| Title:
|
Meromorphic observer-based pole assignment in time delay systems (English) |
| Author:
|
Zítek, Pavel |
| Author:
|
Kučera, Vladimír |
| Author:
|
Vyhlídal, Tomáš |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
5 |
| Year:
|
2008 |
| Pages:
|
633-648 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with a novel method of control system design which applies meromorphic transfer functions as models for retarded linear time delay systems. After introducing an auxiliary state model a finite-spectrum observer is designed to close a stabilizing state feedback. The observer finite spectrum is the key to implement a state feedback stabilization scheme and to apply the affine parametrization in controller design. On the basis of the so- called RQ-meromorphic functions an algebraic solution to the problem of time- delay system stabilization and control is presented that practically provides a finite spectrum assignment of the control loop. (English) |
| Keyword:
|
retarded time-delay system |
| Keyword:
|
meromorphic transfer function |
| Keyword:
|
reduced-order observer |
| Keyword:
|
state feedback |
| Keyword:
|
affine parametrization of stabilizing controllers |
| MSC:
|
93B55 |
| MSC:
|
93C05 |
| MSC:
|
93D15 |
| idZBL:
|
Zbl 1177.93043 |
| idMR:
|
MR2479309 |
| . |
| Date available:
|
2009-09-24T20:38:40Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135879 |
| . |
| Reference:
|
[1] Breda D., Maset S., Vermiglio R.: Computing the characteristic roots for delay differential equations.IMA J. Numer. Anal. 24 (2004), 1, 1–19 Zbl 1054.65079, MR 2027286 |
| Reference:
|
[2] Hale J. K., Lunel S. M. Verduyn: Introduction to Functional Differential Equations (Mathematical Sciences Vol.99). Springer-Verlag, New York 1993 MR 1243878 |
| Reference:
|
[3] Goodwin G. C., Graebe S. F., Salgado M. E.: Control System Design.Prentice Hall, Englewood Cliffs, N.J. 2001 |
| Reference:
|
[4] Kim J. H., Park H. B.: State feedback control for generalized continuous/discrete time-delay systems.Automatica 35 (1999), 8, 1443–1451 MR 1831484 |
| Reference:
|
[5] Loiseau J. J.: Algebraic tools for the control and stabilization of time-delay systems.Ann. Review in Control 24 (2000), 135–149 |
| Reference:
|
[6] Michiels W., Engelborghs K., Vansevenant, P., Roose D.: Continuous pole placement method for delay equations.Automatica 38 (2002), 5, 747–761 MR 2133350 |
| Reference:
|
[7] Michiels W., Roose D.: Limitations of delayed state feedback: a numerical study.Internat. J. Bifurcation and Chaos 12 (2002), 6, 1309–1320 |
| Reference:
|
[8] Michiels W., Vyhlídal T.: An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type.Automatica 41 (2005), 991–998 Zbl 1091.93026, MR 2157698 |
| Reference:
|
[9] Mirkin L., Raskin N.: Every stabilizing dead-time controller has an observer-predictor-based structure.Automatica 39 (2003), 1747–1754 Zbl 1039.93026, MR 2141770 |
| Reference:
|
[10] Niculescu S. I., (eds.) K. Gu: Advances in Time-Delay Systems.Springer-Verlag, Berlin – Heidelberg 2004 Zbl 1051.34002, MR 2092594 |
| Reference:
|
[11] Olbrot W.: Stabilizability, detectability and spectrum assignment for linear autonomous systems with general time delays.IEEE Trans. Automat. Control 23 (1978), 5, 887–890 Zbl 0399.93008, MR 0528786 |
| Reference:
|
[12] Picard P., Lafay J. F., Kučera V.: Feedback realization of non-singular precompensators for linear systems with delays.IEEE Trans. Automat. Control 42 (1997), 6, 848–853 MR 1455716 |
| Reference:
|
[13] Trinh H.: Linear functional state observer for time delay systems.Internat. J. Control 72 (1999), 18, 1642–1658 Zbl 0953.93012, MR 1733875 |
| Reference:
|
[14] Vyhlídal T., Zítek P.: Mapping the spectrum of a retarded time-delay system utilizing root distribution features.In: Proc. IFAC Workshop on Time-Delay Systems, TDS’06, L’Aquila 2006 |
| Reference:
|
[15] Vyhlídal T., Zítek P.: Mapping based algorithm for large-scale computation of quasi-polynomial zeros.IEEE Trans. Automat. Control (to appear) MR 2478083 |
| Reference:
|
[16] Wang Q. E., Lee T. H., Tan K. K.: Finite Spectrum Assignment Controllers for Time Delay Systems.Springer, London 1995 |
| Reference:
|
[17] Zhang W., Algower, F., Liu T.: Controller parametrization for SISO and MIMO plants with time-delay.Systems Control Lett. 55 (2006), 794–802 MR 2246741 |
| Reference:
|
[18] Zítek P., Hlava J.: Anisochronic internal model control of time delay systems.Control Engrg. Practice 9 (2001), 5, 501–516 |
| Reference:
|
[19] Zítek P., Kučera V.: Algebraic design of anisochronic controllers for time delay systems.Internat. J. Control 76 (2003), 16, 1654–1665 MR 2019076 |
| Reference:
|
[20] Zítek P., Vyhlídal T.: Quasi-polynomial based design of time delay control systems.In: Fourth IFAC Workshop on Time Delay Systems, Rocquencourt 2003 |
| . |
