Simplified Design Method for Data-Driven Cascade Control Systems

Abstract

This provides a simplified measurement method for data-driven cascade control systems. [Solution] When considering a normative model for a cascade control system, a "linear representation" is applied to the nonlinear equations relating to the controller parameters. By iteratively applying the least squares method to the resulting "linearly represented regression model," it is possible to sequentially optimize the controller parameters. This method allows for the design of data-driven cascade control systems.

Description

[Technical Field]

[0001] This invention relates to a method for designing control systems. [Background technology]

[0002] Instead of designing a controller for a model being controlled, methods such as IFT (Non-Patent Document 1), VRFT (Non-Patent Document 2), and non-falsifying control (Non-Patent Documents 3 and 4) have been proposed to directly optimize the controller from input and output data. These control methods, which emphasize the direct use of behavioral data, are also called data-driven control.

[0003] In motor positioning control, control systems like the one shown in Figure 1 are still used. A multiple feedback system like this, where the control input of the outer loop is used as the target value of the inner loop, is called a cascade control system. In Figure 1, P is the motor speed system, C1 is the position controller, and C2 is the speed controller. Here, s is the Laplace operator. u is the control input to the motor, θ and ω are the motor angle and motor speed, and their target values ​​are r and r ω Therefore, the control input for position control (output of position controller C1) is set to the target value r of the speed control system. ω This configuration stems from the fact that motor control began with speed control. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] H. Hjalmarsson, M. Gevers, S. Gunnarsson, and O. Lequin, Iterative Feedback Tuning: Theory and Applications, IEEE Control Systems Magazine, Vol.18, No.4, pp.26-41, 1998 [Non-Patent Document 2] M. Campi, A. Lecchini, and S. Savaresi, Virtual Reference Feedback Tuning: A Direct Method for the Design of Feedback Controllers, Automatica, Vol.38, pp.1337-1346, 2002 [Non-Patent Document 3] M. Safonov and T. Tsao, The Unfalsified Control Concept and Learning, IEEE Transactions on Automatic Control, Vol.AC-42, No.6, pp.843-847, 1997 [Non-Patent Document 4] M. Jun and M. Safonov, Controller Parameter Adaptation Algorithm using Unfalsified Control Theory and Gradient Method, 15th IFAC World Congress, pp.283-287, 2002 [Patent Documents]

[0005] [Patent Document 1] A simplified design method for a cascade-type motor positioning control system with added speed feedforward (Patent No. 6149291) [Disclosure of the Invention] [Problems that the invention aims to solve]

[0006] The present invention provides a simple method for directly adjusting the controller parameters of a cascade control system from input and output data. [Means for solving the problem]

[0007] The method of the present invention will be explained using the cascade control system in Figure 1 as an example. First, as shown in Figure 2, the desired characteristics are given by a reference model L of the loop transfer function.M is given. By comparing Figure 1 and Figure 2, the number 1 is obtained.

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[0008] The parameter K of the number 7 i The first thing to consider in order to determine is the parameter X of the number 9 i is redefined, and consider the linear regression model (number 10) regarding X i However, in this case, constraint conditions of the number 11 are generated due to the parameter redefinition, so a solution considering this is necessary.

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[0009] In the present invention, sequential estimation of parameter K i is considered, and the expression (linear expression) of Equation 12 is applied to Equation 7. Here, K i curr represents the estimated value of K at the current time point. i

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[0010] The method of the present invention first gives an initial value to K of Equation 13 i curr to create matrix Φ, and obtains x by Equation 16. This x is used as K of Equation 13 i curr ​A new Φ is created by substituting the values, and x is recalculated using equation 16. This recalculation of Φ and x is repeated until x converges. Thus, the method of the present invention is a method for sequentially optimizing controller parameters by iteratively applying the least squares method to a linearly represented regression model.

[0011] This example demonstrates the application of behavioral data generated using a motor speed system (and integrator) of type 17 as a hypothetical control target. m D is the moment of inertia of the motor. m This is the coefficient of viscous friction.

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[0012] Figure 3 shows the behavior data when the controller parameter is set to number 20.

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[0013] [Figure 1] Cascade control system [Figure 2] Desired characteristics [Figure 3] Examples of input / output data [Figure 4] Changes in controller parameters [Figure 5] Changes in the evaluation function [Figure 6] Changes in controller parameters (when initial values ​​are changed) [Figure 7] Example of response from a cascade control system [Explanation of Symbols]

[0014] 1 Position Controller 2 Speed ​​Controllers 3. Motor speed system (controlled object) 4. Integral elements (controlled objects) 5. Normative Models

Claims

[Claim 1] A control method characterized by directly and sequentially optimizing the controller parameters of a cascade control system using behavioral data by iteratively applying the least squares method to a regression model that utilizes a linear representation.

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