Stability Margins for Minimum-Phase SISO Plants: A Case Study

We consider the conflict between the stability margins and the degree of stability (the latter determines speed of response) as engineering performance indices of closed loop system for a plant with stable zeros. The H
∞
synthesis and the pole placement control design procedures are used to show through examples that assignment of "overly stable" closed loop poles leads to dramatic decrease of stability margins. It is shown that stability margins do not indicate the system robust properties in the case of the plant with the relative order being no more than one when the controller cancels all plant zeros. The continuous time and discrete time cases are studied.