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

• Published in: ISA transactions Vol. 137; pp. 303 - 313
• Main Authors: Fang, Jiayi, Liu, Kang-Zhi
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.06.2023
• Subjects: Gain-scheduled control; Generalized Popov transformation; Input saturation; Meta-heuristics optimization; Phase-shaping; Positive-real method; Input saturation; Meta-heuristics optimization; Gain-scheduled control; Generalized Popov transformation; Phase-shaping; Positive-real method
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2023.01.017

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. •Propose gain-scheduling with phase-shaping method for input-saturated linear systems.•Fully utilize the passivity in phase-shaping to maximize the system’s phase margin.•Actively use the magnitude bound in gain-scheduling to reduce conservative design.•Extend the matrix phase-shaping by placing the nominal system’s frequency locus.