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In this paper, the approximation of a fractional-order PIDcontroller is proposed to control a DC–DC converter. The synthesis and tuning process of the non-integer PID controller is described step by step. A biquadratic approximation is used to produce a flat phase response in a band-limited frequency spectrum. The proposed method takes into consideration both robustness and desired closed-loop characteristics, keeping the tuning process simple. The transfer function of the fractional-order PID controller and its time domain representation are described and analyzed. The step response of the fractional-order PID approximation shows a faster and stable regulation capacity. The comparison between typical PID controllers and the non-integer PID controller is provided to quantify the regulation speed introduced by the fractional-order PID approximation. Numerical simulations are provided to corroborate the effectiveness of the non-integer PID controller.

Fractional-Order Approximation and Synthesis of a PID Controller for a Buck Converter