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Minimax approach to design of robust controller

Given a systems with uncertainty, a performance index and a controller structure, the design problem of robust control system can be formulated as a minimax optimization problem. In this problem the control and plant uncertainty 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 the robust stability and the best performance under worst case scenario. This talk is organized as follows, after starting the overview of minimax optimization problem in a game theory, typical two types of the LQ controller synthesis is reviewed. One is the design method of controller chosen to minimize the maximum linear quadratic regulator (LQR) cost from all the plants with parameters in the given set. Another example is a controller design method to minimize the weighted sum of the maximum linear quadratic gaussian (LQG) performance objectives over a set of worst plant parameter changes. Then 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 approximant is also included. ;
Type of Seminar:
Public Seminar
Prof. Toru Kawabe
ETH Zurich Automatic Control Lab. Physikstrasse 3 CH-8092 Zuirich
May 04, 2001   17:15

ETH Zentrum, ETL K 25, Physikstrasse 3, 8006 Zurich
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Biographical Sketch:
Toru Kawabe received the B.Eng. degree in applied mathematics and physics, M.Eng. degree in applied systems science and Dr.Eng. degree in applied mathematics and physics all from Kyoto university in 1988, 1990 and 1997, respectively. >From 1990 to 1995, he was a Research Associate of the Department of Information Science and Intelligent Systems, University of Tokushima, and from 1995 to 1997, he was a Lecturer in the Information Processing Center, University of Tokushima. Since 1997, he has been an Assistant Professor of the Institute of Information Sciences and Electronics, University of Tsukuba. And since July 2000, he has been visiting the Automatic Control Laboratory (IfA), the Swiss Federal Institute of Technology (ETH) in Zurich. His current research interests include Robust Control Synthesis and Optimization Theory.