Fuzzy robust control of MIMO nonlinear uncertain systems

This paper describes robust H₂/H_∞ multi-objective state feedback controller for nonlinear uncertain systems. To apply the H₂/H_∞ multi-objective state feedback method, the nonlinear dynamics is represented by a T-S fuzzy model. First, uncertain parameters and Quantification of uncertainty on physical parameters is defined by affine parameter-dependent systems method. Next, the Takagi and Sugeno´s fuzzy linear model is utilized to approximate uncertain nonlinear systems. Then, some states (error of tracking) are augmented to the system in order to improve tracking control. Finally, based on fuzzy linear model with augmented state, a H₂/H_∞ multi-objective state feedback controller is developed to achieve the robustness design of nonlinear uncertain systems. LMI (Linear Matrix Inequality) method and PDC (Parallel Distributed Compensation) are used to design the controller for the whole system. The results show that the proposed method can effectively meet the performance requirements like robustness, disturbance rejection and tracking for the 3-phase permanent magnet synchronous motor (PMSM).