Comprehensive Modelling of a Capacitor Charger Boost Converter with PID Control

The DC-DC converter is used to convert the DC voltage, and the conversion is carried out to increase or decrease the voltage. This paper discusses the modeling of a boost converter for charging high-capacity capacitors using PID control. PID control is used to overcome changing voltages and long times to steady-state due to capacitor changes. The boost converter has a 24 V input voltage and a 350 V output voltage. Boost converter modeling is performed by electrically reviewing the circuit and then converting the differential equation from the electrical analysis into a state space that depicts the characteristics of boost converter. The simulation was performed using MATLAB software. For the initial conditions, a simulation was carried out using the calculated critical capacitor value to determine whether the boost converter output voltage reached 350 V. Furthermore, when the boost converter was replaced with a 4700 uF capacitor, the boost converter experienced underdamp oscillations with a settling time of up to 9 s. Therefore, PID control was used to overcome oscillations and long settling times. The Ziegler–Nichols 2 and Routh–Hurwitz stability methods were used to determine the parameters Kp, Ki, and Kd. From the calculation results, the parameters Kp = 0.6, Ki = 21.39, and Kd = 0.0042 are obtained. The output voltage response still has a high undershoot when using the parameters obtained from Ziegler–Nichols 2 tuning, but it already has a fast-settling time. By fine-tuning the PID control, the values Kp = 2, Ki = 90, and Kd = 0.09 were obtained. With these values, the boost converter voltage response has an overshoot of 388 V, an undershoot of 312 V, and a settling time of 0.6 s at 351 V.