An experimental evaluation of the PID controller represented by the delta operator

This study explores two digital PID controller representations: one using the shift operator and one using the delta operator. Both shift and delta-operator-based difference equations are derived from the continuously-designed transfer function. The difference equations reveal a numerical advantage of the delta operator in digital controls: its models are less susceptible to the limited range of numbers that can be represented in finite word-length conditions. The two controllers' abilities to compensate a dc-dc buck converter initial transient are compared through simulation and experimentation. The results demonstrate that the delta operator outperforms the shift operator when modeling a continuously-designed PID controller.