The Design of a Fractional-order Predictive Functional Controller for the Magnetic Levitation System

Magnetic levitation systems (Maglev) are widely used in various industries. The open loop Maglev system is highly nonlinear and unstable. Therefore, designing a simple, but effective controller for such a system is a challenging issue. In this paper, a fractional order predictive functional controller (FPFC) is proposed for the control of the magnetic levitation system based on its linearized unstable model. At first, the unstable plant is decomposed into two stable models. Then, using these two stable models and employing fractional order cost function, the PFC controller is designed. Because of more degrees of freedom and its flexibility of fractional order calculus, the proposed fractional PFC would improve the performance of closed loop systems, noticeably. Robust stability of closed-loop systems has also been studied considering the uncertainties and model mismatches via the small gain theorem. Simulation results show good performance of the proposed controller in nominal and perturbed conditions. Based on provided simulations, via the proposed controller, overshoot has been omitted and performance indices have been improved more than 50% with respect to the first and second orderof freedom integer/fractional order PID controllers, designed for this system, in the literature.