Nonlinear adaptive fractional order fuzzy PID control of a 2-link planar rigid manipulator with payload

The main objective of this paper is to demonstrate that fractional order operators (differentiator/integrator) can increased the robustness of an intelligent controller. In this paper, a nonlinear adaptive fractional order fuzzy proportional integral derivative (NLA - FOFPID) controller is presented to control a nonlinear, coupled, multi-input and multi-output and uncertain system i.e. a 2-link planar rigid robotic manipulator with payload. The NLA - FOFPID controller is realized using non-integer order differentiator and integrator operators in nonlinear adaptive fuzzy proportional integral derivative (NLA - FPID) controller. The control objective is to track a reference trajectory in virtual industrial environment and under model uncertainties by minimizing the combination of integral of time weighted absolute error and integral of time weighted absolute change in controller output. The industrial environment was simulated by incorporating measurement noise, sinusoidal disturbance and model uncertainties. The gains of NLA - FPID and NLA - FOFPID controllers are optimized using recently reported Backtracking Search Algorithm. Intensive simulations were performed to assess the performances of NLA - FPID and NLA - FOFPID controllers for servo and regulatory mode. It has been observed that NLA - FOFPID controller outperforms NLA - FPID controller by offering much better performance. Particularly in uncertain environment it offered very robust behavior as compared to NLA - FPID controller. The sufficient stability conditions are also established for bounded-input and bounded-output stability of overall closed loop system by using small gain theorem.