×

zbMATH — the first resource for mathematics

Analysis of steady-state tracking errors in sampled-data systems with uncertainty. (English) Zbl 0979.93069
The paper deals with robust steady-state \(\varepsilon\)-tracking of sampled data systems in the presence of structured norm bounded time-varying finite memory uncertainty. An appropriate steady-state norm has been defined, and a steady-state norm matrix has been constructed based on this norm. Exact conditions for robust \(\varepsilon\)-tracking of sampled data systems were derived in terms of the spectral radius of this matrix. The results show that even if zero steady-state tracking can be achieved for the nominal system, the steady-state tracking error may no longer be zero in the presence of time-varying uncertainty in the system, and that it can be arbitrarily large. An example for computing the steady-state tracking error for a sampled data system with uncertainty is provided.
MSC:
93C57 Sampled-data control/observation systems
93B51 Design techniques (robust design, computer-aided design, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bartle, R.G.; Sherbert, D.R., Introduction to real analysis, (1982), Wiley New York · Zbl 0494.26002
[2] Bamieh, B.A.; Pearson, J.B., A general framework for linear periodic systems with application to \(H∞\) sampled-data control, IEEE transactions on automatic control, 37, 418-435, (1992) · Zbl 0757.93020
[3] Bamieh, B.A.; Pearson, J.B., The \(H2\) problem for sampled-data systems, Systems and control letters, 19, 1-12, (1992) · Zbl 0765.93050
[4] Bamieh, B.A.; Dahleh, M.A.; Pearson, J.B., Minimization of the \(L\^{}\{∞\}\)-induced norm for sampled-data systems, IEEE transactions on automatic control, 38, 5, 717-732, (1993) · Zbl 0784.93072
[5] Chen, T.; Francis, B., On the \(L2\)-induced norm of a sampled-data system, Systems and control letters, 15, 211-219, (1990) · Zbl 0724.93053
[6] Chen, T.; Francis, B., Optimal sampled-data control systems, (1995), Springer New York · Zbl 0847.93040
[7] Dullerud, G. (1990). Tracking and\(L1\)performance in sampled-data control systems. Master’s thesis, University of Toronto.
[8] Dullerud, G.; Francis, B.A., \(L1\) performance in sampled-data systems, IEEE transactions on automatic control, 37, 436-446, (1992) · Zbl 0756.93053
[9] Dullerud, G.; Glover, K., Robust stabilization of sampled-data systems to structured LTI perturbations, IEEE transactions on automatic control, 38, 1497-1508, (1993) · Zbl 0790.93111
[10] Horn, R.; Johnson, C., Matrix analysis, (1985), Cambridge University Press Cambridge · Zbl 0576.15001
[11] Kabamba, P. T., & Hara, S. (1990). On computing the induced norm of a sampled-data system. Proceedings of American control conference (pp. 319-320).
[12] Khammash, M.; Pearson, J.B., Performance robustness of discrete-time systems with structured uncertainty, IEEE transactions automatic control, 36, 4, 398-412, (1991) · Zbl 0754.93063
[13] Khammash, M., Necessary and sufficient conditions for the robustness of time-varying systems with applications to sampled-data systems, IEEE transactions on automatic control, 38, 1, 49-57, (1993) · Zbl 0777.93018
[14] Khammash, M.; Pearson, J.B., Analysis and design for robust performance with structured uncertainty, Systems and control letters, 20, 179-187, (1993) · Zbl 0768.93065
[15] Khammash, M., Robust steady-state tracking, IEEE transactions on automatic control, 40, 11, 1872-1880, (1995) · Zbl 0847.93013
[16] Sivashankar, N.; Khargonekar, P.P., Induced norms of sampled-data systems, Automatica, 28, 1267-1272, (1992) · Zbl 0763.93056
[17] Sivashankar, N.; Khargonekar, P.P., Robust stability and performance analysis of sampled-data systems, IEEE transactions on automatic control, 38, 1, 58-69, (1993) · Zbl 0773.93069
[18] Toivonen, H.T., Sampled-data control of continuous-time systems with an \(H∞\) optimality criterion, Automatica, 28, 45-54, (1992) · Zbl 0746.93062
[19] Yamamoto, Y. (1990). New approach to sampled-data systems: A function space method. Proceedings of the conference on decision and control (pp. 1882-1887).
[20] Yamamoto, Y., A function space approach to sampled-data control systems and tracking problems, IEEE transactions on automatic control, 39, 703-712, (1994) · Zbl 0807.93038
[21] Zou, Z., & Khammash, M. (1997). Robust steady-state tracking of sampled-data systems, Proceedings of the American Control Conference, 3616-3620.
[22] Zou, L. (1998). Studies in robust control: Analysis of sampled-data systems and aircraft pitch control. Ph.D. thesis, Iowa State University, Ames, Iowa, USA.
[23] Zou, L., & Khammash, M. (1998). Robust steady-state tracking for periodic systems, Proceedings of the American Control Conference, 660-664.
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.