A robust fractional order fuzzy P + fuzzy I + fuzzy D controller for nonlinear and uncertain system

Abstract

In this paper, a robust fractional order fuzzy P + fuzzy I + fuzzy D (FOFP + FOFI + FOFD) controller is presented for a nonlinear and uncertain 2-link planar rigid manipulator. It is a nonlinear fuzzy controller with variable gains that makes it selfadjustable or adaptive in nature. The fractional order operators further make it more robust by providing additional degrees of freedom to the design engineer. The integer order counterpart, fuzzy P + fuzzy I + fuzzy D (FP + FI + FD) controller, for a comparative study, was realized by taking the integer value for the fractional order operators in FOFP + FOFI + FOFD controller. The performances of both the fuzzy controllers are evaluated for reference trajectory tracking and disturbance rejection with and without model uncertainty and measurement noise. Genetic algorithm was used to optimize the parameters of controller under study for minimum integral of absolute error. Simulation results demonstrated that FOFP + FOFI + FOFD controller show much better performance as compared to its counterpart FP + FI + FD controller in servo as well as the regulatory problem and in model uncertainty and noisy environment FOFP + FOFI + FOFD controller demonstrated more robust behavior as compared to the FP + FI + FD controller. For the developed controller bounded-input and bounded-output stability conditions are also developed using Small Gain Theorem.