Optimal tuning of fractional PIDCα controller in the frequency domain

Abstract

A new frequency-domain algorithm for optimization of PID regulators having a fractional differential compensator connected in series (PIDCα) has been developed. The adjustable parameters of the regulator are: proportional gain k, integral gain ki, relative attenuation factor of PID zeros ζ, zero of the fractional differential compensator-1/τ and fractional power a of the differential compensator. The optimization procedure is based on maximization of integral or proportional gain, given values of the maximum sensitivity Ms and sensitivity to measurement noise Mn. By solving the optimization procedure one obtains parameters of PIDCα regulator which results in minimum IAE (Integrated Absolute Error). The analysis of optimal PIDCα is performed through a series of simulations for several dynamic processes representative for industrial applications.