The major goal of this paper is to tune PID and PIλDδ controllers using Particle Swarm Optimization (PSO) algorithm via El-Khazali’s approach. This is the first time that such a method is employed for meeting this problem. El-Khazali’s approach is, usually, used to approximate fractional-order Laplacian operators of order α; s±α, 0 < α ≤ 1, by finite-order rational transfer functions. The significance of this approach lies in developing an algorithm that depends only on α, which enables one to synthesize both fractional-order inductors and capacitors. To illustrate the proposed design method, an objective function is presented as well as the results of using the PIλDδ controller are compared with the results of using the conventional PID controller to minimize several error functions; ITAE, IAE, ISE and ITSE. These results of such comparisons that are related to step response specifications, allow us to see the effectiveness of the best controller.
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