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Sliding order and sliding accuracy in sliding mode control
Abstract
The synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay.
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Citations
Cited by
Levant, A. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2041973 · Cited by 482
Self-citationStability notions and Lyapunov functions for sliding mode control systems
Polyakov, A., & Fridman, L. (2014) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2014.01.002 · Cited by 420
The 2017 IEEE International Conference on Fuzzy Systems
(2016) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2016.2545826 · Cited by 308
Lechappe, V., Rouquet, S., Gonzalez, A., Plestan, F., Leon, J. D., Moulay, E., & Glumineau, A. (2016) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2016.2527692 · Cited by 87
Microscale Precision Control of a Computer-Assisted Transoral Laser Microsurgery System
Lee, J., Deshpande, N., Caldwell, D. G., & Mattos, L. S. (2020) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2020.2973381 · Cited by 26
Metadata
- Authors
- LEVANT, A.
- Venue
- International Journal of Control
- Publisher
- Informa UK Limited
- Published
- 1993-12
- Volume
- 58
- Issue
- 6
- Pages
- 1247-1263
- ISSN
- 0020-7179 (ISSN-L)
- 1366-5820
- OpenAlex
- W2018851823
- Cited by
- 3,093
- References
- 0
- FWCI
- 2.72
- Type
- journal article
- Language
- en
- Open access
- closed
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- LEVANT, A. (1993). Sliding order and sliding accuracy in sliding mode control. International Journal of Control. https://doi.org/10.1080/00207179308923053
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