Design of robust particle swarm optimization - tuned fuzzy controller for a Single Axis Small Magnetic Levitation System

A control system is robust when it has low sensitivity, it is stable over the range of parameter variations and the performance continues to meet the specification in the presence of a set of changes in the system parameters and disturbances. In this work the design of the robust linear and nonlinear controllers for Single Axis Magnetic Levitation System are presented. These controllers must overcome the problems of the high steady state error and robustness in the magnetic levitation system. The design of H∞ robust controller is presented first and the system dynamics are linearized to be suitable for applying the H∞ robust control technique. The magnetic force is regulated using this controller to achieve robust stability and performance, disturbance/noise rejection and asymptotic tracking with zero steady state error. The plant with structured uncertainty is expressed in terms of unstructured multiplicative uncertainty to cover the overall change in system parameters. The unstructured multiplicative uncertainty is determined using curve fitting method. The designed H∞ controller has assured robust stability and robust performance of the single axis magnetic levitation system with parametric uncertainty. The parameters of the performance and control weighting functions that are obtained using trial and error lead to obtain a robust controller that achieves force control of magnetic levitation system. The design of PD like fuzzy robust controller is presented secondly in this work. The Particle Swarm Optimization method (PSO) is used to find the optimal values of the Scalar gains and the membership functions subject to the robust control and minimum error constraints. The designed PD like fuzzy controller has assured robust stability and robust performance of the nonlinear model of single axis magnetic levitation system. This controller minimizes the rules from 64 rules to 16 rules and achieved zero steady state error without using the integral. Finally, a comparison between the performances of the H∞ controller and the optimal fuzzy logic controller has been made. It shows that the nonlinear optimal fuzzy logic controller achieve better performance than the linear H∞ controller.

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