制御システムの入力信号を前記相補感度関数に印加したときの出力である第４時系列データを算出すること、
    　を含む算出方法。     A controller, a control target having an output of the control target as an input, and a disturbance compensator for compensating for a disturbance of the input of the control target are provided, and the output of the control target is fed back to the input of the controller. This is a calculation method for calculating the first parameter, which is a parameter of the controller, and the second parameter, which is a parameter of the disturbance compensator, in the control system.
    Acquiring the first time series data which is the time series data obtained by adding the output of the disturbance compensator to the output of the controller.
    Acquiring the second time series data which is the time series data of the output of the controlled object,
    To calculate the third time series data, which is a pseudo reference signal of the control system, from the first parameter, the second parameter, the first time series data, and the second time series data.
    It is an output when the complementary sensitivity function for the controller is calculated based on the second time series data and the third time series data, and when the input signal of the control system is applied to the complementary sensitivity function. Calculating the 4th time series data,
    Calculation method including.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2022112300A (en) * 2021-01-21 2022-08-02 いすゞ自動車株式会社 Parameter adjusting device and parameter adjusting method

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2017182624A (en) * 2016-03-31 2017-10-05 ブラザー工業株式会社 Parameter updating method, parameter updating device and program
JP2018112857A (en) * 2017-01-11 2018-07-19 横河電機株式会社 Data processing apparatus and data processing method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2017182624A (en) * 2016-03-31 2017-10-05 ブラザー工業株式会社 Parameter updating method, parameter updating device and program
JP2018112857A (en) * 2017-01-11 2018-07-19 横河電機株式会社 Data processing apparatus and data processing method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
ISHII, YUKI ET AL.: "Fictitious Reference Iterative Tuning for Disturbance Attenuation Based on Variance Evaluation for Non-minimum Phase Plants", TRANSACTIONS OF THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS, vol. 52, no. 5, 25 May 2016 (2016-05-25), pages 1593 - 1598, XP032809838, DOI: 10.1109/CCA.2015.7320837 *
KANEKO, OSAMU: "Direct Data-Driven Controller Tuning -FRIT Approach", JOURNAL OF THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS, vol. 52, no. 10, October 2013 (2013-10-01), pages 853 - 859, XP055782861 *
WAKAYAMA, NAOYA ET AL.: "Correlation-based Multivariable Controller Parameter Tuning by Using One-shot Experimental Data", TRANSACTIONS OF THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS, vol. 43, no. 5, 2007, pages 391 - 399, XP055770268, DOI: 10.9746/ve.sicetr1965.43.391 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2022112300A (en) * 2021-01-21 2022-08-02 いすゞ自動車株式会社 Parameter adjusting device and parameter adjusting method

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