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In this paper an Optimal Fractional Order proportional-integral-derivative (FOPID) controller is designed to levitate the iron ball in the air space using an electromagnetic coil. The infra-red sensor fixed on the vertical sides of the magnetic levitation system (MLS) is being helpful to sense the position of the ball. The controller enables the electromagnetic coil to maintain a specified force so that the ball is levitated. To achieve the desired electro-magnetic force the performance index i.e. the integral square error (ISE) of the system is minimized. The parameters of FOPID controller are optimized using Nelder's-Mead (NM) optimization algorithm. The integer order approximation of the FOPID controller is done by using Oustaloup's method. The performance of the proposed controller is validated by comparing it with the conventional PID controller.
Verma et al. (Tue,) studied this question.