Robust H∞ control of Magnetic Levitation system based on parallel distributed compensator

Abstract

This paper concerns with designing of a robust H∞ controller for Magnetic Levitation system exposed to external disturbances. First, the Maglev is modeled in a discrete form of Takagi–Sugeno fuzzy (TSF) system. Then the nonlinear fuzzy controller is synthesized based on such a technique called Parallel Distributed Compensation (PDC) schemes and sufficient conditions are developed to control and guarantee the robust stabilization of a complex nonlinear system. So the proposed algorithm is used to enhance the performance and to ensure the stability of the system. Furthermore, the design conditions and criteria for quadratic stability of the TSF system are formulated as a Linear Matrix Inequality (LMI) to robustly stabilize the position of the iron ball in a Maglev system in the existence of disturbances. The proposed technique will guarantee H∞ performance to be less than one and attenuate the effect of exogenous disturbances. Moreover, the comparison results for the control of Maglev will show the capability of the proposed approach. Keywords: Takagi–Sugeno fuzzy (TSF) system, Magnetic Levitation (Maglev) system, Parallel Distributed Compensator (PDC), Linear Matrix Inequality (LMI), Robust H∞ controller