*Article* **Fractional-Order Approximation of PID Controller for Buck–Boost Converters**

**Allan G. S. Sánchez 1,\* , Josué Soto-Vega <sup>2</sup> , Esteban Tlelo-Cuautle <sup>3</sup> and Martín Antonio Rodríguez-Licea <sup>1</sup>**


**\*** Correspondence: allan.soriano@itcelaya.edu.mx

**Abstract:** Viability of a fractional-order proportional–integral–derivative (PID) approximation to regulate voltage in buck–boost converters is investigated. The converter applications range not only to high-power ones but also in micro/nano-scale systems from biomedicine for energy management/harvesting. Using a classic closed-loop control diagram the controller effectiveness is determined. Fractional calculus is considered due to its ability at modeling different types of systems accurately. The non-integer approach is integrated into the control strategy through a Laplacian operator biquadratic approximation to generate a flat phase curve in the system closed-loop frequency response. The controller synthesis considers both robustness and closed-loop performance to ensure a fast and stable regulation characteristic. A simple tuning method provides the appropriate gains to meet design requirements. The superiority of proposed approach, determined by comparing the obtained time constants with those from typical PID controllers, confirms it as alternative to controller non-minimum phases systems. Experimental realization of the resulting controller, implemented through resistor–capacitor (RC) circuits and operational amplifiers (OPAMPs) in adder configuration, confirms its effectiveness and viability.

**Keywords:** fractional-order PID controller; DC–DC converters; Non-minimum phase systems; experimental validation
