JP7256327B1 - Control parameter adjustment method and adjustment device for digital control system - Google Patents

Abstract

Kind Code: A1 In a nonlinear system in which a controlled object has saturated nonlinearity, it is possible to apply the least-squares method used in a linear system in adjusting the control parameters of a controller by data-driven control. In the present invention, output data y fed back from a controlled object is input to a controller, and an output signal of the controller obtained through a transfer function C(z; θ) is used as input data u of the controlled object, By linearly separating the transfer function C(z; Anti-windup compensation that eliminates non-linearity of saturation can be applied in multiplicative control parameter adjustment. [Selection drawing] Fig. 1

Description

The present invention relates to a method for adjusting control parameters of a digital control system and a device for adjusting control parameters of a control system.

In digital controllers such as DC/DC converters, in addition to control that feeds back the output voltage via a feedback loop, as feedback control to stabilize the output voltage, in addition to the voltage feedback loop that feeds back the output voltage Digital control is known in which a feedback loop of an inductor current or a capacitor current is used as a minor loop, and an output voltage error signal and a feedback current are input to a PWM modulator.

In a digital control system, it is desirable to design a controller based on widely used PID control or PI control, but the PID gain or PI gain of the controller should be easily adjusted by the nonlinearity contained in the controller. It has been pointed out that it is difficult to The present invention relates to adjustment of control parameters of a controller controlled by a digital control system.

Data-driven control, which adjusts the control parameters of the controller by directly using the experimental data, which is the input/output data of the controlled object, is known as a method that reduces the burden of control system design without the need for repeated experiments. It is This data-driven control optimizes the control parameters such as the PID gain or PI gain of the controller in a closed loop system based on input/output data obtained by one or more experiments. This is a method of adjusting so as to approach the model.

A VRFT (Virtual Reference Feedback Tuning) method is known as one of the data-driven controls. VRFT is a control method that obtains virtual input data from output data and a reference model based on input/output data obtained in an experiment, and adjusts the control parameters of the controller using the input data and data related to the virtual input data. be.

In the VRFT method, a linear system is usually set as a reference model of the control system. It is known that if the control system is linear, it is possible to adjust the control parameters of the controller by applying the method of least squares to the difference between the input data and the virtual input data.

However, when the control system is nonlinear, there is a limit to treating the closed loop system of the control system as a linear system, so it is difficult to adjust the control parameters using the least squares method.

Nonlinearity due to saturation is one of the nonlinearities of digital control systems. Nonlinearity due to saturation includes saturation due to the control characteristics of the control system, or saturation nonlinearity due to the physical characteristics of the controlled object itself. Nonlinearity caused by physical factors includes, for example, nonlinearity caused by magnetic saturation of an inductor of a DC-DC converter.

In addition, the nonlinearity of saturation due to the control system is due to control characteristics such as the output being limited to a specified value in PWM control, for example, and the controlled object is controlled by PWM control (pulse width modulation control) in the digital control system In doing so, the pulse width used in PWM control is limited between 0 and 1. Therefore, when the duty command value of PWM control is less than 0 or exceeds 1, the pulse width becomes saturated, the lower limit is limited to 0, and the upper limit is limited to 1. Due to the saturation nonlinearity of PWM control, the pulse width of PWM control used for digital control of the controlled object does not accurately reflect the Duty command value. For this reason, it has been pointed out that the PI gain adjustment (tuning) using VRFT degrades the performance of the controller due to the nonlinearity of saturation.

If the digital control system has saturated nonlinearity, the control parameters of the controller cannot be adjusted using the least-squares method because the controller deals with a nonlinear system.

Conventionally, as a method to eliminate saturation nonlinearity without applying the least squares method,
(a) In data-driven control, a method of introducing a nonlinearity compensating function into a controller as a nonlinearity compensator (Non-Patent Document 1).
(b) A method of limiting feedback associated with nonlinearity by anti-windup compensation (Patent Document 1, Non-Patent Document 2).
(c) A method of asymptotically obtaining control parameters by a numerical optimization method in which operations are repeated multiple times (Non-Patent Document 3).
is proposed.

JP 2007-252114 A

"Nonlinear Compensation and Optimization Techniques in Data Driven Control" Instrumentation and Control Vol.52 No.10 P872-877 "Conditioning Technique, a General Anti-Windup and Bumpless Transformer Method" Automatica, Vol.23, No.6, pp.729-739, 1987 R.HANUS, M.KINNAERT and J.-L. HENROTTE "Anti-windup Control of Input Saturated Systems." Systems/Control/Information, Vol. 46, No.2, pp.1-7, 2002

(a) Non-linearity compensator, (b) Anti-windup compensation, and (c) Numerical optimization methods for eliminating saturation non-linearity, which have been proposed in the past, are When the system has saturated nonlinearity, it is difficult to apply the least-squares method to adjust the control parameters.

(a) Nonlinearity Compensator In the method of compensating for saturation nonlinearity by introducing a nonlinearity compensator function into the controller, linear separation between the control parameter and the transfer function of the controller is difficult. If the control system has saturation nonlinearity, the least squares method cannot be applied in adjusting the control parameters of the controller.

(b) Anti-windup compensation In the anti-windup compensation, there are two types of anti-windup compensation: the integration stop type that sets the gain K _I of the control parameter to be multiplied by the feedback value to "0", and the automatic matching type that replaces the gain K _A with "1/K _P ". , the method of least squares is not applied to adjust the control parameters, so there is a problem in improving the control performance of the controller.

(c) Numerical optimization The numerical optimization method of Non-Patent Document 3 is not a method that applies the least squares method, but requires a stable condition, so optimization for maximizing control performance is required separately. In addition, since it is determined asymptotically by repeating the arithmetic processing a plurality of times, there is also a problem that it takes time to adjust the control parameters.

The present invention solves the above-described conventional problems by applying the least-squares method to the nonlinear system for adjusting the control parameters of the controller by data-driven control in the nonlinear system whose control system has saturated nonlinearity. The purpose is to enable
A further object of the present invention is to enable the application of anti-windup compensation that eliminates the nonlinearity of saturation in the adjustment of control parameters using the least squares method.

The present invention is a method and apparatus for adjusting the control parameter .theta. of a digital control system that performs data-driven control using input/output data of a controlled object in a digital controller.

In the digital control system of the present invention, in a closed loop consisting of a controlled object and a controller, an initial control parameter θ ₀ is set in the transfer function C of the controller, and the controller obtained through this transfer function C (z; θ) is the input data u of the controlled object, and the input signal fed back from the controlled object to the controller is the output data y.

The present invention linearly separates the transfer function C(z; θ) of the controller by the control parameter θ in the adjustment of the control parameter θ of the controller performed by data-driven control, and linearly separates the linear component and the nonlinear component. By separating them, the linearity component and the nonlinearity component can be separately adjusted in the calculation process of the transfer function C, and the least squares method can be applied to the nonlinear system. Furthermore, it is possible to apply anti-windup compensation that eliminates the nonlinearity of saturation in adjusting the control parameters using the least squares method.

The transfer function C(z; θ) of the controller of the present invention is represented by the product (C ₀ ^T ·θ) of the operational term C ₀ ^T and the parameter term θ. The operational term C ₀ ^T has a linear component C _{0 -linear} and a nonlinear component C _{0 -nonlinear} , the parameter term θ has a linear component θ _-linear and a nonlinear component θ _-nonlinear , and the operational term Between C ₀ ^T and the parameter term θ, and between the linearity component and the nonlinearity component of each term, are linearly separated.

(Calculation processing of transfer function C)
In the data-driven control evaluation function, the calculation processing of the transfer function C is as follows:
(1) linearly separating the operational term of the control operation _C0 and the parameter term of the control parameter θ into a linear component and a nonlinear component;
(2) a linearity calculation performed using the output data y of the controlled object and the linearity component obtained by linear separation in (1);
(3) performing a nonlinear operation using a compensating signal for compensating for the nonlinearity of the digital control system and the nonlinear component obtained by linear separation in (1);
(4) The linear calculation of (2) and the nonlinear calculation of (3) are individually performed, and the control parameter θ that minimizes the evaluation function is adjusted by the least squares method.

