DISCRETE-TIME CONTROL OF LINEAR MULTIVARIABLE SYSTEMS WITH EITHER SINGULAR OR ILL-CONDITIONED TRANSFER FUNCTION MATRICES
DOI:
https://doi.org/10.18372/2306-1472.59.6769Keywords:
bounded disturbance, discrete time, noninvertible matrix, multivariable system, optimality pseudo-inversionAbstract
The control of multivariable linear discrete-time, time-invariant systems whose transfer function matrices are either singular or ill-conditioned is considered. It is assumed that there are arbitrary unmeasurable but bounded disturbances, and the parameters of these systems may be somewhat unknown. The optimal controller is derived by using the pseudoinverse of the system transfer function matrix. The boundedness of all signals caused by this controller and also the robustness properties of the controller in the presence of parameter uncertainty are proved. Numerical examples are given to support the theoretical investigations.
References
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Dorato, P. On the inverse of linear dynamical systems. IEEE Trans. Syst. Sc. and Cyber. 1969. Vol. 5, N 1. P. 43-48.
Francis, B.A. The linear multivariable regulator problem. SIAM J. Control Optimiz. 1977. Vol 15, N 3. P. 486–505.
Lee, T.; Adams, G.; Gaines, W. Computer Process Control: Modeling and Optimization. New York, Wiley. 1968. 437 p.
Lovass-Nagy, V.; Miller, J.R.; Powers, L.D. On the application of matrix generalized inversion to the construction of inverse systems. Int. Journal of Control. 1976. Vol. 24, N 5. P. 733–739.
Lyubchik, L.M. Inverse model control and subinvariance in linear discrete multivariable systems. Proceedings of the 3rd European Control Conference. Roma, Italy. 1995. Vol. 4, Part 2.
P. 3651–3659.
Seraji, H. Minimal inversion, command tracking and disturbance decoupling in multivariable systems. Int. J. Control. 1989. Vol. 49, N 6.
P. 2093–2191.
Voevodin, V.V.; Kuznetsov, Yu.A. Matrices and Computations. Moscow, Nauka. 1984. 320 p. (in Russian)
Wolovich, W.A. Linear Multivariable Systems. New York, Springer. 1974. 582 p.
Wonham, W.M. Linear Multivariable Control. A Geometrical Approach. New York, Springer. 1985. 613 p.
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Published
04-07-2014
How to Cite
Azarskov, V., Zhiteckii, L., & Solovchuk, K. (2014). DISCRETE-TIME CONTROL OF LINEAR MULTIVARIABLE SYSTEMS WITH EITHER SINGULAR OR ILL-CONDITIONED TRANSFER FUNCTION MATRICES. Proceedings of National Aviation University, 59(2), 19–27. https://doi.org/10.18372/2306-1472.59.6769
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AEROSPACE SYSTEMS FOR MONITORING AND CONTROL
