An Internal Model Control based design method for Single input Fuzzy PID controllers

In this paper, the analytic formulation of the single input Fuzzy PID (FPID) controller output is derived to present an Internal Model Control (IMC) based design method. In this context, we have firstly derived the input-output relationship of the fuzzy controller and investigated the effect of the membership function (MF) parameters on the output of the Single input FPID (SFPID). Based the presented observations, design guidelines are presented on how to tune MF parameters of the controller to obtain aggressive and smooth control actions. Moreover, we have derived the analytic formulation of the SFPID controller output. It has been shown that the output formulation is analogous to the Conventional FPID (CFPID) and the PID controller ones. Moreover, we have also shown that the SFPID controller can be seen as combination of a PID controller and nonlinear compensation term. Thus, we have used this analytical information to employ the well-known IMC based design method to tune the design parameters of the SFPID structure. Comparative simulation results have been conducted on a benchmark nonlinear system to show that the SFPID improved the transient state performance while providing an identical disturbance rejection performance of the CFPID structure.