Parameter Optimization of Fractional Order PI λ D μ Controller Using Response Surface Methodology

Abstract

This chapter presents optimization of fractional order PI λ D μ control parameters by using response surface methodology. The optimization process is observed on a fractional order diffusion system subject to input hysteresis which is defined with Riemann–Liouville fractional derivative. The system is transferred to a fractional order state space model by using eigenfunction expansion method and then Grünwald–Letnikov approximation is applied to solve the system numerically. The necessary data for response surface analysis are read from the obtained numerical solution. Finally, second-order polynomial response surface mathematical model for the experimental design is presented and the optimum control parameters are predicted from this response surface model. The proposed optimization method is compared with the technique of minimization of integral square error by means of settling time and the results are discussed.