Exact linearization and fuzzy logic applied to the control of a Magnetic Levitation System

Abstract

In recent years the area of nonlinear control systems has been the subject of many studies. Computational developments have enabled more complex applications to provide solutions to nonlinear problems. The purpose of this paper is to use a combination of two techniques to control a nonlinear system: the Magnetic Levitation System. First, the exact linearization technique with state feedback is applied to obtain a linear system. Second, the linearization is made via direct cancellation of nonlinear functions, which represent the phenomenological model of the system. Finally, to deal with the presence of uncertainty in the system model, an adaptive controller is used. The controller is based on fuzzy logic to estimate the functions that contain the nonlinearities of the system. The fuzzy system is a zero-order Takagi-Sugeno-Kang structure and the adaptive controller is implemented in a simulated environment (Matlab Simulink ©). The methodology guarantees the convergence of the estimates to their optimal values, and in turn the overall stability of the system. The results show the controller output signal tracks a reference input signal. For future work this adaptive controller should be implemented in a real physical system.