A Nonlinear-System Approach to Analysis and Design of Power-Electronic Converters With Saturation and Bilinear Terms

• Published in: IEEE transactions on power electronics Vol. 26; no. 2; pp. 399 - 410
• Main Author: Hu, Tingshu
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Applied sciences; Bilinear system; Circuit properties; Convertors; DC-DC power converters; Design optimization; Electric currents; Electric, optical and optoelectronic circuits; Electrical engineering. Electrical power engineering; Electrical machines; Electronic circuits; Electronics; Exact sciences and technology; Feedback control systems; Linear matrix inequalities; linear-matrix inequality (LMI); Lyapunov method; Medical equipment; Nonlinear systems; Optimization algorithms; Piecewise linear techniques; Power electronics; Power electronics, power supplies; power-electronic converters; Regulation and control; Robust stability; saturation; Signal convertors; stability; State feedback; tracking; Bilinear system; Power converter; Lyapunov method; Control synthesis; Robust estimation; Stability region; Non linear phenomenon; tracking; Optimization; Quadratic approximation; Linear matrix inequality; Piecewise linear system; System analysis; stability; Non linear estimation; Robust stability; Up converter; power-electronic converters; Saturation; linear-matrix inequality (LMI); Power electronics; Non linear system; Algorithm performance; Non linear effect; Lyapunov function; Quadratic function; Piecewise linearization
• ISSN: 0885-8993; 1941-0107
• DOI: 10.1109/TPEL.2010.2054115

Power-electronic converters are intrinsically nonlinear. This paper proposes a Lyapunov approach to analysis and design of a class of nonlinear systems arising from power-electronic converters. The system has a bilinear term as the product of the state and the input-the duty cycle, which is subject to strict constraint (or saturation). The nonlinearities and the input saturation are considered in this paper by using piecewise-quadratic Lyapunov functions and by describing the system with a piecewise-linear differential inclusion. The problems considered include controller design for robust stability, and estimation of stability region and tracking domain. These analysis and design problems are converted into numerically efficient optimization algorithms involving linear-matrix inequalities (LMIs). A buck-boost dc-dc converter is used to demonstrate the proposed methods. The optimization results show that a simple state-feedback law can be constructed to achieve practically global stabilization and tracking, which is theoretically confirmed by the Lyapunov approach. An experimental buck-boost converter is constructed to verify the tracking of a square reference varying almost between the upper and the lower limit.