Optimal tuning of fractional PIDCα controller in the frequency domain

A new frequency-domain algorithm for optimization of PID regulators having a fractional differential compensator connected in series (PIDC^α) has been developed. The adjustable parameters of the regulator are: proportional gain k, integral gain k_i, 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 M_s and sensitivity to measurement noise M_n. By solving the optimization procedure one obtains parameters of PIDC^α regulator which results in minimum IAE (Integrated Absolute Error). The analysis of optimal PIDC^α is performed through a series of simulations for several dynamic processes representative for industrial applications.