Efficient control of a 3-link planar rigid manipulator using self-regulated fractional-order fuzzy PID controller

Abstract

A self-regulated fractional-order fuzzy proportional–integral–derivative (SRFOFPID) controller is proposed to control a highly non-linear, complex and coupled 3-link planar rigid robotic manipulator in a virtual industrial environment. Industrial environment was simulated by introducing different kind of disturbances in the system and sensor noise. Proposed SRFOFPID controller is a direct non-linear adaptive controller having self-regulating feature and has been realized using fractional-order operators i.e. integrator and differentiator in self-regulated integer-order fuzzy PID (SRIOFPID) controller. Gains of SRFOFPID and SRIOFPID controllers are optimized using Backtracking Search Algorithm by minimizing an amalgamation of integral absolute error signal and integral absolute change in control signal as cost function. Performance of SRFOFPID and SRIOFPID controllers are assessed and compared with reference path under virtually simulated industrial environment. Presented intensive simulation studies revealed that both the controllers offered decent reference trajectory tracking performance under nominal operating conditions while SRFOFPID controller offered exceptionally robust performance under industrial scenario and uncertainties. Finally, the stability analysis of overall closed loop system is performed using small gain theorem and necessary and sufficient bounded-input and bounded-output stability conditions are established.