Process step response based fractional PID controller parameters tuning for desired closed loop response

In this paper, a tuning method of the fractional PIλDμ controllers for classical feedback control systems is proposed. The PIλDμ controller design strategy is drawn up such that the closed loop system is equivalent to a desired fractional order model whose transfer function is Bode's ideal function Gd(s)=11+s/ωum$G_d {\rm (}s{\rm )} = \frac{{\rm 1}}{{{\rm 1} + \left( {s/\omega _u } \right)^m }}$, a widely used function in the fractional order control domain because of its iso-damping property which is an important robustness feature. In this tuning technique, the values of the five parameters of the fractional PIλDμ controller are derived analytically using only the step response of a stable process without requirement of its model. The derived formulations of the tuning technique are presented. Illustrative examples are given to test the effectiveness and the usefulness of the proposed PIλDμ controller tuning approach.