Multi-Objective Robust Design and Performance Analysis of Two-DOF-FOPID Controller for Magnetic Levitation System

The magnetic levitation system (MLS) is a nonlinear system and the existence of time-changing parameters and external disturbances adversely affects its performance. This paper presents a multi-objective robust design and parameters tuning approach of two-degree of freedom fractional order proportional-integral-derivative (2-DOF-FOPID) controller applied to MLS. In this work, the minimization of performance index integrated absolute error (IAE) for both set-point tracking and external disturbance rejection are considered as the objective functions. To assure the robust design, maximum sensitivity of the system is considered as a constraint. The tuning of all controller parameters is achieved through nondominated sorting genetic algorithm (NSGA-II). A set of Pareto optimal solutions is evolved and Nash solution criteria is used to obtain final most reasonable solution. The comparative performance analysis of proposed 2-DOF-FOPID controller against classical PID, FOPID, and 2-DOF-PID controllers is presented. The effectiveness of controller for variable set-point tracking and rejection of external disturbances is exhibited through proper simulation results and found that the proposed 2-DOF-FOPID controller accomplishes predominant results compared to its conventional counterparts.