| Title:
|
Output feedback problems for a class of nonlinear systems (English) |
| Author:
|
Čelikovský, Sergej |
| Author:
|
Ruiz-León, J. J. |
| Author:
|
Sapiens, A. J. |
| Author:
|
Torres-Muñoz, J. A. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
[389]-414 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the construction of the output feedback controllers for the systems that are transformable into a simpler form via coordinate change and static state feedback and, at the same time, via (possibly different) coordinate change and output injection. Illustrative examples are provided to stress the major obstacles in applying the above scheme, especially as far as its global aspects are concerned. The corresponding results are then applied to the problem of the real-time control of the water-storing plant. Using the methods developed in the theoretical part of the paper, the control of the water levels is designed to handle the unknown influx of the water into the first tank using measurements of water levels only. Simulations results are presented showing good performance of the designed controller. Some preliminary laboratory experiments have shown promising results of the real time implementation as well. (English) |
| Keyword:
|
output feedback |
| Keyword:
|
nonlinear systems |
| Keyword:
|
output regulations |
| MSC:
|
93B52 |
| MSC:
|
93C10 |
| MSC:
|
93D20 |
| idZBL:
|
Zbl 1249.93073 |
| idMR:
|
MR2024522 |
| . |
| Date available:
|
2009-09-24T19:55:12Z |
| Last updated:
|
2015-03-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135542 |
| . |
| Reference:
|
[1] Atassi A. N., Khalil H. K.: A separation principle for the stabilization of a class of nonlinear systems.IEEE Trans. Automat. Control 44 (1999), 1672–1687 Zbl 0958.93079, MR 1709863, 10.1109/9.788534 |
| Reference:
|
[2] Atassi A. N., Khalil H. K.: A separation principle for the control of a class of nonlinear systems.IEEE Trans. Automat. Control 46 (2001), 742–746 Zbl 1055.93064, MR 1833028, 10.1109/9.920793 |
| Reference:
|
[3] Bacciotti A.: Local Stabilizability of Nonlinear Control Systems.World Scientific, Singapore 1992 Zbl 0757.93061, MR 1148363 |
| Reference:
|
[4] Bacciotti A., Rosier L.: Liapunov Functions and Stability in Control Theory.Springer, London 2001 Zbl 1078.93002, MR 1826052 |
| Reference:
|
[5] Lopez-Morales V., Čelikovský S.: Constructive dynamic output feedback stabilization of nonlinear systems.In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 1999, pp. 4885–4890 |
| Reference:
|
[6] Gauthier J. P., Hammouri, H., Orthman S.: Simple observer for nonlinear systems application to bioreactors.IEEE Trans. Automat. Control 37 (1992), 875–880 MR 1164571, 10.1109/9.256352 |
| Reference:
|
[7] Hartman P.: Ordinary Differential Equations.Wiley, New York 1964 Zbl 1009.34001, MR 0171038 |
| Reference:
|
[8] Isidori A.: Nonlinear Systems.Third edition. Springer, New York 1995 Zbl 1203.93178, MR 1410988 |
| Reference:
|
[9] Jo N. H., Seo J. H.: Local separation principle for non-linear systems.Internat. J. Control 73 (2000), 292–302 Zbl 1038.93077, MR 1767045, 10.1080/002071700219641 |
| Reference:
|
[10] Krener A. J.: Nonlinear stabilizability and detectability.In: Systems and Networks: Mathematical Theory and Applications, Vol. I (U. Helmke, R. Mennicken, and J. Saurer, eds.), Akademie Verlag, Berlin 1994, pp. 231–250 Zbl 0816.93067, MR 1288114 |
| Reference:
|
[11] Krener A. J., Isidori A.: Linearization by output injection and nonlinear observers.Systems Control Lett. 3 (1983), 47–52 Zbl 0524.93030, MR 0713426 |
| Reference:
|
[12] Krener A. J., Respondek W.: Nonlinear observers with linearizable error dynamics.SIAM J. Control Optim. 23 (1985), 197–216 Zbl 0569.93035, MR 0777456, 10.1137/0323016 |
| Reference:
|
[13] Khalil H. K.: Nonlinear Systems.MacMillan, New York 1992 Zbl 1140.93456, MR 1201326 |
| Reference:
|
[14] Marino R., Tomei P.: Dynamic output feedback linearization and global stabilization.Systems Control Lett. 17 (1991), 115–121 Zbl 0747.93069, MR 1120756, 10.1016/0167-6911(91)90036-E |
| Reference:
|
[15] Marino R., Tomei P.: Nonlinear Control Design: Geometric, Adaptive and Robust.Prentice Hall, London 1995 Zbl 0833.93003 |
| Reference:
|
[16] Mazenc F., Praly, L., Dayawansa W. P.: Global stabilization by output feedback: examples and counterexamples.Systems Control Lett. 23 (1994), 119–125 Zbl 0816.93068, MR 1287604, 10.1016/0167-6911(94)90041-8 |
| Reference:
|
[17] Nijmeijer H., Shaft A. van der: Nonlinear Dynamical Control Systems.Springer, Berlin 1990 MR 1047663 |
| Reference:
|
[18] Sastry S.: Nonlinear Systems.Analysis, Stability and Control. Springer, New York 1999 Zbl 0924.93001, MR 1693648 |
| Reference:
|
[19] Teel A.: Semi-global stabilization of minimum phase nonlinear systems in special normal forms.Systems Control Lett. 19 (1992), 187–192 Zbl 0763.93039, MR 1180506, 10.1016/0167-6911(92)90112-6 |
| Reference:
|
[20] Teel A., Praly L.: Global stabilizability and observability imply semiglobal stabilizability by output feedback.Systems Control Lett. 22 (1994), 313–325 MR 1274906, 10.1016/0167-6911(94)90029-9 |
| Reference:
|
[21] Vaněček A., Čelikovský S.: Control Systems: from Linear Analysis to the Synthesis of Chaos.Prentice Hall, London 1996 MR 1481725 |
| Reference:
|
[22] Vidyasagar M.: On the stabilizability and detectability of nonlinear systems using state detection.IEEE Trans. Automat. Control AC-25 (1980), 504–509 MR 0571757, 10.1109/TAC.1980.1102376 |
| Reference:
|
[23] Zeitz M.: The extended Luenberger observer for nonlinear systems.Systems Control Lett. 9 (1987), 149–156 Zbl 0624.93012, MR 0906234, 10.1016/0167-6911(87)90021-1 |
| . |
