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Design of Fractional-Order PID Controller for Fractional-Order System via Flower Pollination Algorithm

In system modeling, the fractional-order (FO) model can perform the system dynamic behavior with more accurate than the integer-order (IO) model. This paper proposes the optimal design of the fractional-order PID controller (or FOPID) for the fractional-order dynamic system by using the flower pollination algorithm (FPA), one of the most powerful metaheuristic optimizers. The FO-model of the brushless DC (BLDC) motor speed control system is conducted as a case study. Based on the modern optimization, the sum of squared error (SSE) between the referent speed and the actual speed of the BLDC motor speed controlled system is set as the objective function to be minimized by the FPA. Results obtained by the FOPID controller will be compared with those obtained by the IOPID controller. From simulation results, it was found that the FOPID controller optimized by the FPA for the fractional-order dynamic system (BLDC motor) can provide very satisfactory responses with faster and smoother than the IOPID controller in both tracking and regulating responses.