(VRFT method evaluation function J _VR )
As an evaluation function for data-driven control, the evaluation function J _VR of the VRFT method using the input data u of the controlled object and the virtual input u _v0 is used. In the VRFT method, the virtual input u _v0 is calculated by computation processing of the transfer function C, and the control parameter θ that minimizes the evaluation function J _VR is adjusted by the least squares method using the calculated virtual input u _v0 as a model function. Note that the model function is a function representing the predicted value of the linear regression model in the method of least squares.

…（１） Output data y(k; θ ₀ ) of the controlled object is represented by the following equation (1). The output data y(k; θ ₀ ) comprises the output components of the output voltage V _C , the inductor current i _L of the switching current, and the feedback signal u _A of the anti-windup compensation. where V _C and i _L are the linear components and u _A is the non-linear component. The following equation (1) shows an example in which the feedback signal u _A has an initial value of 0. Since the feedback signal u _A has an initial value of 0, the output data y(k; θ ₀ ) at this time has linearity is an ingredient.

…(1)

In the parameter term of _the control parameter θ, the gains related to the linearity system are the gains K _P and KI for the output voltage _VC and the feedback gain _KL for the inductor current i _L corresponding to the output data y. On the other hand, the gain associated with the nonlinear system is the anti-windup gain _KA with respect to the anti-windup compensation feedback signal _uA .

(Compensation signal that compensates for nonlinearity)
The nonlinearity of the digital control system is the nonlinearity due to the saturation element. The nonlinearity due to the saturation element includes saturation due to the control characteristics of the control system, or saturation nonlinearity due to the physical characteristics of the controlled object itself. Nonlinearity of saturation due to the control system is due to control characteristics such as the output being limited to a specified value in PWM control, for example. , there is nonlinearity caused by magnetic saturation of the inductor provided in the DC-DC converter.

…（２）
ここで、ｕ_ｒは制御器から制御対象へ入力する指令入力値であり、入力データｕの条件に応じて次式（３）で表される。

ただし、

…（３） A compensation signal that compensates for nonlinearity is a feedback signal u _A that anti-windup compensates for saturation nonlinearity, and is expressed by the following equation (2). The feedback signal u _A represented by the equation (2) is limited by the limit value u _lim that is saturated. The limit value u _lim is a limit value limited by saturation, and the present invention compensates for not only the control limit due to the saturation of the control system but also the physical limit due to the saturation of physical factors.

…(2)
Here, _ur is a command input value input from the controller to the controlled object, and is represented by the following equation (3) according to the conditions of the input data u.

however,

…(3)

…（４）
なお、ＰＷＭ制御はＤuｔｙの範囲を０～１の範囲で使用するが、リミット値がｕ_ｌｉｍの場合のＤuｔｙ範囲は０～ｕ_ｌｉｍに制限される場合がある。 In the case of PWM control, the following formula (3) is represented by the following formula (4).

…(4)
PWM control uses a duty range of 0 to 1, but the duty range may be limited to 0 to u _lim when the limit value is u _lim .

…（５） In the feedback signal u _A for anti-windup compensation in equation (2), the upper limit value of the limit value u _lim that becomes saturated in PWM control is 1 and the lower limit value is 0, and is expressed by the following equation (5) .

…(5)

…（６） (virtual input u _v0 )
In the virtual input u _v0 , the linearity calculation is performed on the difference between the virtual input signal and the output data y obtained by calculating the output data y and the inverse function M ⁻¹ of the transfer function M of the reference model. This is done by applying the linearity component of the operand of _C0 . On the other hand, the nonlinearity calculation is performed by applying the nonlinearity component of the operational term of the control calculation _C0 to the compensation signal.
Therefore, the virtual input u _v0 is calculated by the following equation (6).

… (6)

(Application of least squares method to nonlinear system)
In the present invention, the transfer function C(z; θ) of the digital control system is in the form of the product C=C ₀ ^T (z) θ of the operational term of the control operation C ₀ and the parameter term of the control parameter θ, and digital control By linearly separating the system transfer function C(z; The compensation signal _uA is treated as the output data y of the controlled object used for data-driven control by the VRFT method. By treating the compensation signal _uA for anti-windup compensation as the output data y and applying the operand of the control operation _C0 , the minimum form in which the compensation signal _uA for compensating for nonlinearity is included in the virtual input _uv0 It enables the application of the square method and adjusts the control parameter θ of the digital control system of the nonlinear system based on the virtual input u _v0 .

In data-driven control based on the VRFT method, the input data u to the controlled object and the virtual input u _v obtained using the transfer function M of the reference (reference) model of the controlled object and the output data y of the controlled object The control parameter θ of the digital control system is tuned by minimizing the based evaluation function _JVR .

In the adjustment of the control parameter θ, if the digital control system has nonlinearity, the control parameter θ of the digital control system can be adjusted by applying the least squares method to the difference between the input data and the virtual input data. Can not. The present invention linearizes the relationship between the input/output data and the control parameter θ by linearly separating the transfer function C(z; θ) of the digital control system in the nonlinear system with the control parameter θ, and controls by the method of least squares. Allows adjustment of the parameter θ.

The present invention linearly separates the control term of the transfer function C(z; θ) into an operating term and a parameter term, and further linearly separates the operating term and the parameter term into a linear component and a nonlinear component. The operational and parametric terms each have a linearity component and a component that compensates for the nonlinearity of the digital control system. The control parameter θ forming the parameter term has an anti-windup gain _KA as a component for compensating the nonlinearity of the digital control system with the feedback system.

In the control term, the present invention linearly separates the operation term and the parameter term including the control parameter θ, and linearly separates each term into a linear component and a nonlinear component, thereby performing a linear calculation and a nonlinear calculation. It enables processing divided into

In PI control, the calculation to _be performed on the feedback anti-windup signal is a calculation based on the product ( _KA · _{KI )} of the anti-windup gain _KA and the integral gain _KI. ) is a nonlinear function. Thus, in the parameter term. A nonlinear component and a linear component representing the control parameter θ by a nonlinear function are linearly separated, and this linear separation enables adjustment of the control parameter θ by the least-squares method.

…（７）
なお、ｕ_ｖ０は仮想入力であり、ｕ_ｒは実現可能なＰＷＭ制御への指令入力値であり、式（３）あるいは式（４）で表される。 (control parameter θ)
The control parameter θ is calculated by the following formula (7) by applying the method of least squares.

… (7)
Note that u _v0 is a virtual input, and u _r is a command input value for realizable PWM control, which is expressed by equation (3) or equation (4).

(PI control)
INDUSTRIAL APPLICABILITY The present invention can be applied to a control system in which a switching regulator is PI-controlled by current mode control in a digital control system.
The transfer function C has a proportional term, an integral term, and a feedback term, and performs PI control (proportional integral control) by inputting the difference between the target voltage and the output voltage of the controlled object into the proportional term and the integral term to perform switching. Current mode control is performed by inputting the switching current of the regulator into the feedback term and feeding back the current, and inputting the compensation signal into the integration term.

In the parameter term of the control parameter θ, the gains related to the linearity system are the proportional gain K _P , the integral gain KI and the feedback gain _KL with respect to the difference between the target voltage and the output _voltage . Also, the gain associated with the nonlinear system is the anti-windup gain _KA with respect to the anti-windup compensation feedback signal _uA .

(PID control)
INDUSTRIAL APPLICABILITY The present invention can be applied to a control system in which a switching regulator is PID-controlled by current mode control in a digital control system.
The transfer function C has a proportional term, an integral term, a differential term, and a feedback term, and inputs the difference between the target voltage and the output voltage of the controlled object into the proportional term, integral term, and differential term to perform PID control (proportional integral term). Differential control) is performed, the switching current of the switching regulator is input to the feedback term and current is fed back to perform current mode control, and the compensation signal is input to the integral term.

In the parameter term of the control parameter θ, the gains related to the linearity system are the proportional gain K _P , the integral gain KI and the feedback gain _KL with respect to the difference between the target voltage and the output _voltage . Also, the gain associated with the nonlinear system is the anti-windup gain _KA with respect to the anti-windup compensation feedback signal _uA .

