Design of fractional order PIλDμ 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 for the design of Fractional-Order Proportional-Integral-Derivative (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 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 CFE (continued fraction expansion) scheme was used in this work. Simulation examples as well as comparisons of DE with two other state-of-the-art optimization techniques (Particle Swarm Optimization and Bacterial Foraging Optimization Algorithm) over the same problems demonstrate the superiority of the proposed approach especially for actuating fractional order plants.

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