| Title:
|
Further results on sliding manifold design and observation for a heat equation (English) |
| Author:
|
Barbieri, Enrique |
| Author:
|
Drakunov, Sergey |
| Author:
|
Figueroa, J. Fernando |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
[133]-147 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This article presents new extensions regarding a nonlinear control design framework that is suitable for a class of distributed parameter systems with uncertainties (DPS). The control objective is first formulated as a function of the distributed system state. Then, a control is sought such that the set in the state space where this relation is true forms an integral manifold reachable in finite time. The manifold is called a Sliding Manifold. The Sliding Mode controller implements a theoretically infinite gain but with finite control amplitudes serving as an effective tool to suppress the influence of matched disturbances and uncertainties in the system behavior. The theory is developed generically for a finite dimensional Jordan Canonical representation of the DPS. The controller manifold design is described in detail and the observer manifold design can be described in a dual manner. Finally, the control law is expressed in terms of the distributed state. However, in a temperature field control problem motivated by a robotic arc- welding application, the simulations presented are done in the standard manner: a reduced-order finite-dimensional model is used to design the controller which is then implemented on a higher-order, still finite- dimensional (truth) model of the system. An analysis of the potential spillover problem shows the effectiveness of our approach. The article concludes with a brief description of the development of an experimental setup that is underway in our Control Systems Lab. (English) |
| Keyword:
|
nonlinear control design |
| Keyword:
|
sliding mode control |
| Keyword:
|
heat equation |
| MSC:
|
35K05 |
| MSC:
|
93B11 |
| MSC:
|
93B12 |
| MSC:
|
93C20 |
| idZBL:
|
Zbl 1249.93024 |
| idMR:
|
MR1760893 |
| . |
| Date available:
|
2009-09-24T19:31:39Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135339 |
| . |
| Reference:
|
[1] Ackermann J., Utkin V.: Sliding mode control based on Ackermann’s formula.IEEE Trans. Automat. Control 43 (1998), 2, 234–237 MR 1605958, 10.1109/9.661072 |
| Reference:
|
[2] Barbieri E., Drakunov S.: Manifold control and observation of Jordan forms with application to distributed parameter systems.In: Proceedings of the 1998 Conference on Decision and Control (CDC), Tampa, Fl |
| Reference:
|
[3] Barbieri E., Özgüner Ü.: Unconstrained and constrained mode expansions for a flexible slewing link.ASME J. Dynamic Systems, Measurement and Control 110 (1988), 4, 416–421 10.1115/1.3152705 |
| Reference:
|
[4] DeCarlo R., Zak S., Drakunov S.: Variable structure and sliding mode control.In: The Control Handbook (W. S. Levine, ed.), CRC Press, Boca Raton, Fl. 1996, pp. 941–950 |
| Reference:
|
[5] Drakunov S., Ozguner U.: Generalized sliding modes for manifold control of distributed parameter systems.In: Variable Structure and Lyapunov Control (Lecture Notes in Control and Information Sciences Series 193, A. S. I. Zinober, ed.), Springer–Verlag, Berlin 1994, pp. 109–132 |
| Reference:
|
[6] S. S. Drakunov, Barbieri E.: Sliding surfaces design for distributed parameter systems.In: Proceedings of the 1997 American Control Conference (ACC), Albuquerque 1997, pp. 3023–3027 |
| Reference:
|
[7] Drakunov S., Barbieri E., Silver D.: Sliding mode control of a heat equation with application to arc welding.In: Proceedings of the 1996 IEEE International Conference on Control Applications, Dearborn 1996, pp. 668–672 |
| Reference:
|
[8] Drakunov S., Utkin V.: Sliding mode control in dynamic systems.Internat. J. Control 55 (1992), 4, 1029–1037 Zbl 0745.93031, MR 1154664, 10.1080/00207179208934270 |
| Reference:
|
[9] Meirovitch L.: Analytical Methods in Vibrations.MacMillan, New York 1967 Zbl 0166.43803 |
| Reference:
|
[10] Oden J. T.: Applied Functional Analysis.Prentice–Hall, Englewood Cliffs, N.J. 1979 Zbl 1200.46001 |
| Reference:
|
[11] Russell D.: Observability of linear distributed–parameter systems.In: The Control Handbook (W. S. Levine, ed.), CRC Press, Boca Raton, Fl. 1996, pp. 1169–1175 |
| Reference:
|
[12] Segel L. A.: Mathematics Applied to Continuum Mechanics.MacMillan, New York 1977 Zbl 1142.74001, MR 0502508 |
| . |