(PI-D control)
INDUSTRIAL APPLICABILITY The present invention can be applied to a digital control system in which a switching regulator is PI-D controlled (differential leading type PID control) by current mode control.
The transfer function C has a proportional term, an integral term, a differential term, and a feedback term, and performs PI control by inputting the difference between the target voltage and the output voltage of the controlled object into the proportional term and the integral term. D control is performed by inputting the output voltage to the differential term, current mode control is performed by inputting the switching current of the switching regulator to the feedback term and current feedback, and the compensation signal is input to the integral term.

In the parameter term of the control parameter θ, the gains related to the linearity system are the proportional gain K _P for the difference between the target voltage and the output voltage, the integral gain K _I , the differential gain K _D for the output voltage, and the feedback gain _KL . Also, the gain associated with the nonlinear system is the anti-windup gain _KA with respect to the anti-windup compensation feedback signal _uA .

In each of the above PI control, PID control, and PI-D control, voltage mode control without a switching current feedback term is also established.

(Control parameter adjustment device for controller in digital control system)
A control parameter adjusting apparatus for a controller in a digital control system according to the present invention adjusts a control parameter θ of a controller that controls a controlled object in a digital control system.

In a digital control system, the transfer function C(z; .theta.) of the controller is linearly separated by the control parameter .theta. in the form of the product of the operational term of the control operation _C0 and the parameter term of the control parameter .theta. The operational term comprises an operation for a linear system and an operation for a non-linear system, and the parameter term comprises a gain for a linear system and a gain for a non-linear system.

The evaluation function of data-driven control is the difference (u−u _{v )} between the input data u and the virtual input u _v obtained by the inverse function M ⁻¹ of the transfer function M of the reference (reference) model of the controlled object. and minimization of this evaluation function is attempted.

In a digital control system, a controller has a linearity input component obtained by performing a linear system-related operation among the operational terms of the control operation _C0 on the output data y, and a compensation signal that compensates for the nonlinearity. A virtual input u _v0 is obtained from the signal obtained by adding , and this virtual input u _v0 is used to adjust the control parameter θ of the controller of the nonlinear system by the least-squares method. The compensation signal that compensates for saturation non-linearity is the anti-windup compensation signal.

(VRFT method evaluation function J _VR )
As an evaluation function for data-driven control, the evaluation function J _VR of the VRFT method using the input data u of the controlled object and the virtual input u _v0 is used. In the VRFT method, the virtual input u _v0 is calculated by computation processing of the transfer function C, and the control parameter θ that minimizes the evaluation function J _VR is adjusted by the least squares method using the calculated virtual input u _v0 as a model function. Note that the model function is a function representing the predicted value of the linear regression model in the method of least squares.
The adjustment of the control parameters of the digital control system of the present invention is applicable not only to VRFT method data-driven control focusing on control input errors, but also to FRIT method data-driven control focusing on control output errors.

INDUSTRIAL APPLICABILITY As described above, according to the present invention, in a nonlinear system in which the controlled object has saturated nonlinearity, the minimum It may be possible to apply the square method.

FIG. 4 is a diagram for explaining a schematic configuration of control parameter adjustment of the controller of the present invention; 4 is a block diagram of each process of control parameter adjustment performed by the control parameter adjustment device; FIG. 4 is a flowchart of each process of control parameter adjustment performed by the control parameter adjustment device; 2 is a diagram showing a configuration example of a controller 2 that performs PI control with initial values; FIG. FIG. 10 is a diagram showing an example of obtaining input/output data by experiment using a DC-DC converter; FIG. 4 is a diagram showing an outline of arithmetic processing by linear separation of a transfer function C(z;θ); FIG. 4 is a block diagram for explaining the relationship between the evaluation function J _VR and the control parameter θ, and the calculation of the control parameter θ; It is a figure which shows the structural example of 2 A of controllers which perform PI control. It is a figure which shows the structural example of the controller 2B which performs PID control. FIG. 3 is a diagram showing a configuration example of a controller 2C that performs PI-D control;

As feedback control for stabilizing the output voltage of a digital control system, there are voltage mode control that feeds back the output voltage via a feedback loop, and current mode control that feeds back the switching current of the circuit in addition to the feedback loop of the output voltage. Are known. PI control, PID control and PI-D control can be applied for voltage mode control and current mode control, respectively.

In current mode control, PI control performs proportional integral control by inputting the difference between target voltage V _r and output voltage V _c (e=(V _r −V _c )) into a proportional term and an integral term, Inductor current _iL is input to the feedback term. In PID control, the difference between the target voltage V _r and the output voltage V _c (e=(V _r −V _c )) is input to the proportional term, the integral term, and the differential term to perform proportional-integral-derivative control. , feed back the inductor current _iL . Furthermore, in the PI-D control, the difference between the target voltage V _r and the output voltage V _c (e = (V _r - V _c )) is input to the proportional term and the integral term to perform proportional integral control, and the output voltage Differential control is performed by feeding back _Vc to the differential term, and the inductor current _iL is input to the feedback term.

The adjustment of the control parameter θ by linear separation according to the present invention can be applied to both current mode control and voltage mode control. The feedback element in current mode control can be applied to inductor current as well as capacitor current.

A schematic configuration of the control parameter adjustment device will be described below with reference to FIG. This configuration can be commonly applied to voltage mode control and current mode control.

(Schematic configuration of control parameter adjustment)
A schematic configuration of control parameter adjustment of a digital control system according to the present invention will be described with reference to FIG. The block diagram of FIG. 1 shows a control system comprising a controlled object 3 , a controller 2 that controls the controlled object 3 , and a control parameter adjusting device 1 that adjusts a control parameter θ of the controller 2 .

(Configuration of digital control system)
The present invention can be applied to any digital control system other than the digital control system of the power supply. In the digital control system of the power supply, the DC-DC converter, which is the main circuit of the power supply, is the object of control 3, and the controller 2 controls the output voltage of the DC-DC converter based on the target voltage.

In FIG. 1, the digital control system inputs a difference signal e between a reference signal r and an output signal y fed back from a controlled object 3 to a controller 2 to generate a control signal. This control signal is input to the controlled object 3 as an input signal u, and the output signal y of the controlled object 3 is fed back to the input end of the controller 2 . A closed circuit of the controller 2 and the controlled object 3 forms a feedback system.

The control parameter adjusting device 1 of the present invention performs data-driven control of the VRFT method using input data u and output data y of the controlled object 3, and adjusts (tuning) the control parameter θ of the controller 2. do. Here, data-driven control of digital control is performed with input signal u as input data u and output signal y as output data y.

The controller 2 of the present invention linearly separates the control parameter .theta. to enable setting of the control parameter .theta. by the method of least squares, and performs control using the set control parameter .theta.

The controller 2 digitally controls the controlled object 3 according to the set control parameter θ. In digital control, nonlinearity occurs in the control output when a nonlinear element imposes control restrictions and a saturation state occurs in the control manipulated value. Here, the control limit means a limit imposed on the control amount due to the control operation of digital control. A block 4 in FIG. 1 indicates a nonlinear element of nonlinearity due to saturation, and input data u becomes a command input value u _r to which nonlinearity is added by the nonlinear element 4 . The command input value u _r is an input signal for controlling the controlled object 3 .

When PWM control (pulse width modulation control) is performed as digital control, the pulse width formed by PWM control is limited within a predetermined width. When the pulse width becomes saturated due to this, non-linearity occurs between the input and output. PWM control physically limits the width of the pulses to be formed between 0 and 1. Therefore, when the duty command value of PWM control is less than 0 or exceeds 1, the pulse width is physically limited between 0 and 1. Due to this physical limitation, nonlinearity occurs between the input and output when the output becomes saturated. The pulse width of PWM control including nonlinearity does not become a value that accurately reflects the Duty command value. This is one factor that degrades the performance of the controller.

The control parameter adjustment of the present invention eliminates nonlinearities by applying anti-windup compensation to saturation nonlinearities. On the other hand, regarding the relationship between the data-driven control of the VRFT method and the nonlinearity of the control system, in the data-driven control of the VRFT method, if the control system has nonlinearity, the control is performed by applying the least squares method. cannot adjust the control parameter θ of the device. Therefore, in the data-driven control of the VRFT method, the saturation nonlinearity cannot be eliminated simply by applying anti-windup compensation to the adjustment of the control parameter θ of the controller to which the least-squares method is applied.

According _to the present invention, the transfer function C(z; ) is linearly separated by the control parameter θ, the control system of the controller 2 and the control parameter adjusting device 1 is made into a linear system.

