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,
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.
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.