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

Abstract

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 Control of Power Electronic Converters in Industrial Drives and Renewable Energy Systems: A Review

“…Soriano-Sánchez et al used another method of approximation to design a FOPID controller for a buck converter based on El-Khazali's frequency-based approach [67]. This method uses biquadratic operators to approximate s α ≈T ( s w c ) [68], such that it behaves like a fractional differentiator around a center frequency,w c .…”

Swarm-Inspired Algorithms to Optimize a Nonlinear Gaussian Adaptive PID Controller

“…Throughout history, several methods for control have been introduced [45,46]. However, none of them have had greater prominence than the traditional Proportional, Integral and Derivative (PID) controller, which was created in the 1940s and is now used by most industries due to its efficiency and robustness and well-known design methodologies [47].…”

“…The DC-DC Buck converter is a typical power electronic converter topology employed in power supplies for most electronic equipment, like computers, TVs, mobile phones, and many others [45,49]. The Buck converter is characterized as a controllable step-down converter (Figure 2) that can achieve a regulated output voltage for a wide range of higher input voltages.…”

Experimental Validation of Voltage Regulation in Buck Converters through Fractional-Order PID Approximation

“…DC-DC Buck converter is one of the most studied from elementary converters due to its wide range of applications, which include control velocity of DC motors and regulated source of power (Soriano-Sánchez et al, 2020) or photovoltaic generation system (Sitbon et al, 2020), to mention a few. As a result of the attracted interest, a significant body of knowledge on control techniques to regulate voltage in Buck converters has been stablished.…”