Simple formula for designing the PID controller of a DC-DC buck converter

Abstract

This paper proposes a simple way to design a proportional integral derivative proportional integral derivative (PID) controller for a DC-DC buck converter. This work concerns getting the formula to calculate Kp, Ki, and Kd parameters from a PID controller easily. The main advantage of this formula is that the tuning process of the K<sub>P</sub>, K<sub>I</sub> and K<sub>D</sub> parameters of the PID controller will be simplified just by entering the R, L, and C component values of the buck converter into the formula. The synthesis process of the formula is explained step by step. State space analysis is used to model the equations and transfer functions of the buck converter. The transfer function of the PID controller and buck converter was analyzed to obtain the Buck Converter system's closed loop transfer function. The formula for calculating the parameters K<sub>P</sub>, K<sub>I</sub> and K<sub>D</sub> of the PID controller is derived from the closed loop transfer function of the buck converter system. Numerical simulations are provided to confirm the effectiveness of the proposed PID controller. The performance of the buck converter controlled by the proposed PID controller was tested under various load conditions.