The present invention realizes a uniform and high-speed response regardless of individual differences of controlled objects by applying data-driven control of the VRFT method, and improves transient response by applying anti-windup compensation.

Let the transfer function C(z; θ) of the controller ₂ of FIG. This enables the control parameter adjusting device 1 to calculate the control parameter θ by the method of least squares. By setting each gain of the control parameter θ of the controller 2 to the control parameter θ acquired by the calculation of the control parameter adjusting device 1, the controller 2 is operated with the transfer function C of the suitable gain obtained by the data-driven control. can be operated.

The terms of the control operation _C0 include terms for linear systems and terms for non-linear systems. On the other hand, the parameter term of the control parameter θ has a gain associated with the linear system and a gain associated with the nonlinear system. Thus, the operational terms and the parameter terms are divided into linear system terms and nonlinear system terms, respectively. This indicates that the transfer function C is linearly separated with the control parameter θ.

The nonlinear element 4 controls the output of the controller 2 to produce nonlinearity between the input and output. The nonlinear element 4 can be treated as an internal element included inside the controller 2 or as an external element added to the outside of the controller 2 .

An example of the nonlinear element 4 is a saturation element by duty control. When the duty command value of duty control is less than 0 or exceeds 1 in PWM control, the pulse width obtained is physically limited between 0 and 1. The saturation element by this duty control can be treated as an internal element of the controller 2 as well as an external element.

Circuit elements such as amplifiers and delay devices connected between the controller 2 and the controlled object 3 can be external elements of the nonlinear element 4 . When the output of the controller 2 is restricted due to the electrical characteristics of circuit elements, etc., it acts as a saturation element.
The nonlinear element 4 is shown as an external element of the controller 2 in FIG.

In FIG. 1 , u(k; θ ₀ ) is the output signal of the controller 2 and u _r (k; θ ₀ ) is the command signal input to the controlled object 3 after passing through the nonlinear element 4 . Here, the nonlinear element 4 indicates a nonlinear element of the control system, and indicates a nonlinear element generated in the controller 2 or when the input data u is PWM-controlled. u _r (k; θ ₀ ) contains the nonlinearity of the nonlinear element 4 .

The control parameter adjusting device 1 of the present invention compensates for the nonlinearity of the nonlinear element 4 by feeding back the anti-windup compensation feedback signal u _A to the controller 2 . A feedback _signal u _A for anti _- windup compensation _is a difference signal e( ={u _r (k; θ ₀ )−u(k; θ ₀ )}).

The control parameter adjusting device 1 of the present invention receives the signal u(k; θ ₀ ) output from the controller 2, the output data y of the controlled object 3, and the feedback signal u _A for anti-windup compensation to control. The parameter .theta. is adjusted, and the obtained .theta. is used to set the control parameter .theta.

The control parameter adjustment device 1 can individually correspond the output data y of the controlled object 3 to the operational terms and parameter terms related to the linearity system of the transfer function C(z; θ) by linear separation. Also, the feedback signal u _A for anti-windup compensation that compensates for the nonlinearity of saturation can be individually corresponded to the operational terms and parameter terms related to the nonlinear system by linear separation, and the least squares method is applied. It is possible to adjust the control parameter .theta.

(control parameter adjustment)
Each operation of the control parameter adjustment of the digital control system performed by the control parameter adjustment device 1 will be described with reference to the block diagram of FIG. 2 and the flow chart of FIG. The flowchart shown in FIG. 3 uses reference symbol S to indicate a schematic procedure for obtaining the control parameter θ by the control parameter adjusting device 1 .

The block diagram of FIG. 2 shows the operations of blocks A, B, C, D, E, and F. In data-driven control by the VRFT method, minimization of evaluation function J _VR , adjustment of control parameter θ, and Each operation such as control of the controlled object is performed using the adjusted control parameter θ.

(Block A)
Block A acquires input/output data (input data u, output data y) necessary for the process of optimizing the control parameter θ through experiments. A data acquisition experiment is performed in a feedback system including the controller 2 and the controlled object 3 using the initial parameter θ ₀ which is the initial value of the control parameter θ, and input data u and output data y for the controlled object 3 are acquired.

Here, the term "experiment" means the operation of driving a digital control system with initial control parameters set to obtain input/output data. is different from

The controller 2 receives the reference signal r and acquires the signal u(k; θ ₀ ) for controlling the controlled object 3 . The signal u(k; θ ₀ ) becomes an input signal u _r (k; θ ₀ ) to the controlled object 3 having nonlinearity due to the nonlinear element 4 . If the nonlinear element 4 is a saturation element, the input signal u _r (k; θ ₀ ) is limited to the limit value u _lim . In the case of PWM control, the limit value u _lim has an upper limit value of 1 and a lower limit value of 0, and the input signal ur(k; θ ₀ ) is limited between 0 and 1.

The controlled object 3 receives an input signal u _r (k; θ ₀ ) and outputs output data y(k; θ ₀ ). Thus, the block A acquires the input data u _r (k; θ ₀ ) and the output data y(k; θ ₀ ) through the data acquisition experiment. This block A corresponds to step (S2).

(Block B)
Block B comprises transfer function C of controller 2 and inverse function M ⁻¹ of transfer function M of reference (reference) model 5 of controlled object 3, and computes virtual reference signal r _v (k; θ ₀ ). . A transfer function M is a transfer function of a reference (reference) model having a desired characteristic that serves as a reference in the controlled object 3 . The control parameter adjusting device 1 adjusts the control parameter θ of the controller 2 so that the transfer function of the controlled object 3 becomes the transfer function of this normative (reference) model.

In block B, the inverse function M ⁻¹ inputs the output data y(k; θ ₀ ) of the controlled object 3 and obtains the virtual reference signal r _v (k; θ ₀ ) by calculation. The virtual reference signal r _v (k; θ) is a reference signal when it is assumed that the controlled object 3 of the standard (reference) model outputs the output data y.

The difference signal {r _v (k; θ ₀ )−y(z; θ ₀ )} between the virtual reference signal r _v (k; θ 0 ) and the output data y (k; θ ₀ ) is _the virtual deviation e _v (k) ; θ ₀ ), and inputting this virtual deviation _ev (k; θ ₀ ) to the controller 2, a virtual input u _v (k; θ) is obtained. Since this virtual input u _v (k; θ) is not in a form in which the transfer function C(z; θ) of the controller 2 is linearly separated, it is not in a form to which the method of least squares can be applied. Therefore, in block C, a virtual input u _v0 (k; θ ₀ ) in a format to which the method of least squares can be applied is obtained. Here, for virtual inputs, an input in a form that is not linearly separated is represented by a virtual input u _v (k; θ), and an input in a form that is linearly separated is represented by a virtual input u _v0 (k; θ ₀ ). ing. This block B corresponds to step (S3).

(Block C)
A block C is a virtual input based on the output data y(k; θ ₀ ) fed back from the controlled object 3 and the anti-windup compensation feedback signal u _A (k; θ ₀ ) that compensates for the nonlinearity of saturation. Compute u _v0 (k; θ ₀ ). The virtual input u _v (k; θ) is in a form unsuitable for the least squares method, whereas the virtual input data u _v0 (k; θ ₀ ) obtained in block C is in a form suitable for the least squares method. be.

The computation of the virtual input u _v0 (k; θ ₀ ) is performed using the linearly separated transfer function C ₀ (z) of the controller 2 . For the _transfer function C ₀ (z), the anti-windup compensation feedback signal u _A ( _k ; θ ₀ ). The virtual deviation e _v (k; _{θ 0} ) is _the difference signal {r _v (k; θ ₀ )−y( _z ; θ ₀ )}, which is a value dependent on the output data y(k; θ ₀ ).

…（２） A feedback signal u _A (k; θ ₀ ) for anti-windup compensation of saturation nonlinearity is expressed by the following equation (2). The feedback signal u _A (k; θ ₀ ) represented by Equation (2) indicates a case where the limit value for saturation is u _lim . Note that Equation (2) is expressed as a transposed ^{matrix u AT} ₍ k; θ ₀ ).

…(2)

…（５）
したがって、仮想入力ｕ_ｖ０は下式（６）の演算により求められる。

…（６） The limit value u _lim of u _A (k; θ ₀ ) in equation (2) varies depending _on the control mode. ).

