Differential Evolution for Tuning Fractional Order Controllers Approximated by Particle Swarm Optimization

Fractional-Order Controllers (FOC) extend PID controllers by using non-integer order integral and derivative actions. They have many advantages even if the tuning methods are still at their infancy. Hence we apply Differential Evolution (DE) optimization to tune parameters of FOC in a unitary feedback linear control system of a first order plana with a lag plus an integrator. The FOC combines two differintegrators. Closed-loop specifications are peak value and settling time of the step response. To determine the controller parameters, DE minimizes the sum of the squared real and imaginary parts of the characteristic equation, expressed in terms of the desired pair of closed-loop dominant poles and of the unknown parameters. Then, the Particle Swarm Optimization with constriction factor approximates the irrational operators of the controller with rational transfer functions that are of low order, stable, minimum-phase, with zeros interlacing poles. Frequency and step responses show the efficiency of the proposed method.