×

Robust pole assignment in linear state feedback. (English) Zbl 0567.93036

Linear time-invariant multivariable continuous-time and discrete-time systems are considered. The aim of the paper is to develop methods for finding a feedback matrix such that the poles of the closed-loop system are as insensitive to perturbations in the coefficient matrices of the system equations as possible. A solution of this problem is said to be robust. Since the sensivity of the eigenvalues depends on the conditioning of the eigenproblem, measures of optimal conditioning are defined. Four novel numerical methods are derived for optimizing these measures. It is shown that minimizing sensivity ensures desirable properties of the closed-loop system. The results for two test problems are given.
Reviewer: R.Tracht

MSC:

93B55 Pole and zero placement problems
93B35 Sensitivity (robustness)
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93B40 Computational methods in systems theory (MSC2010)
93C55 Discrete-time control/observation systems
93C99 Model systems in control theory

Software:

EISPACK; LINPACK; Matlab
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] BARNETT S., Introduction to Mathematical Control Theory (1975) · Zbl 0307.93001
[2] CHU E.-K.-W., Proc. 4th IMA Conf. on Control Theory (1984)
[3] DONGARRA J. J., UNPACK User’s Guide (1979)
[4] FAHMY M. M., I.E.E.E. Trans, autom. Control 27 pp 27– (1982)
[5] FLAMM O. S., I.E.E.E. Trans, autom. Control 25 pp 25– (1980) · Zbl 0471.93018
[6] GOURISHANKAR V., Int. J. Control 23 pp 23– (1976) · Zbl 0317.93031
[7] KAUTSKY , J. , and NICHOLS , N. K. , 1983 a , Numerical Analysis Report NA/2/83, Department of Mathematics , University of Reading; 1983 b, I.E.E. Colloquium on Reliable Numerical Procedures in Control Systems Design, pp. 5/1–5/3; 1984, Robust pole assignment in singular linear systems, (to be published) .
[8] KAUTSKY J., IMA/SERC Meeting on Control Theory (1983)
[9] KAUTSKY , J. , NICHOLS , N. K. , VAN DOOREN , P. , and FLETCHER , L. , 1983 b ,Numerical Treatment of Inverse Problems for Differential and Integral Equations, edited by P. Deuflhard and E. Hairer ( Boston Birkhauser ), pp. 171 – 178 .
[10] KLEIN G., I.E.E.E. Trans, autom. Control 22 pp 140– (1977) · Zbl 0346.93020
[11] MAKI M. C., I.E.E.E. Trans, autom. Control 19 pp 19– (1974)
[12] MAYNE D. Q., Int. J. Control 11 pp 11– (1970) · Zbl 0186.48204
[13] MINIMIS G. S., Int. J. Control 35 pp 341– (1982) · Zbl 0478.93022
[14] MOLER , C. B. , 1981 , MATLAB User’s Guide , Department of Computer Science, University of New Mexico .
[15] MOORE B. C., I.E.E.E. Trans, autom. Control 21 pp 21– (1978)
[16] MUNRO N., Proc. Instn elect. Engrs 126 pp 126– (1979)
[17] NICHOLS N. K., Electron Lett. 20 pp 20– (1984)
[18] PORTER B., Int. J. Control 27 pp 27– (1978)
[19] SMITH B. T., Matrix Eigensystem Routines–EISPACK Guide (1976) · Zbl 0325.65016
[20] SMITH R. A., Numer. Math. 10 pp 10– (1967) · Zbl 0189.47801
[21] THOMPSON R. C., Linear Algebra Appl. 5 pp 5– (1972)
[22] VAN DOOREN P., I.E.E.E. Trans, autom. Control 26 pp 26– (1981) · Zbl 0462.93013
[23] VARGA A., I.E.E.E. Trans, autom. Control 26 pp 26– (1981) · Zbl 0475.93040
[24] WILKINSON J. H., The Algebraic Eigenvalue Problem (1965) · Zbl 0258.65037
[25] WONHAM W. M., Linear Multivariate Control A Geometric Approach (1979) · Zbl 0424.93001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.