Uncertain SISO systems with fixed stable minimum-phase controllers: relationship of closed-loop systems to plant RHP poles and zeros

Abstract

The relationship is explored between the SISO open-loop and closed-loop system structures associated with the use of stable minimum-phase controllers in the face of unrestricted plant uncertainty. All types of plant structure and uncertainty, including arbitrary numbers of right half-plane poles and zeros, are considered in a progressive manner within a Nyquist-Bode framework. In the face of increasingly severe types of plant uncertainty, it is shown why meeting closed-loop system performance objectives becomes increasingly difficult for such plants; there remains, however, a strict relationship between open-loop and closed-loop system structures.