A control-theoretic approach for input saturated linear systems: Integration of phase-shaping and gain-scheduling

Abstract

Saturation is mainly characterized by its passivity and magnitude bound. But most of the saturation control methods only make use of either of these features. To enhance the performance of saturated systems, this paper develops a novel method capable of fully using both of these two features. This method is a two-stage design scheme which integrates the phase-shaping technique with the gain-scheduled control. The phase-shaping fully uses the passivity of saturation while the gain-scheduling actively utilizes the magnitude bound of saturation. In this way, the design conservatism associated with existing methods is reduced substantially. Specifically, a matrix-type phase-shaping method is developed through the placement of systems' frequency loci, and a meta-heuristic method is devised for the design of the phase-shaping function. Furthermore, the gain-scheduled control is transformed into the robust performance problem of a passive uncertain system, and designed by the passivity-based robust control method of the authors. Application to two practical control systems validates the effectiveness of the proposed method. The superiority is demonstrated via comparisons with typical saturation control methods.

Keywords: Gain-scheduled control; Generalized Popov transformation; Input saturation; Meta-heuristics optimization; Phase-shaping; Positive-real method.