Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties
Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-tim...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/14/11/3011 |
| _version_ | 1827691758362820608 |
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| author | Paweł Latosiński Andrzej Bartoszewicz |
| author_facet | Paweł Latosiński Andrzej Bartoszewicz |
| author_sort | Paweł Latosiński |
| collection | DOAJ |
| description | Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-time sliding mode control (DSMC) strategies only drive the system representative point to a certain vicinity of that hyperplane. In established literature on DSMC, the width of this vicinity has always been strictly greater than zero in the presence of uncertainties. Thus, ideal sliding motion was considered impossible for discrete-time systems. In this paper, a new approach to DSMC design is presented with the aim of driving the system representative point exactly onto the sliding hyperplane even in the presence of uncertainties. As a result, the quasi-sliding mode band width is effectively reduced to zero and ideal discrete-time sliding motion is ensured. This is achieved with the proper selection of the sliding hyperplane, using the unique properties of relative degree two sliding variables. It is further demonstrated that, even in cases where selection of a relative degree two sliding variable is impossible, one can use the proposed technique to significantly reduce the quasi-sliding mode band width. |
| first_indexed | 2024-03-10T11:08:07Z |
| format | Article |
| id | doaj.art-3266a195bb2f45a8af0efb1800ec12c3 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-10T11:08:07Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-3266a195bb2f45a8af0efb1800ec12c32023-11-21T20:57:17ZengMDPI AGEnergies1996-10732021-05-011411301110.3390/en14113011Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched UncertaintiesPaweł Latosiński0Andrzej Bartoszewicz1Institute of Automatic Control, Lodz University of Technology, 18/22 Bohdana Stefanowskiego St., 90-924 Łódź, PolandInstitute of Automatic Control, Lodz University of Technology, 18/22 Bohdana Stefanowskiego St., 90-924 Łódź, PolandSliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-time sliding mode control (DSMC) strategies only drive the system representative point to a certain vicinity of that hyperplane. In established literature on DSMC, the width of this vicinity has always been strictly greater than zero in the presence of uncertainties. Thus, ideal sliding motion was considered impossible for discrete-time systems. In this paper, a new approach to DSMC design is presented with the aim of driving the system representative point exactly onto the sliding hyperplane even in the presence of uncertainties. As a result, the quasi-sliding mode band width is effectively reduced to zero and ideal discrete-time sliding motion is ensured. This is achieved with the proper selection of the sliding hyperplane, using the unique properties of relative degree two sliding variables. It is further demonstrated that, even in cases where selection of a relative degree two sliding variable is impossible, one can use the proposed technique to significantly reduce the quasi-sliding mode band width.https://www.mdpi.com/1996-1073/14/11/3011robust controldiscrete-time systemssliding mode control |
| spellingShingle | Paweł Latosiński Andrzej Bartoszewicz Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties Energies robust control discrete-time systems sliding mode control |
| title | Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties |
| title_full | Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties |
| title_fullStr | Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties |
| title_full_unstemmed | Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties |
| title_short | Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties |
| title_sort | zero width quasi sliding mode band in the presence of non matched uncertainties |
| topic | robust control discrete-time systems sliding mode control |
| url | https://www.mdpi.com/1996-1073/14/11/3011 |
| work_keys_str_mv | AT pawełlatosinski zerowidthquasislidingmodebandinthepresenceofnonmatcheduncertainties AT andrzejbartoszewicz zerowidthquasislidingmodebandinthepresenceofnonmatcheduncertainties |