Two Stability Results for Discrete One Step Ahead Adaptive Control.
Abstract
In this thesis, two stability results are developed for one step ahead adaptive controllers. In Chapter 2, an analysis is presented of the local behavior of a one step ahead adaptive controller around a tuned solution. Instead of placing assumptions on the order, delay or minimum phase properties of the plant, the existence of a unique tuned solution is assumed. This implies that for a particular reference model output there exists a unique stabilizing parameter vector such that the plant output will track the reference model output exactly. Assuming this tuned solution exists, the closed-loop system was shown to be locally stable, and small departures from the nominal do not disturb this stability. The second stability result presented in this thesis deals with the problems associated with direct adaptive control of a sampled data process. Even if a continuous time plant is minimum phase, sampling will often introduce nonminimum phase zeros in the equivalent discrete model. These nonminimum phase zeros cannot be cancelled if system stability is to be maintained. Johansson (1983) has shown that the minimum a priori knowledge needed is the unstable zero locations. Fortunately, Astrom et al. (1984) have established the location of these zeros for very rapidly sampled systems. Using this information, the algorithm presented in Section 3.2 retains the unstable zeros in the tracking transfer function. The analysis presented in Section 3.3 represents the first step towards establishing a robust direct adaptive scheme for sampled data systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1985
- Accession Number
- ADA161306
Entities
People
- Douglas S. Rhode
Organizations
- University of Illinois Urbana–Champaign