Tuning of fractional order PIλDμ controller with response surface methodology

This paper presents response surface methodology for tuning of fractional order PI λ D μ controller of a fractional order diffusion system subject to input hysteresis which is defined with Riemann-Liouville fractional derivative. Eigenfunction expansion method and the Grünwald-Letnikov numerical technique are used to solve the system. The necessary data for response surface analysis are read from the obtained numerical solution. Then second-order polynomial response surface mathematical model for the experimental design is presented and the optimum controller parameters are predicted from this model. The proposed tuning method is compared with the technique of minimization of integral square error by means of settling time and the results are discussed.