Abstract
In this article the robustness of tracking controllers acting on multivariable linear systems under parametric uncertainty is investigated. After a system transformation we design PID-like tracking controllers for the resulting subsystems taking nominal parameters into account. Robustness is studied under parametric uncertainty: it splits into the robust stability of an autonomous linear system and into the robust stability of the same autonomous system being perturbed by secalled “quasi-exogenous” signals. The article is concluded by a DC drive example.
This work was financially supported by the German Academic Exchange Service (DAAD)
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References
Ackermann, J.(1993) Robust Control:Systems with Uncertain Physical Parameters. Springer-Verlag, London
Barmish, B. R.(1994) New Tools for Robustness of Linear Systems. Macmillan, New York
Bitauld, L., Fliess, M. and Lévine, J. (1997) Flatness based control synthesis of linear systems: an application to windshield wipers. Proceedings of ECC, Brussels
Delaeau, E. (1997) Suivi de trajectoires pour les systèmes linéaires. Actes Coll. Cetsis — Eea, Orsay, 149–154
Fliess, M. and Marquez, R. (2000) Continous-time linear predictive control and flatness: a module-theoretic setting with examples. Internat. J. Control 73, 606–623
Francis, B. A. (1977) The linear multivariable regulator problem. SIAM Contr. Opt. 15, 486–505
Frazer, R. and Duncan, W. (1929) On the criteria for the stability of small motions. In Proceedings of the Royal Society A 124, 642–654
Hagenmeyer, V. (2000) Robust tracking of linear systems under parametric uncertainty. Proceedings of MTNS 2000, Perpignan
Hagenmeyer, V., Kohlrausch, P. and Delaleau, E. (2000) Flatness based control of the separately excited DC drive. In “Nonlinear Control in the Year 2000” (this very book), eds. Isidori, A., Lamnabhi-Lagarrigue, F. and Respondek, W., Springer-Verlag, London
Hunt, L. R., Meyer, G. and Su, R. (1996) Noncausal inverses for linear systems. IEEE Trans. Automat. Contr. 41, 608–611
Hunt, L. R., Meyer, G. and Su, R. (1997) Driven dynamics of time-varying linear systems. IEEE Trans. Automat. Contr. 42, 1313–1317
Hopp, T. H., and Schmitendorf, W. E.(1990) Design of a linear controller for robust tracking and model following. Trans. ASME, J. Dynamic Syst., Measurement, and Contr. 112, 552–558
Kharitonov, V. L. (1978) Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsial'nye Uravneniya 14, 2086–2088
Kokotović, P., Khalil, H. K. and O'Reilly, J. (1986) Singular Perturbation Methods in Control: Analysis and Design. Academic Press, London
Leonhard, W. (1996) Control of Electrical Drives. Springer, Berlin
Luenberger, D. G.(1967) Canonical Forms for Linear Multivariable Systems. IEEE Trans. Automat. Contr., 290–293
Moore, R. E.(1979) Methods and Applications of Interval Analysis. SIAM, Philadelphia
Rugh, W. J. (1996) Linear System Theory (2nd edition). Prentice-Hall, Upper Saddle River
Schmitendorf, W. E. and Barmish, B. R. (1986) Robust asymptotic tracking for linear systems with unknown parameters. Automatica 22, 335–360
Schmitendorf, W. E. and Barmish, B. R. (1987) Guaranteed output stability for systems with constant disturbances. Trans. ASME, J. Dynamic Syst., Measurement, and Contr. 109, 186–189
Schmitendorf, W. E. (1987) Methods for obtaining robust tracking control laws. Automatica 23, 675–677
Sontag, E. D. (1998) Mathematical Control Theory (2nd edition). Springer-Verlag, New York
Walter, E. and Jaulin, L. (1994) Guaranteed Characterization of Stability Domains Via Set Inversion. IEEE Trans. Automat. Contr. 39, 886–889
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Hagenmeyer, V. (2001). Robust tracking of multi-variable linear systems under parametric uncertainty. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the Year 2000. Lecture Notes in Control and Information Sciences, vol 258. Springer, London. https://doi.org/10.1007/BFb0110231
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DOI: https://doi.org/10.1007/BFb0110231
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