Reduction of Conservativeness of RobustPIDControl System Design Method: An Approach Using the Mapping Theorem and theCremer–Leonhard–MikhailovCriterion

Abstract

This paper gives a novel method to design less-conservative robust PID control systems. The partial model matching method is a design method for PID control systems. That is a method to design a control system that matches a reference model as closely as possible. This method does not guarantee robust stability of a PID control system because it is assumed that there are no uncertainties on the coefficients of the lower-order terms of the plant. Therefore, in our previous work, a robust design method based on the partial model matching method was proposed. However, the drawback of this conventional method is that the results of stability analysis are conservative. In this paper, we aim to reduce the conservativeness caused by the conventional method. To achieve this goal, we use a robust stability analysis method based on the Cremer-Leonhard-Mikhailov criterion and the mapping theorem. Moreover, we also propose a new method to update the value of a design parameter. A numerical example shown in this paper implies that the conservativeness is reduced by the proposed method.

Zero/low overshoot conditions based on maximally‐flatness for PID‐type controller design for uncertain systems with time‐delay or zeros

“…Several different approaches for PID controller design are given in the literature. Robust PID design [13], direct frequency domain method [14], numerical optimization method [15] etc.…”