Conic Sector Analysis of Hybrid Control Systems

Abstract

A hybrid control system contains an analog plant and a hybrid (or sampled-data) compensator. In this thesis a new conic sector is determined which is constructive and can be used to: (1) determine closed loop stability, (2) analyze robustness with respect to modelling uncertainties, (3) analyze steady state response to commands, and (4) select the sample rate. The use of conic sectors allows the designer to treat hybrid control systems as though they were analog control systems. The center of the conic sector can be used as a rigorous linear time invariant approximation of the hybrid control system, and the radius places a bound on the errors of this approximation. The hybrid feedback system can be multivariable, and the sampler is assumed to be synchronous. Algorithms to compute the conic sector are presented. Several examples demonstrate how the conic sector analysis techniques are applied. Extensions to single loop multirate hybrid feedback systems are presented. Further extensions are proposed for multiloop multirate hybrid feedback system and for single rate systems with asynchronous sampling.