Abstract
This paper studies the solution of the robust asymptotic tracking/disturbance rejection problem with minimum sensitivity for general feedback multivariable systems, namely, those in which the plant is two-input two-output and the compensator is two-input one output and there are exogenous signals in the two junctions between plant and compensator. The exogenous signals into the plant and junctions are asymptotically rejected, while the exogenous signal into the compensator is asymptotically tracked by one of the plant's output. Resides, the system is stable and the sensitivities are minimized, taking advantage of the two degrees of freedom provided by the compensator. The problem is solved for plant and compensator whose transfer function matrices are rational, using the factorization approach with the transfer function matrices factorized over proper and stable rational matrices. The paper is a development of results obtained in the solution of the asymptotic tracking/disturbance rejection problem with stability [3].
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Carl N. Nett, "Algebraic aspects of linear control system stability", IEEE Trans. on Autom. Contr., vol. AC-31. pp. 941–949, Oct. 1986.
C. A. Desoer and A. N. Gündeş, "Algebraic theory of linear time — invariant feedback systems with two — input two — output plant and compensator", Memo. UCB/ERL M87/1, Electron. Research Laboratory, University of California, Berkeley. To appear in Intern. Journ. of Contr.
Pedro M. G. Ferreira, "Four — input four — output feedback systems: robust asymptotic behaviour", July 1987, to be presented and published in the Proceedings of 1988 American Control Conference.
M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press, 1985.
W. A. Wolovich, "Skew prime polynomial matrices", IEEE Trans. on Autom. Contr. vol. AC-23, pp. 880–887, Octob. 1978.
V. Kučera, Discrete Linear Control: The Polynomial Equation Approach. New York: Wiley, 1978.
M. G. Safonov and B. S. Chen, "Multivariable stability-margin optimization with decoupling and output regulation", IEE Proceedings, vol. 129, Pt. D, pp. 276–282, Nov. 1982.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Ferreira, P.M.G. (1988). Optimal robust multi-purpose general feedback systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042202
Download citation
DOI: https://doi.org/10.1007/BFb0042202
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19237-4
Online ISBN: 978-3-540-39161-6
eBook Packages: Springer Book Archive