Formulation of PID control for dc-dc converters based on capacitor current: A geometric context

The output-voltage-derivative term of a proportional-integral-derivative (PID) controller injects significant noise in a dc-dc converter. This is mainly due to the presence of 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 cut-off frequency of the low-pass filter associated with the voltage derivative, it degrades the closed-loop bandwidth. A new 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 this new formulation preserves the fundamental principle of a PID controller and incorporates a load current feed-forward 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.