…(5)
Therefore, the virtual input u _v0 is calculated by the following equation (6).

… (6)

The virtual input u _v (k; θ) obtained in block B is data that does not include data related to saturation nonlinearity. On the other hand, the virtual input u _v0 (k; θ ₀ ) obtained in block C is the data with saturation nonlinearity added by introducing the anti-windup compensation feedback signal u _A (k; θ ₀ ). It's becoming The calculation of the virtual input u _v0 (k; θ ₀ ) in this block C corresponds to step (S4).

(Block D)
Block D obtains the input signal u _r (k; θ ₀ ) in block A. The evaluation function J _VR is the difference {u _v0 (k; θ ₀ ) between the input signal u _r (k; θ 0 ) obtained in block _A and the virtual input u _v0 (k; θ ₀ ) obtained in block C. )−u _r (k; θ ₀ )}. Acquisition of the input signal u _r (k; θ ₀ ) corresponds to step (S5).

(Block E)
Block E obtains the optimum control parameter θ by minimizing the evaluation function _JVR in data-driven control by the VRFT method. A feedback signal u _A ( _k ; θ ₀ ) for anti-windup compensation that compensates for saturation nonlinearity is added to the virtual input u v0 (k; θ ₀ ). Therefore, the control parameter θ obtained in block E will include an anti-windup gain to compensate for saturation non-linearity in addition to linearity gain. The minimization of the evaluation function _JVR and the calculation of the control parameter θ in this block E correspond to step (S6).

(Block F)
A block F sets a control parameter .theta. of the controller 2 based on the control parameter .theta. The control of this block F corresponds to step (S7).

As feedback control for stabilizing the output voltage of a digital controller, in addition to voltage mode control that feeds back the output voltage via a feedback loop, there is a voltage feedback loop that feeds back the output voltage and a switching current feedback loop. PI control, PID control, and PI-D control can be applied in feedback control to the configuration of current mode control using .

The linear separation of the control parameter θ in the transfer function C(z; θ) of the controller according to the invention can be applied to any control mode, an example of which follows.
In the following, (a) PI control in current mode control that feeds back the inductor current i _L mainly to the minor loop will be described using the flowchart of FIG. 3 and the block diagrams of FIGS. 4 to 8. FIG. The flowchart in FIG. 3 shows steps (S1) to (S6), and the block diagrams in FIGS. 4 to 8 show the configuration of the controller and the setting of the optimized control parameter θ.

(b) PID control and (c) PI-D control can apply control similar to (a) PI control in setting the control parameter θ by linear separation. Therefore, for PID control (b) and PI-D control (c), only the configuration of each controller will be described using FIGS. 9 and 10, and the description of setting the control parameter θ will be omitted.
Further, the PI control, PID control and PI-D control in the voltage mode control have the same configuration by removing the current feedback element, so the explanation of the figures is omitted.

(a) PI control Hereinafter, steps (S1) _to (S6) will be described with reference to the flow chart of FIG. The configuration of the controller and the setting of the optimized control parameter θ will be described using the block diagram of FIG.

(S1: Determination of initial parameters)
Adjustment of the control parameter θ is performed using the input/output data (input data u, output data y) of the controlled object. Acquisition of this input/output data requires that the object to be controlled be driven, and for this reason it is necessary that some value be set as the control parameter θ.

In the present invention, the initial value of the control parameter θ is determined as the initial parameter θ ₀ in step (S2), a suitable control parameter θ is obtained in steps (S3 to S6), and the obtained control parameter θ is set to the controller 2 drives the controlled object 3 . As a result, the output data y, which is the response result of the controlled object 3, approaches the response result of the normative (reference) model 5. FIG.

Therefore, the initial parameter θ ₀ is determined as the first step. This initial parameter θ ₀ can be determined, for example, by the pole placement method. The present invention sets θ ₀ ^T =[K _P0 , K _I0 , -K _L0 , K _A0 ] as the initial parameter θ ₀ of the control parameter θ.

(S2: Acquisition of input/output data)
An experiment was conducted in which the controlled object 3 was driven by _the controller 2 with _the initial parameter θ ₀ determined in step (S1). ). Since the obtained input/output data is data obtained based on the initial parameter _θ0 as the control parameter θ of the controller 2, there is a deviation when compared with the input/output data obtained by the appropriate control parameter θ.

FIG. 4 shows a configuration example of the controller 2 that performs PI control when the inductor current is added to feedback as a minor loop. In PI control, the difference between the target voltage V _r and the output voltage V _c (e = (V _r - V _c )) is input to the proportional term and the integral term to perform proportional integral control, and the output of the controlled object 3 The inductor current i _L is input to the feedback term.

The proportional term, the integral term, and _the inductor current feedback term have proportional gain K _P , integral gain KI, and feedback gain _KL , respectively, as control parameters θ, and control the added output obtained by adding the outputs of these terms. Output as target input data u. The input data u becomes the PWM command input _ur due to the saturation factor. The command input _ur becomes a signal having nonlinearity due to the saturation element.

A signal obtained by subtracting the input data u _from the command input ur is fed back to the controller 2 as a feedback signal _uA for anti-windup compensation that compensates for saturation nonlinearity. Feedback signal u _A is input to the integral term through anti-windup gain K _A .

In experiments using the initial parameter θ ₀ , the proportional gain K _P , the integral gain _KI , the linearity gain of the feedback gain _KL , and the anti-windup gain _KA are set to the initial values of the initial parameter θ ₀ [K _P0 , K _I0 , -K _L0 , K _A0 ] to obtain the output data y. In FIG. 4, a delay term of 1/z due to a unit step delay is introduced between the nonlinear element 4 and the controlled object 3 .

FIG. 5 shows an example in which a DC-DC converter 3A is used as the controlled object 3 for acquisition of input/output data by experiment. The DC-DC converter 3A includes a switch SW1 connected in series to the input voltage _Vin , a switch SW2 connected in parallel, an inductor L connected in series to the load R, and a capacitor _Ca connected in parallel. The switches SW 1 and SW 2 are switched by the PWM signal of the controller 2 .

The input data u input from the controller 2 to the DC-DC converter 3A controls the ON/OFF of the switches SW1 and SW2 by the PWM signal to control the input voltage _Vin . On the other hand, the output data y output from the DC-DC converter 3A is generated by the output signals of the capacitor voltage V _C of the capacitor C _a , the inductor current i _L of the inductor L, and the nonlinear elements of the PWM control of the controller 2. Anti-windup compensation feedback signal u _A that compensates for saturation non-linearity.

The following equations ₍ 8) to (11 ₎ are for _the circuit example of the DC-DC converter _3A shown in FIG ^. , K _A0 ]. Note that ω ₀ is the resonance frequency 1/√LC.

…（８）

…（９）

…（１０）

…（１１）
ここで、アンチワインドアップゲインＫ_Ａの初期値は０としている。

... (8)

... (9)

... (10)

…(11)
Here, the initial value of the anti-windup gain _KA is set to zero.

…（１２）

…（１３）

…（１４） However, α ₁ , α ₂ and α ₃ are the coefficients of the denominator polynomial D(z) of the pulse transfer function from the target voltage value to the output voltage value, and are represented by the following equations (12) to (14) respectively. be.

…(12)

…(13)

…(14)

…（１５）
安定条件を満たすために必要なｐ_１の条件は、ｐ_１が実数の場合には次のようになる。

…（１６） Furthermore, ignoring higher terms of the Maclaurin expansion of cos ω ₀ T, p ₁ and p ₄ have the following relationship.

…(15)
The condition of _p1 necessary to satisfy the stability condition is as follows when _p1 is a real number.

…(16)

…（１７）
０＜ｘ＜１を満たすｘとｐ^*を用いることで、次のようにしてモデルベースでの制御パラメータのチューニングを行うことができる。

…（１８） Furthermore, if p ₁ =p ₄ , the following equation is obtained using p ^* =p ₁ =p ₄ .

…(17)
By using x and p ^* that satisfy 0<x<1, model-based tuning of control parameters can be performed as follows.

…(18)

(S3: Determination of normative (reference) model)
A transfer function M of a normative (reference) model 5 is determined for the controlled object 3 . The reference (reference) model 5 is a controlled object model in which the input and output of the controlled object 3 have desired characteristics, and the desired input/output characteristics can be set by the transfer function M of the reference (reference) model.

