Real time implementation of fractional order PID controllers for a magnetic levitation plant

Abstract

Fractional calculus has been a topic of great interest for the last few decades. The applications of fractional calculus can be found in the area of viscoelastic and chaotic systems, whose dynamics is expressed in the form of fractional differential equations. The ongoing research work is based on the design of 1-Degree of Freedom (1-DOF) and 2-Degrees of Freedom (2-DOF) Fractional Order PID (FOPID) controllers for a Magnetic levitation (Maglev) plant and the performance has been compared with that of 1-DOF and 2-DOF Integer Order PID (IOPID) controllers in both simulation and real time. The Degree of Freedom (DOF) represents the number of feed-forward control loops in a closed loop system. A 2-DOF controller configuration comprises of a serial compensator and a feed-forward compensator in a closed loop structure. An FOPID controller has a structure similar to that of a conventional IOPID controller, except that its derivative and integral orders are fractional numbers. The design of such a controller requires the determination of five parameters: Kp, Ki, Kd, α and β, where α and β are the derivative and integral orders of the FOPID controller. The controller design problem has been framed as an optimization problem, in which the cost function is formulated from the characteristic equation of the closed loop system at dominant poles that are identified from the given performance specifications. The closed loop response shows that the proposed2-DOF FOPID controller exhibits superior response and robustness with respect to its integer order counterpart.