Formulation of PID Control for DC-DC Converters Based on Capacitor Current: A Geometric Context

The output voltage derivative term associated with a PID controller injects significant noise in a dc-dc converter. This is mainly due to the parasitic resistance and inductance of the output capacitor. Particularly, during a large-signal transient, noise injection significantly degrades phase margin. Although noise characteristics can be improved by reducing the cutoff frequency of the low-pass filter associated with the voltage derivative, this degrades the closed-loop bandwidth. A formulation of a PID controller is introduced to replace the output voltage derivative with information about the capacitor current, thus reducing noise injection. It is shown that this formulation preserves the fundamental principle of a PID controller and incorporates a load current feedforward, as well as inductor current dynamics. This can be helpful to further improve bandwidth and phase margin. The proposed method is shown to be equivalent to a voltage-mode-controlled buck converter and a current-mode-controlled boost converter with a PID controller in the voltage feedback loop. A buck converter prototype is tested, and the proposed algorithm is implemented using a field-programmable gate array.