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Abstract: This paper deals with the design, implementation and analysis of an integer order (IO) and fractional order (FO) based Proportional Integral Derivative (PID) controller, for speed regulation in a chopper fed Direct Current (DC) motor drive. The interdependent parameters of PID and FOPID controllers are designed in both time and frequency domain. In both domains, designs of controllers are formulated as a single objective optimization problem based on time indices integrals and frequency domain rules. Time domain based design of controllers focus mainly on minimization of indices like rise time, settling time etc. On the other hand frequency domain based design of controllers focuses on achieving iso-damping characteristics, which tries to meet user specified gain crossover frequency or phase margin while also maintaining constant overshoot for wide range of motor gain apart from maintaining optimum time indices. A newly evolved artificial bee colony (ABC) algorithm enhanced with opposition search has been used to perform the optimization task. This type of multiple designs enables users to choose the controller based on their requirement. A comparative study has been made to highlight the advantage of using fractional order controller over conventional integer order PID control scheme for speed regulation. To illustrate the efficacy of the opposition based ABC, we also compared the performance with the conventional ABC, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) methods. Computer simulations and extensive analysis over results obtained shows the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: 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 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 proportional–integral–derivative (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. [Copyright &y& Elsevier]