A Robust Controller and its Optimization for a Nonlinear Dynamical System

This paper formulates a robust controller for a nonlinear dynamical system which is subjected to external disturbances and nonlinear friction with adaptive fuzzy logic compensator. Adaptive fuzzy system is used to estimate unknown disturbance, hysteresis phase plane, zero slip displacement and friction torque. After formulating the model, the controller is derived and closed loop stability is proved using Lyapunov function. The sliding mode control tracks the reference position command while fuzzy logic system compensates for friction and unknown disturbance torque. Parameters of controller are optimized using mixed integer optimization as first step and multi island genetic algorithm as second step. Numerical simulations are presented to prove effectiveness of the derived controller.