Optimal Minimax Controller for Plants with Four Oscillatory Modes Using Grobner Basis

Abstract

Optimal minimax rate feedback controller design problems was proposed and partially solved by R.S. Bucy et al in 1990. The application of the problem have found in the oscillation suppressor design of large space structure with multiple oscillatory/resonance modes. By employing Grobner basis technique, the complete symbolic solution for the case when the cardinality of the plant oscillatory mode is three or fewer was later found by N.K. Bose and the author. In this paper, the case when the cardinality is four is considered based on the use of Grobner bases. In general, the higher order (four or more) problem is analytically intractable and suboptimal solutions based on numerical techniques are then the only recourse.
In addition, it is also shown that, for a specified generic plant, by incorporating in rate feedback controller the additional parameter available in the basic design procedure, significant improvement in feedback system performance over what was believed to be possible can be realized . This proposed additional design parameter expands the searching space for optimal solution (i.e. provides higher degree of freedom). Various numerical examples are shown to illustrate the e®ectiveness of the proposed method.