Control of nonlinear systems by alternative design of fuzzy logic controllers subject to Lyapunov stability theory

• Published in: Advances in mechanical engineering Vol. 10; no. 6
• Main Authors: Tsai, Shun-Hung, Chen, Chin-Sheng, Li, Shih-Yu
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.06.2018; Sage Publications Ltd; SAGE Publishing
• Subjects: Authorship; Construction standards; Control stability; Control systems design; Controllers; Design; Design engineering; Design standards; Error detection; Fuzzy control; Fuzzy logic; Fuzzy sets; Fuzzy systems; Liapunov functions; Nonlinear control; Nonlinear systems; Quadratic forms; Lyapunov stability theory; fuzzy logic theory; Intelligent control
• ISSN: 1687-8132; 1687-8140
• DOI: 10.1177/1687814018778422

In this article, a set of fuzzy logic controller is alternatively designed for control of nonlinear systems in Lyapunov sense. Through referencing the statuses of error states and error dynamics, the corresponding fuzzy if–then rules can be constructed based on Lyapunov Stability Theory following the proposed standard design procedure, where simple quadratic form is decided for candidate Lyapunov function. Different from previous research achievements, the resulting controllers are simple constant forces, and for control of two nonlinear systems with different structures, the design procedure is still the same without any further information. Furthermore, appropriate and adjustable control forces with less maximum magnitude are stably supplied through exciting the weighting through the constructed fuzzy if–then rules, which leads the proposed fuzzy logic controllers compensate control system more flexible and in real time. Two examples, control of two identical and different nonlinear systems, are illustrated for simulation examples. In comparison to the previous work, the simulation results reveal the effectiveness, flexibility, as well as convenient design of the proposed method.