Robust multi-objective H 2 /H ∞ tracking control based on the Takagi–Sugeno fuzzy model for a class of nonlinear uncertain drive systems

Abstract

In this paper a robust H₂/H_∞ multi-objective state-feedback controller and tracking design are presented for a class of multiple input/multiple output nonlinear uncertain systems. First, some states (error of tracking) are augmented to the system in order to improve tracking control. Next, uncertain parameters and the quantification of uncertainty on physical parameters are defined by the affine parameter-dependent systems method. Then, to apply the H₂/H_∞ controller, the uncertain nonlinear system is approximated by the Takagi–Sugeno fuzzy model. After that, based on each local linear subsystem with augmented state, an H₂/H_∞ multi-objective state-feedback controller is designed by using a linear matrix inequalities approach. Finally, parallel distributed compensation is used to design the controller for the overall system and the total linear system is obtained by use of the weighted sum of the local linear subsystems. Several results show that the proposed method can effectively meet performance requirements such as robustness, good load disturbance rejection, good tracking and fast transient responses for a three-phase interior permanent magnet synchronous motor system.