Global High-Order Sliding Mode Controller Design Subject to Mismatched Terms: Application to Buck Converter

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 66; no. 12; pp. 4840 - 4849
• Main Authors: Shi, Shang, Xu, Shengyuan, Gu, Jason, Min, Huifang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: buck converter; Buck converters; Control systems; Control systems design; Controllers; high-order sliding mode control; Mathematical analysis; mismatched term; Nonlinear system; Nonlinear systems; Polynomials; Sliding mode control; Stability analysis; Time-varying systems; Uncertainty; Upper bound; Upper bounds
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2019.2933164

This paper studies the high-order sliding mode (HOSM) control for a general class of uncertain nonlinear systems. Firstly, the standard sliding mode system is extended to a new sliding mode system subject to mismatched terms. The use of the new sliding mode system can reduce the system uncertainties in the control channel and relax the well defined relative degree assumption. Secondly, the conventional constant upper bounds assumption is relaxed to time-varying positive functions, which enables us to obtain a global result. For the new sliding mode system under the new global assumption, a novel HOSM controller, that has a simple relay polynomial form, is then proposed. By introducing a new continuous component in the controller, the discontinuous component of the controller only needs to be selected to suppress the uncertainties and thus a controller with minimal discontinuous component magnitude can be implemented. Finally, strict Lyapunov analysis is provided to show the globally finite-time stability of the closed-loop sliding mode system and an application to Buck converter is presented.