…（１９）
を設定して用いる。 As an example of the transfer function M of the reference (reference) model 5 of the controlled object,

…(19)
is set and used.

…（２０）
なお、ｄｉａｇ［ ］は対角行列を表し、Ｍ_ｖ ^－１は制御対象をＤＣ－ＤＣコンバータとしたときの規範（参照）モデルの出力電圧Ｖ_ｃ（ｋ）である。 For the reference (reference) model 5 of the controlled object of the transfer function M exhibiting the desired input/output characteristics, the inverse function M _inv (z) of the inverse system is defined by the following equation (20).

... (20)
Note that diag[ ] represents a diagonal matrix, and M _v ⁻¹ is the output voltage V _c (k) of the normative (reference) model when the controlled object is a DC-DC converter.

As shown in block B, the output data y(k; θ ₀ ) of the controlled object 3 is input to the inverse function M ⁻¹ to obtain the virtual reference signal r _v (k; θ ₀ ). The virtual reference signal r _v (k; θ) is a reference signal for outputting the output data y when the controlled object 3 is a reference (reference) model of the transfer function M. The difference {r _v (k; θ ₀ )−y(z; θ ₀ )} between the virtual reference signal r _v (k; θ ₀ ) and the output data y (k; θ ₀ ) is the virtual deviation e _v (k; θ ₀ ) and used for the calculation of the virtual input u _v0 in step (S4).

…（７） (S4: Calculation of virtual input u _v0 )
In the data-driven control based on the VRFT method, the optimum control parameter θ can be analytically determined by the following equation (7) using the least squares method.

… (7)

The control parameter θ obtained by Equation (7) is proportional gain K _P , integral gain _KI , feedback gain _KL linearity gain, and anti-windup gain _KA nonlinearity gain in the case of PI control. is the gain _and is expressed by θ ^T =[K _{P, KI} , _-KL , KI _KA ]. The sign of the feedback gain K _L , which is the current term of the control parameter θ, is negative because the current term i _L (k; θ ₀ ) of the output data y(k; θ ₀ ) expressed by Equation (1) ) is input to the controller as a negative value. N in Equation (7) is the number of data samples.

…（４） In the above equation (16) for the control parameter θ, u _v0 (k; θ ₀ ) is a virtual input, and u _r (k; θ ₀ ) is a command input value to realizable PWM control.
Note that u _r (k; θ ₀ ) of the command input value is represented by the following equation (4).

…(4)

…（２１） The transfer function C(z; θ) of the controller is represented by the following equation (21), where the operational term C ₀ ^T and the parameter term θ ^T (=[K _P , _KI , _-KL , KI _{K A} ]), and linear separation is performed.
In the PI control in the current mode control, the transfer function C of the controller 2A is represented by the following formula with respect to the input [V _r -V _c i _L u _A ].

…(21)

The operand C ₀ ^T comprises an operand portion for a linear system and an operand portion for a nonlinear system. _In PI control _{, the parameter} term _? Prepare.

FIG. 6 shows an outline of arithmetic processing by linear separation of the transfer function C(z; θ). The controller input term 100 is a signal term corresponding to the input signal In to the controller, and the linearity component 100a of the deviation e (=ry) obtained from the reference signal r and the output data y fed back from the controlled object, and a nonlinearity component 100b of the anti-windup compensation feedback signal _uA that compensates for saturation nonlinearity.

The controller term 101 is an operational term for calculating the transfer function C, and performs the calculation of the transfer function C(z; θ) on the controller input term 100 . An input data term 102 is a data term of input data for the controlled object, and indicates input data u (=In·C) obtained by the operation result of the controller input term 100 and the controller term 101 .

The input signal In includes a linear component 100a and a nonlinear component 100b.
The deviation e (=ry) obtained from the reference signal _r and the output data _y is a _linear Since it is the output signal, [Vr-V _c , -i _L ] is the linearity component 100a. On the other hand, [u _A ] of the feedback signal, which is another component of the input signal In, is a nonlinear component 100b because it is a signal that compensates for nonlinearity due to saturation. Therefore, of the input signal In of [V _r −V _c , −i _L , u _A ], [V _r −V _c , −i _L ] of the linearity component 100a is the linearity input In _−linear and nonlinear [u _A ] of the linear component 100b is the nonlinear input In _-nonlinear .

The transfer function C(z; θ) of the controller term 101 is represented by the product of the operational term C ₀ ^T and the parameter term θ. The operational term C ₀ ^T has C _{0 -linear for the linear} component 101a and C _{0 -nonlinear} for the nonlinear component 101b, and the parameter term θ is θ _−linear for the linear component 101c and θ ₋ for the nonlinear component 101d. _nonlinear . The θ _-linear of the linear component 101c is [K _P , K _I , −K _L ] ^T , and the θ _-nonlinear of the nonlinear component 101d is [K _A ·K _I ] ^T.

The input data u (=In C) resulting from the operation of the controller input term 100 and the controller term 101 is u _-linear of the linearity component 102a obtained by the operation of the linearity components 100a, 101a, and 101c, It is obtained by adding u _-nonlinear to the nonlinear component 102b obtained by computing the nonlinear components 100b, 101b, and 101c.

In the controller term 101, the operation term C ₀ ^T and the parameter term θ are linearly separated, so that the calculation of the linear component and the calculation of the nonlinear component can be performed separately.
u _−linear of the linearity component 102a is the sum of [V _r −V _c , −i _L ] of the linearity component 100a of the input signal In and C ₀ -linear of the linearity component 101a of the operational term C ₀ ^T and the parameter term θ is obtained by calculation {K _P +K _I (T/(z−1))}·(V _r −V _c )−KI·i _L between linear components by θ _−linear of the linearity component 101c of .

On the other hand, u _-nonlinear of the nonlinear component 102b is a calculation of nonlinear components by [u _A ] of the input signal of the nonlinear component 100b, C _{0 -nonlinear} of the nonlinear component 101b, and θ _-nonlinear of the nonlinear component 101d. It is obtained by [K _A ·K _I ·(T/(z−1))·u _A ].

In other words, [V _r −V _c , −i _L ], which is In _−linear of the linearity component 100a of the input signal In, is the operator term C ₀₋ of the linearity component 101a of the transfer function C(z;θ). Calculations related to the linearity system are performed in correspondence with _linear and the parameter term θ _-linear of the linearity component 101c.

On the other hand, the feedback signal [u _A ] for anti-windup compensation that compensates for the saturation nonlinearity, which is In _−nonlinear , of the nonlinear component 100b of the input signal In is the nonlinear component 101b of the transfer function C(z; θ). , and the parameter term θ _-nonlinear of the nonlinear component _101d are associated with each other to perform calculations related to the nonlinear system.
By linearly separating the saturation anti-windup nonlinearity component from the linearity component, the least squares method can be applied and the control parameter θ of the controller can be adjusted.

…（６） As described above, by linearly separating the transfer function C (z; θ) with the control parameter θ, the virtual input u _v0 used in the equation (7) representing the control parameter θ is calculated by the following equation (6) can do.

… (6)

In equation (6), the first term is the virtual reference signal r _v (k; θ ₀ ), the second term is the output data y(k; θ ₀ ), and the third term is the feedback signal u _A for anti-windup compensation. (k; θ ₀ ). The virtual input u _v0 is the difference signal {r _v (k; θ ₀ )−y(z; θ ₀ )} between the virtual reference signal _rv (k; θ ₀ ) and the output data y (k; θ ₀ ). It shows that the sum of a virtual deviation e _v (k; θ ₀ ) and the anti-windup compensation feedback signal u _A (k; θ ₀ ) is multiplied by C ₀ .

ただし、

…（３） (S5: Acquisition of command input _ur )
The command input u _r is the output signal of the nonlinear element 4, and u _r (k; θ ₀ ) is expressed by the following equation (3), where u _lim is the limit value.

however,

…(3)

…（６）
ＰＷＭ制御ではリミット値ｕ_ｌｉｍが１となるため、このときの指令入力値ｕ_ｒ（ｋ；θ_０）は以下の式（４）で表される。

…（４） Therefore, the virtual input u _v0 is calculated by the following equation (6).

