A Class Of T-s Fuzzy Control System Stability Analysis And Controller Design

Fuzzy control is a control strategy based on fuzzy set theory, fuzzy language variables and fuzzy logic inference, belongs to the field of the intelligent control, with the incomparable advantage of traditional control. Over the years, it’s an important research topic to determine the stability of a fuzzy control system and to improve its stability.Due to the inherent serious nonlinearity of fuzzy control system, it is very difficult for its stability analysis and controller design. So far, many conclusions and controller design methods can guarantee the stability of fuzzy control system, but there is not yet a complete theoretical system, many theoretical problems have to be further studied.The proposed T-S fuzzy model brings stability analysis of fuzzy control system to a new height, and far-reaching influence to the theory of fuzzy control and its development. The main knowledge of the fuzzy control system which expressed by T-S fuzzy model is expressed with identified fuzzy model, and Lyapunov method is one of the most commonly used stability theory which analyzes the stability and controller design for such system.Using a new Lyapunov function, the stability of T-S continuous fuzzy systems based on linear matrix inequality(LMI) is studied, and a new stability criterion of the open-loop T-S fuzzy control system is proposed in this paper, which is more relaxed. Also, with a fuzzy controller based on parallel distributed compensation method, a new criterion for stability of T-S closed-loop fuzzy control system is presented. A specific example is used to demonstrate the effectiveness of the algorithm. This paper includes the following five sections:In the first chapter, the background, basic principles and characteristics of fuzzy control theory are mainly introduced, also a brief overview to its research development. The development trends and the problems to be solved for fuzzy control system are analyzed.The second chapter mainly introduces the basic concepts of fuzzy control theory and the composition of fuzzy control system. Mamdani and T-S fuzzy control system are introduced.The third chapter first reviews the preliminary knowledge of linear matrix inequality(LMI) and discusses its application in control theory. The establishment of T-S fuzzy model and the stability of continuous T-S fuzzy model are investigated. Using a new Lyapunov function, a new stability criterion for open-loop fuzzy control system based on continuous T-S model is proposed. Finally, a specific example combined with the LMI theory demonstrates the validity of the algorithm.By parallel distributed compensation (PDC), chapter four gives the controller design method for closed-loop continuous T-S fuzzy system. Using a new Lyapunov function, the stability criterion for closed-loop T-S continuous fuzzy control system is studied. A specific example is used to demonstrate the validity of the algorithm.The fifth chapter summarizes the full text, and the prospect for further research is given.