Combining differential evolution and particle swarm optimization to tune and realize fractional-order controllers

In recent years, several research works proposed fractional-order controllers as means to improve the performances of common proportional, integral and derivative controllers. However, the design and tuning methods for these new controllers are still at their infancy. As a contribute for filling this gap, this article proposes a two-step design approach. First, differential evolution determines the fractional integral and derivative actions satisfying the required time-domain performance specifications. Second, particle swarm optimization determines rational approximations of the irrational fractional operators as low-order, stable, minimum-phase transfer functions with poles interlacing zeros. Extensive time- and frequency-domain simulations validate the efficiency of the proposed approach.