Minimax approach for robust controller design

Prof. Dr. Eng. Toru Kawabe

   Zeit: Dienstag, 26. 06. 2001, 16:00
   Ort: Hörsaal V 9.31 Pfaffenwaldring 9, Universitätsbereich Stuttgart-Vaihingen

Abstract:

A tutorial introduction to the minimax approach for robust controller design is presented.

Given a system with uncertainty, a performance index and a controller structure, the design problem of a robust control system can be formulated as a minimax optimization problem. In this problem the control and plant uncertainties are viewed as strategies employed by opposing players in a game. Namely the controller minimizes the performance index maximized by the plant. And the controller designed by this formulation guarantees robust stability and the best performance under the worst case scenario.

This talk is organized as follows: after starting with an overview of the minimax optimization problem in a game theoretical setting, the typical two types of LQ controller synthesis are reviewed. First, to choose a controller such that the maximum linear quadratic regulator (LQR) cost for all plants with parameters in a given set is minimized. Second, to design a controller such that the weighted sum of the maximum linear quadratic gaussian (LQG) performance objectives over a set of worst plant parameter changes is minimized.

Then the minimax propotional-integral-derivative (PID) controller design method is presented. This method is based on the generalized integral of squared error (ISE) criterion, with a penalty of the derivative of the manipulated variable. Extention of this method to the exact computation of the generalized ISE for time-delay systems without using Pade approximations is also included.

Biographical Sketch:

Toru Kawabe received his B. Eng. (1988), M. Eng. (1990) and Dr. Eng. (1997) degrees all from Kyoto University in Applied Mathematics and Physics, in Applied Systems Sciences and Applied Mathematics and Physics respectively. From 1990 to 1995 he was a research associate at the Department of Information Science & Intelligent Systems at the University of Tokushima, where he stayed as an assistant professor within the Information Processing Center from 1995 to 1997. Since 1997 he is an assistant professor at the Institute of Information Sciences and Electronics at the University of Tsukuba. Currently he is with the automatic control laboratory (IfA) of the Swiss Federal Institute of Technology Zurich (ETHZ) as an academic guest. Prof. Kawabe's main research interests lie in the areas of robust control theory and hybrid systems.