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Particle swarm optimization (PSO) is extensively used for real parameteroptimization in diverse fields of study. This paper describes an application ofPSO to the problem of designing a fractional-orderproportional-integral-derivative (FOPID) controller whose parameters compriseproportionality constant, integral constant, derivative constant, integralorder (lambda) and derivative order (delta). The presence of five optimizableparameters makes the task of designing a FOPID controller more challenging thanconventional PID controller design. Our design method focuses on minimizing theIntegral Time Absolute Error (ITAE) criterion. The digital realization of thedeigned system utilizes the Tustin operator-based continued fraction expansionscheme. We carry out a simulation that illustrates the effectiveness of theproposed approach especially for realizing fractional-order plants. This paperalso attempts to study the behavior of fractional PID controller vis-a-vis thatof its integer order counterpart and demonstrates the superiority of the formerto the latter.

Tuning PID and FOPID Controllers using the Integral Time Absolute Error Criterion