Real-Time Implementation of Fractional-Order PID Controller for Magnetic Levitation Plant With Time Delay

Abstract

The design of a Fractional Order PID controller (FOPID), to stabilize a second-order unstable magnetic levitation plant (MLP) with time delay, is proposed in this paper. The proposed two stage approach involves estimating the lower and upper bounds of the controller gains using an extension of the Hermite-Biehler theorem. Further, the optimal gains within the search space, determined in the first stage, are obtained by formulating the controller design task as a constrained optimization problem seeking to minimize the root mean square error ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</i> ) of reference tracking, in terms of the ball position measured by the IR Sensor. The optimization problem is solved using a recently proposed agent based evolutionary algorithm, namely, Multi-Agent based Symbiotic Organisms Search (MASOS). It has been confirmed that the theorem is effective in determining the stable ranges of the controller gains, while the MASOS algorithm is able to provide the optimal gain values. The obtained results have been verified by simulation in MATLAB® Simulink®. The findings from the simulation results have been further validated by real-time experiments on the hardware setup of MLP. The comparative analysis with 1-Degree of Freedom (DOF) FOPID, fractional-order Integral-Proportional-Derivative (FOIPD), Linear Quadratic Regulator (LQR), Active Disturbance Rejection Controller (ADRC), Radial Basis Function Sliding Mode Controller (RBFSMC) and Stable Inversion approach using both offline numerical simulation and real-time experiment corroborates the superiority of the FO-IPD controller.