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A Robust fractional order Fuzzy P ＋ Fuzzy I ＋ Fuzzy D Controller for Nonlinear and Uncertain System

International Journal of Automation and computing 2017年第4期14卷 474-488页

作者： Vineet Kumar K. P. S. Rana Jitendra Kumar Puneet Mishra Sreejith S Nair Division of Instrumentation and Control Engineering Netaji Subhas Institute of Technology (NSIT) University of Delhi New Delhi 110078 India

In this paper, a robust fractional order fuzzy P ＋ fuzzy I ＋ fuzzy D （FOFP ＋ FOFI ＋ FOFD） controller is presented for a nonlinear and uncertain 2-1ink planar rigid manipulator. It is a nonlinear fuzzy controller with variable gains that makes it self- adjustable 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.

关键词： Fuzzy P + fuzzy I + fuzzy D (FP + FI + FD) controller fractional order fuzzy P + fuzzy I + fuzzy D (FOFP + FOFI+ FOFD) controller fractional order operator robust control model uncertainty noise suppression.

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