Design of fractional-order PI?D? controllers with an improved differential evolution
Differential evolution (DE) has recently emerged as a simple yet very powerful technique for real parameter optimization. This article describes an application of DE to the design of fractional-order proportionalintegralderivative (FOPID) controllers involving fractional-order integrator and fractional-order differentiator. FOPID controllers parameters are composed of the proportionality constant, integral constant, derivative constant, derivative order and integral order, and its design is more complex than that of conventional integer-order proportionalintegralderivative (PID) controller. Here the controller synthesis is based on user-specified peak overshoot and rise time and has been formulated as a single objective optimization problem. In order to digitally realize the fractional-order closed-loop transfer function of the designed plant, Tustin operator-based continuous fraction expansion (CFE) scheme was used in this work. Several simulation examples as well as comparisons of DE with two other state-of-the-art optimization techniques (Particle Swarm Optimization and binary Genetic Algorithm) over the same problems demonstrate the superiority of the proposed approach especially for actuating fractional-order plants. The proposed technique may serve as an efficient alternative for the design of next-generation fractional-order controllers.
differential evolution fractional-order controllers fractional calculus pid controllers evolutionary algorithms