| Title:
|
Reaching phase elimination in variable structure control of the third order system with state constraints (English) |
| Author:
|
Bartoszewicz, A. |
| Author:
|
Nowacka, A. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
111-126 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the design of a time varying switching plane for the sliding mode control of the third order system subject to the velocity and acceleration constraints is considered. Initially the plane passes through the system representative point in the error state space and then it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops and remains motionless. The plane parameters (determining angles of inclination and the velocity of its motion) are selected to ensure the minimum integral absolute error without violating velocity and acceleration constraints. The optimal parameters of the plane for the system subject to the acceleration constraint are derived analytically, and it is strictly proved that when both the system velocity and acceleration are limited, the optimal parameters can be easily found using any standard numerical procedure for solving nonlinear equations. The equation to be solved is derived and the starting points for the numerical procedure are given. (English) |
| Keyword:
|
variable structure systems |
| Keyword:
|
sliding mode control |
| Keyword:
|
switching plane design |
| MSC:
|
93A30 |
| MSC:
|
93B12 |
| MSC:
|
93B40 |
| MSC:
|
93B50 |
| MSC:
|
93C10 |
| idZBL:
|
Zbl 1249.93025 |
| idMR:
|
MR2208523 |
| . |
| Date available:
|
2009-09-24T20:14:23Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135702 |
| . |
| Reference:
|
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| Reference:
|
[2] Bartoszewicz A.: Time-varying sliding modes for second-order systems.Proc. IEE-D Control Theory and Applications 143 (1996), 455–462 Zbl 0867.93020 |
| Reference:
|
[3] Choi S. B., Cheong C. C., Park D. W.: Moving switching surfaces for robust control of second-order variable structure systems.Internat. J. Control 58 (1993), 229–245 Zbl 0777.93012, MR 1222145, 10.1080/00207179308922999 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Slotine J. J., Li W.: Applied Nonlinear Control.Prentice–Hall, Englewood Cliffs, NJ 1991 Zbl 0753.93036 |
| Reference:
|
[9] Tokat S., Eksin, I., Gűzelkaya M.: A new design method for sliding mode controllers using a linear time-varying sliding surface.Proc. Inst. Mechanical Engineers – Part I 216 (2002), 455–466 |
| Reference:
|
[10] Tokat S., Eksin I., Gűzelkaya, M., Sőylemez M. T.: Design of a sliding mode controller with a nonlinear time-varying sliding surface.Trans. Inst. of Measurement and Control 25 (2003), 145–162 10.1191/0142331203tm079oa |
| Reference:
|
[11] Utkin V.: Variable structure systems with sliding modes.IEEE Trans. Automat. Control 22 (1977), 212–222 Zbl 0382.93036, MR 0484664, 10.1109/TAC.1977.1101446 |
| . |
