Compensator plane design for engineering models

We characterize value sets and feasible compensation regions for simple plants widely used in engineering applications. We obtain compensation regions that guarantee specified bounds on the control ratio in the compensation plane. We show that for simple plant families the value set is bounded by a subset under fixed feedback compensation and show its invariance under fixed cascade compensation. We illustrate the results with a design example. Our results may explain why practicing engineers show little interest in much of the recent developments in control theory.