Design of robust fractional order fuzzy sliding mode PID controller for two link robotic manipulator system

Abstract

A two link planar rigid robotic manipulator is a highly nonlinear, coupled and multi-input multi-output system. For its effective control, an intelligent adaptive fractional order fuzzy sliding mode proportional integral and derivative controller (FOFSMCPID) has been presented in this work. Sliding mode controller (SMC) is designed by using exponential law and closed loop stability analysis is demonstrated by using Lyapunov theorem. The chattering in the SMC controller has been effectively reduced with the help of boundary layer along with the fuzzy logic. For tuning of the controller, a weighted sum of integral of absolute error and chatter has been considered as the objective function to be minimized using cuckoo search optimization algorithm. To demonstrate the efficacy of FOFSMCPID controller, the results have been compared with integer order fuzzy sliding mode proportional, integral and derivative controller (IOFSMCPID), integer order fuzzy sliding mode proportional and derivative controller (IOFSMCPD) and fractional order fuzzy sliding mode proportional and derivative (FOFSMCPD) controller for trajectory tracking, disturbance rejection, noise suppression and model uncertainties. The detailed presented investigations have demonstrated that FOFSMCPID controller exhibits much superior performance over IOFSMCPID, IOFSMCPD and FOFSMCPD controllers.