… (6)
Since the limit value u _lim is 1 in PWM control, the command input value u _r (k; θ ₀ ) at this time is represented by the following equation (4).

…(4)

(S6: Calculation of control parameter θ)
By applying the virtual input u _v0 of the equation (6) and the command input value u _r of the equation (4) to the equation (7) of the control parameter θ described above, the optimum control parameter θ is required.

FIG. 7 is a block diagram for explaining the relationship between the evaluation function J _VR and the control parameter θ, and the calculation of the control parameter θ.

(A) Evaluation function J _VR
The process of adjusting the control parameter θ so that the output data y(k; θ) becomes the ideal response y _d (k; θ) is to minimize the evaluation function _JVR in data-driven control by the VRFT method. corresponds to

…（２２） Block 20 in FIG. 7 represents the process of obtaining the evaluation function _JVR ([theta]) and the process of optimizing the control parameter [theta].
Note that the evaluation function J _VR (θ) is represented by the following equation (22).

…(22)

In equation (22) of the evaluation function J _VR (θ), u is the collected input data and u _v is the virtual input.

…（２３）
式（２３）で表される仮想的な入力ｕ_ｖはθで線形分離されていないため最小二乗法に適用できる形式ではなく、アンチワインドアップ補償ｕ_Ａを考慮していない。 The virtual input u _v is represented by the following equation (23), and the inverse function M ⁻¹ of the reference (reference) model of the controlled object and the transfer function C of the controller are processed for the output data y obtained by

…(23)
Since the virtual input u _v represented by Equation (23) is not linearly separated by θ, it is not in a form applicable to the least squares method, and anti-windup compensation u _A is not considered.

…（６） On the other hand, instead of the transfer function C, the control operation C ₀ of the linearly separated transfer function is used to convert to a form applicable to the least squares method, and the virtual input u _v0 to which the anti-windup compensation u _A is added is used. .

… (6)

The virtual input u _v0 represented by Equation (6) is a process 21 of the inverse function M ⁻¹ of the reference (reference) model of the controlled object and the control operation C ₀ of the transfer function C of the controller for the output data y. It is calculated from the linear component obtained by applying the processing 22 and the nonlinear component of the anti-windup compensation feedback signal _uA .

(B) Adjustment of control parameter θ of nonlinear control system The control parameter θ to which anti-windup compensation is applied is the virtual input u _v0 of formula (6) and the realizable PWM control of formula (3) or formula (4) It is calculated by Equation (7) using the command input value _ur to .

Here, in general, minimization of the evaluation function J _MR used for parameter tuning for an ideal response is not necessarily equivalent to minimization of the evaluation function J _VR (θ) by the VRFT method. The filter L(z) obtained by is used for the command input value u _r and the virtual input u _v0 .

…（２４） In the closed loop, the filter L(z) is represented by Equation (24) below.

…(24)

FIG. 7 shows an example in which the processing 23 of the filter L(z) is applied to the command input value u _r , and the processing 24 of the filter L(z) is applied to the virtual input u _v0 . Note that the processing of the filter L(z) is not essential, and the control parameter θ can be obtained by applying the command input value u _r and the virtual input u _v0 to the equation (6) without performing the processing of the filter L(z). good too.

(C) Setting the control parameter θ The control parameter θ adjusted in the control parameter θ process 20 is set as the control parameter of the controller.

(S7: Control by control parameter θ)
The value of the control parameter θ obtained in the calculation step of S6 is used to set the control parameter of the controller 2, and the output signal of the controller 2 is input to the controlled object 3 to perform control.

At this time, a target voltage _Vr as a reference signal is input to the controller 2, and an output signal y and a feedback signal _uA for anti-windup compensation for compensating nonlinearity of saturation are fed back from the controlled object 3. .

(Example of controller configuration)
FIG. 8 is a block diagram showing a controller using PI control in current mode control. The controller 2A shows an example of PI control and has gains of proportional gain K _P , integral gain K _I , feedback gain −K _L , and anti-windup gain K _A .

The proportional gain K _P is the gain for the difference ₍ V _r −V _C ) between the target voltage V _r and the output voltage V _C , and the integral gain K _I is the _difference (V _r − V _C ) plus the feedback signal u _A for anti-windup compensation. Feedback gains K _L and K _iC are gains for inductor current _iL and capacitor current _iC . The anti-windup gain _KA is the gain for the anti-windup compensation feedback signal _uA . These gains K _P , _KI , _KL , and _KA are set using the control parameter θ obtained by adjusting the control parameters described above. In FIG. 8, the configuration of the feedback gain K _L is indicated by a solid line, and the configuration of the feedback gain K _iC is indicated by a chain line. Minor loop control is performed using either of these feedback gains K _L and K _iC .

The controller 2A includes a target voltage _Vr , an output voltage Vc obtained from the controlled object 3, a feedback signal of any one of the inductor current _iL and the capacitor current _iC fed back in the minor loop, and a saturation nonlinearity compensation signal. A feedback signal _uA for anti-windup compensation is input, and an input signal u for the controlled object 3 is output. When the controlled object 3 is a DC-DC converter, it converts the input signal u into a PWM signal to control the switching operation of the switching elements of the DC-DC converter.

Moreover, when generating the PWM signal, nonlinearity due to saturation occurs because the amplitude of the PWM signal is limited to a range between 0 and 1. To compensate for this non-linearity of saturation, the difference between the input and output of the saturation element forms the anti-windup compensation feedback signal _uA which is input to the controller 2A.

Since the control parameter θ of the controller 2A is set to each gain value adjusted by the control parameter adjusting device 1, the controller 2A performs control along the response characteristics determined by the transmission control M of the reference (reference) model. I do.

(b) PID Control Hereinafter, the configuration of the controller will be described with reference to the block diagram of FIG. 9 for PID control.
FIG. 9 shows a configuration example of a controller 2B that performs PID control in current mode control. Also, FIG. 9 is a block diagram showing a controller based on PID control.

The proportional term, integral term, differential term, and feedback term of the controller 2B have proportional gain K _P , integral gain KI, differential gain K _D , and _feedback gain _KL as control parameters θ. The output is output as the input data u to be controlled.

The proportional gain K _P is the gain for the difference ₍ V _r −V _C ) between the target voltage V _r and the output voltage V _C , and the integral gain K _I is the _difference (V _r − V _C ) plus the feedback signal u _A for anti-windup compensation. Differential gain K _D is the gain for the difference (V _r −V _C ) between target voltage V _r and output voltage V _C , and feedback gains K _L and K _iC are the gains for inductor current i _L and capacitor current i _C. be. The anti-windup gain _KA is the gain for the anti-windup compensation feedback signal _uA . These gains K _P , _KI , _KL , and _KA are set using the control parameter θ obtained by adjusting the control parameters described above. In FIG. 9, the configuration of the feedback gain K _L is indicated by a solid line, and the configuration of the feedback gain K _iC is indicated by a chain line. Minor loop control is performed using either of these feedback gains K _L and K _iC .

In PID control, the difference between the target voltage V _r and the output voltage V _c (e=(V _r −V _c )) is input to the proportional term, the integral term, and the differential term to perform proportional-integral-derivative control. A feedback signal of either the inductor current i _L or the capacitor current i _C fed back in the loop is input to the feedback term.

Anti-windup compensation can be similar to the PI control shown in FIG. The input data u is a PWM command input _ur via a saturation element, and the command input _ur is a signal having nonlinearity due to the saturation element.

A signal obtained by subtracting the input data u from the command input u _r is fed back to the controller as an anti-windup compensation feedback signal u _A that compensates for the nonlinearity of saturation. Feedback signal u _A is input to the integral term through anti-windup gain K _A .

In the experiment _{using the} initial parameter _{θ 0} , _the initial value of _{the initial parameter θ 0 was} set to Set [K _P0 , K _I0 , K _D0 , -K _L0 , K _A0 ] and acquire the output data y.

…（２５） In PID control in current mode control, the transfer function C of the controller 2B is represented by the following equation (25) with respect to the input [V _r -V _C i _L u _A ].

…(25)

(c) PI-D Control The configuration of the controller for PI-D control will be described below with reference to the block diagram of FIG.
FIG. 10 shows a configuration example of a controller 2C that performs PI-D control. FIG. 10 is a block diagram showing the state of the controller during control by PI-D control in current mode control.

