State Augmented Feedback Controller Design Approach for T-S Fuzzy System with Complex Actuator Saturations

The control problem of T-S fuzzy system with actuator amplitude, rate and acceleration saturations is addressed in this paper, where state augmented feedback controller with LMIs (Liner Matrix Inequalities) constraint conditions are proposed. Dynamic decoupling method is applied to fuzzify the input magnitude saturation nonlinearity into several sub-linear systems with fuzzy rules, thus a new T-S fuzzy system with input rate and acceleration saturations can be obtained. Then PDC (parallel distributed compensation) and NPDC (non-PDC) controller are both designed for the new T-S fuzzy system. The first and second order derivatives of input variable are given to obtain an augmented fuzzy system. As the augmented system output variable, the input rate is represented by first order derivative of the input term, the rate saturation constraint is described through norm bounded method. Moreover, the polytopic approach is used to replace the second order derivative of the input term, and a state augmented feedback NPDC controller is designed, the domain of attraction optimization process is also given. Finally, two practical examples are presented to show the effectiveness of proposed method.