Analysis of Multivariable Control Systems in the Presence of Structured Uncertainties
Abstract
An analysis of the stability properties of uncertain multivariable control systems in the frequency domain is presented. Necessary and sufficient stability criteria are reviewed along with singular value scaling techniques for characterizing permissible uncertainties. Such scaling methods have become widely accepted tools for the analysis of control systems in the presence of structured uncertainties. Included in this study are the general block similarity scaling techniques advanced by Doyle and the nonsimilarity scaling approach of Kouvaritakis and Latchman. For element-by-element structured uncertainties, both scaling methods reliably compute Doyle's structured singular value, micron, which provides an indication of system stability. However, the similarity scaling formulation has the disadvantage of expanding an n x n system matrix to an n squared x n squared matrix requiring n squared - 1 optimization variables to compute micron. Using nonsimilarity scaling, the system size remains n with the additional benefit of requiring only 2(n-1) optimization variables. The results of this work show that for scalar uncertainties, the structure may be exploited to yield a similarity scaling method which requires no more than the 2(n-1) optimization variables needed for nonsimilarity scaling. Substantial savings in floating point operations are observed for various system sizes enhancing the capability of this method for analysis and iterative design. A similar reduction in optimization variables is shown to hold for the important class of general block structured uncertainties. This reduction leads to a complete solution for the 2 x 2 block uncertainty problem.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1990
- Accession Number
- ADA227976
Entities
People
- Robert J. Norris
Organizations
- Air Force Institute of Technology