Loop transfer recovery for nonminimum phase plants and ill-conditioned plants.

Abstract

The purpose of this dissertation to study the applications of the loop transfer recovery (LTR) design procedure to nonminimum phase and ill-conditioned plants. Explicit expressions are given for the asymptotic behavior of the loop transfer and the sensitivity functions resulting from application of the LTR procedure. Both the continuous and the discrete-time cases are treated. These expressions enable us to provide theoretical justifications to some empirical results and observations. It is observed that the limitations imposed by nonminimum phase zeros upon feedback properties manifest themselves as a tradeoff between the feedback properties of the state feedback loop and our ability to recover those properties using the LTR procedure. How this knowledge can be incorporated into design is also discussed. For ill-conditioned plants, the problem of obtaining stability robustness in the presence of simultaneous input and output uncertainties is considered. It is demonstrated how the LQG/LTR design methodology can be effectively applied to this problem. The key in the application is the special weight selection procedure proposed in the target state feedback loop design. Explicit expressions are also given for the optimal cost of the cheap control LQ regulator and the asymptotic solution of the associated Riccati equation for nonminimum phase systems.