In PI-D control, the difference between the target voltage V _r and the output voltage V _c (e=(V _r −V _c )) is input to the proportional term and the integral term to perform proportional integral control, and the output voltage V _c is It is input to the differential term to perform differential control, and the inductor current _iL or the capacitor current _iC fed back in the minor loop is input to the feedback term.

The proportional term, integral term, differential term, and feedback term of the controller 2C have proportional gain K _P , integral gain _KI , differential gain K _D , and feedback gain _KL as control parameters θ. The output is output as the input data u to be controlled.

The proportional gain K _P is the gain for the difference ₍ V _r −V _C ) between the target voltage V _r and the output voltage V _C , and the integral gain K _{I is} the difference (V _r −V _C ) plus the feedback signal u _A for anti-windup compensation. Differential gain _KD is a gain for output voltage _VC , and feedback gains _KL and _KiC are gains for inductor current _iL and capacitor current _iC . The anti-windup gain _KA is the gain for the anti-windup compensation feedback signal _uA . These gains K _P , _KI , K _D , _KL , _KA and K _iC are set using the control parameter θ obtained by adjusting the control parameters described above. In FIG. 10, the configuration of the feedback gain K _L is indicated by a solid line, and the configuration of the feedback gain K _iC is indicated by a chain line. Minor loop control is performed using either of these feedback gains K _L and K _iC .

Anti-windup compensation can be similar to the PI control shown in FIG. The input data u is a PWM command input _ur via a saturation element, and the command input _ur is a signal having nonlinearity due to the saturation element.

A signal obtained by subtracting the input data u from the command input u _r is fed back to the controller as an anti-windup compensation feedback signal u _A that compensates for the nonlinearity of saturation. Feedback signal u _A is input to the integral term through anti-windup gain K _A .

In the experiment using _the initial _{parameter θ 0} , _the initial value of _{the initial parameter θ 0 was} set to [K _P0 , K _I0 , K _D0 , -K _L0 , K _A0 ] are set and the output data y is acquired.

…（２６） In the PI-D control in _the current _mode control, the transfer function C of the controller 2C is expressed by the following equation (26) with respect to the input [ _{Vr - VCVCiLuA} ].

…(26)

…（２７） Each of PI control, PID control, and PI-D control can be applied to voltage mode control. As an example, in PI control, the transfer function C of the controller 2A is expressed by the following equation (27) with respect to the input [V _r -V _{Cu A} ].

…(27)

(Experimental example)
Experimental examples of the present invention will be described below. Example experimental results are set forth in Table 1 below.

Comparing the present invention applying the VRFT method including the anti-windup compensation of the present invention with the conventional method applying the VRFT method not including the anti-windup compensation, according to the present invention, the evaluation function J _MR becomes smaller. , 5% is confirmed to reduce the settling time. Assuming that the sampling period and PWM period are 10 μs and the experiment time is 1 ms, 100 samples of input/output data (input data u, output data y (output voltage V _C , inductor current i _L )) for one experiment are obtained. Collected.

The control parameter adjustment method and adjustment device of the controller of the present invention can be applied to a control system that performs PI control in current mode control using minor loop feedback of inductor current _iL . Further, it can be applied to PID control and PI-D control, and can be applied to voltage mode control in addition to current mode control using capacitor current as minor loop feedback.

1 control parameter adjustment devices 2, 2A, 2B, 2C controller 3 controlled object 4 nonlinear element 100 controller input term 101 controller term 102 input data term In input signal u input data (input signal)
y Output data (output signal)
e Differential signal u _A Feedback signal for anti-windup compensation u _v Virtual input u _v0 Virtual input u _r Command input value r Reference signal V _r Target voltage V _C Output voltage i _L Inductor current V _in Input voltage
θ control parameter θ ₀ initial parameter C transfer function of controller C ₀ control operation M transfer function of reference (reference) model of controlled object J _VR evaluation function K _P proportional gain KI _integral gain KL feedback gain K _{ic feedback} gain K _A Anti-windup gain C _a Capacitor L Inductor SW1, SW2 Switch

Claims (10)

A method for adjusting a control parameter θ of a digital control system by data-driven control using input/output data of a controlled object, comprising:
(a) the transfer function C(z; θ) of the digital control system is linearly separated by the control parameter θ to obtain the product of the operational term of the control calculation _C0 and the parameter term of the control parameter θ;
(b) in the data-driven control evaluation function,
The arithmetic processing of the transfer function C is
(b1) linearly separating the operational term of the control operation _C0 and the parameter term of the control parameter θ into a linear component and a nonlinear component;
(b2) a linearity calculation using the output data y of the controlled object and the linearity component;
(b3) performing a nonlinear calculation using a compensation signal for compensating the nonlinearity of the digital control system and the nonlinearity component;
(c) adjusting a control parameter θ that minimizes the evaluation function of the data-driven control by the method of least squares;
Control parameter adjustment method for digital control system. The evaluation function of the data-driven control is a VRFT method evaluation function J _VR using the input data u of the controlled object and the virtual input u _v0 ,
Calculate the virtual input u _v0 by arithmetic processing of the transfer function C,
Adjust the control parameter θ that minimizes the evaluation function J _VR by the least squares method using the calculated virtual input u _v0 as a model function,
2. The control parameter adjusting method for a digital control system according to claim 1. The input data u and the output data y are, in a closed loop consisting of the controlled object and the controller,
An input signal and an output signal of the controlled object obtained by setting the initial control parameter θ ₀ to the transfer function C of the controller,
3. The control parameter adjusting method for a digital control system according to claim 2 . The nonlinearity of the digital control system is nonlinearity due to a saturation element,
The compensation signal is a feedback signal u _A that anti-windup compensates for saturation nonlinearity of the input data u when u _lim is a limit value for saturation,

is
3. The control parameter adjusting method for a digital control system according to claim 2 . At the virtual input u _v0 ,
The linearity calculation is performed by calculating the difference between a virtual input signal obtained by calculation of the output data y and the inverse function M ⁻¹ of the transfer function M of the reference model and the output data y, the control calculation C ₀ Apply the linearity components of the operands,
The non-linearity calculation is performed by subjecting the compensation signal to the non-linearity component of the operational term of the control calculation _C0 ,
The virtual input u _v0 is calculated by the following formula,

5. The control parameter adjustment method for a digital control system according to claim 4. The control parameter θ is expressed by the following formula,

u _r is a command input value to the PWM control that can be realized, and is represented by the following equation according to the conditions of the input data u

however,

6. The control parameter adjusting method for a digital control system according to claim 5. The digital control system is any feedback control system of PI control, PID control, and PI-D control,
The output data y is an output voltage to be controlled and a minor loop element,
The compensation signal that compensates for the nonlinearity is the feedback signal u _A of the anti-windup compensation for saturation nonlinearity.
3. The control parameter adjustment method for a digital control system according to claim 1 or 2. The minor loop element is either an inductor current or a capacitor current,
8. The control parameter adjusting method for a digital control system according to claim 7. A device for adjusting a control parameter θ of a controller that controls a controlled object with a digital control system,
The controller is
(a) The transfer function C (z; θ) is linearly separated by the control parameter θ and provided as the product of the operational term of the control operation C ₀ and the parameter term of the control parameter θ,
(b ) In the data- driven control evaluation function,
The arithmetic processing of the transfer function C is
(b1) linearly separating the operational term of the control operation _C0 and the parameter term of the control parameter θ into a linear component and a nonlinear component;
(b2) a linearity calculation using the output data y of the controlled object and the linearity component;
(b3) performing a nonlinear calculation using a compensation signal for compensating the nonlinearity of the digital control system and the nonlinearity component;
(c) adjusting a control parameter θ that minimizes the evaluation function of the data-driven control by the method of least squares;
Control parameter adjuster for digital control system. The evaluation function of the data-driven control is a VRFT method evaluation function J _VR using the input data u of the controlled object and the virtual input u _v0 ,
Calculate the virtual input u _v0 by arithmetic processing of the transfer function C,
Adjusting the control parameter θ that minimizes the evaluation function J _VR by the least squares method using the calculated virtual input u _v0 as a model function,
10. A control parameter adjustment device for a digital control system according to claim 9.

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