Optimization of fractional PID controller by maximization of the criterion that combines the integral gain and closed-loop system bandwidth

This paper describes one novel design procedure for acquiring an optimal fractional PID (FPID) controller that rejects load disturbance under constraints on robustness and performance. The parameters of FPID controller have been tuned by using particle swarm optimization (PSO). FPID, apart from conventional gains k_p, k_i and k_d, has two more parameters α and β to be optimized, being the non-integer orders of integral and derivative part respectively. In this paper the order of the integral part is fixed to be 1 as in this way the steady state error elimination is preserved. Also, this enables comparison of the FPID and classical PID as the performance criteria directly dependable on k_i are the same in sense of both regulators. Noise cancellation filter of the same order as fractional differentiator is included within the structure of the FPID in order to cancel the noise amplification on high frequencies. Results are given through many numerical simulations.