Design method for the magnetic bearing control system with multi-objective requirements via linear matrix inequality approach

Linear local Takagi-Sugeno (TS)-fuzzy models for magnetic bearing subsystem and nonlinear model for the overall system were given. Based on the TS-fuzzy model, a linear matrix inequality (LMI)-based design method for the fuzzy control of nonlinear systems with multi-objective requirements was presented. The method combines stable conditions of close-loop TS-fuzzy system, desired control performance and constraints on the control input into a framework of LMIs, and the parameters of controller can be obtained by convex programming techniques for LMIs. The fuzzy state feedback nonlinear controller for the overall system was obtained via parallel-distributed compensation (PDC) approaches, which can satisfy multi-objective requirements simultaneously, and the method avoided the repeat of design process. Through application in the magnetic bearing control system, the effect of this method is proved.