PUBLICATIONS - International Conferences
| Title: |
The Use of Symbolic Algebra in Control |
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Author: |
N Munro, E Kontogiannis, S T Impram, M T Söylemez and H Baki |
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Year: |
1999 (9) |
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Conference: |
European Conference on Control (ECC'99) |
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Place: |
Karlsruhe, Germany |
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Session: |
DA-1 |
| Keywords: | Symbolic algebra, uncertain nonlinear SISO systems, uncertain MIMO systems |
| Extended Abstract: | This paper will present several tools for model manipulation, model-order reduction, analysis,
and the design/synthesis of uncertain control systems, developed in the symbolic algebra environment Mathematica. New control objects, namely, more compact and visually pleasing forms of the state-space and transfer-function objects have been developed, and several new system objects, in the form of Rosenbrock’ s system matrix in polynomial and state-space form, and left and right matrix fraction forms; have been introduced in the framework of Mathematica’s Control System Professional package. Some new associated transformations; namely, a MatrixLeftGCD and MatrixRightGCD for coprime factorisations, the Smith form, and the McMillan form, and a new simple minimal realisation algorithm have also been implemented. A new model-order reduction method called the quasi-generalised singular perturbation method has been implemented that allows the designer, by varying a simple parameter between 0 and 1, to select a compromise between Moore’s Balanced Truncation approach (s = \infty) and Samar, Postlethwaite and Gu’s Balanced Residualisation approach (s = 0). Interesting observations on appropriate pole assignment algorithms for use with systems containing symbols are reported, and some recent tests have shown that the mapping algorithm, which is not considered as reliable as or as fast as Ackermann’s algorithm (currently implemented in both Matlab and Mathematica’s Control System Professional), is in fact one of the best methods for use with symbolic data. Some recent results on the robust diagonal dominance of uncertain multivariable systems, consisting of recent extensions of Rosenbrock’s Direct Nyquist Array design method, and similar extensions to Limebeer’s generalised diagonal dominance and Bryant and Leung’s fundamental diagonal dominance, will be presented. The prediction of limit cycles in uncertain non-linear systems, and the absolute stability of nonlinear systems with structured and unstructured uncertainties are considered using describing function and the Popov criterion, respectively. |
   
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