Proper implicit discretization of the super-twisting controller—without and with actuator saturation
The discrete-time implementation of the super-twisting sliding mode controller for a plant with disturbances with bounded slope, zero-order hold actuation, and actuator constraints is considered. Motivated by restrictions of existing implicit or semi-implicit discretization variants, a new proper im...
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| Published in | Automatica (Oxford) Vol. 173; p. 112027 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.03.2025
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| Online Access | Get full text |
| ISSN | 0005-1098 1873-2836 |
| DOI | 10.1016/j.automatica.2024.112027 |
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| Abstract | The discrete-time implementation of the super-twisting sliding mode controller for a plant with disturbances with bounded slope, zero-order hold actuation, and actuator constraints is considered. Motivated by restrictions of existing implicit or semi-implicit discretization variants, a new proper implicit discretization for the super-twisting controller is proposed. This discretization is then extended to the conditioned super-twisting controller, which mitigates windup in presence of actuator constraints by means of the conditioning technique. It is proven that the proposed controllers achieve best possible worst-case performance subject to similarly simple stability conditions as their continuous-time counterparts. Numerical simulations and comparisons demonstrate and illustrate the results. |
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| AbstractList | The discrete-time implementation of the super-twisting sliding mode controller for a plant with disturbances with bounded slope, zero-order hold actuation, and actuator constraints is considered. Motivated by restrictions of existing implicit or semi-implicit discretization variants, a new proper implicit discretization for the super-twisting controller is proposed. This discretization is then extended to the conditioned super-twisting controller, which mitigates windup in presence of actuator constraints by means of the conditioning technique. It is proven that the proposed controllers achieve best possible worst-case performance subject to similarly simple stability conditions as their continuous-time counterparts. Numerical simulations and comparisons demonstrate and illustrate the results. |
| ArticleNumber | 112027 |
| Author | Andritsch, Benedikt Seeber, Richard |
| Author_xml | – sequence: 1 givenname: Richard surname: Seeber fullname: Seeber, Richard email: richard.seeber@tugraz.at organization: Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Institute of Automation and Control, Graz University of Technology, Graz, Austria – sequence: 2 givenname: Benedikt surname: Andritsch fullname: Andritsch, Benedikt email: benedikt.andritsch@tugraz.at organization: Institute of Automation and Control, Graz University of Technology, Graz, Austria |
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| Cites_doi | 10.1002/rnc.5710 10.1016/j.automatica.2020.108921 10.1016/j.sysconle.2010.03.002 10.1109/TAC.2019.2953091 10.1080/00207179308923053 10.1109/CDC45484.2021.9683643 10.1016/0005-1098(87)90029-X 10.1016/j.automatica.2017.07.002 10.1016/j.automatica.2020.109282 10.1016/j.automatica.2019.05.040 10.1109/TAC.2011.2174676 10.1007/978-1-4419-9467-7 10.1016/j.jfranklin.2014.01.002 10.1109/TIE.2022.3229380 10.3182/20110828-6-IT-1002.00489 10.1109/TIE.2023.3274855 10.1016/j.automatica.2023.111206 10.1016/j.ifacol.2023.10.1862 10.1109/TAC.2024.3370494 10.1023/A:1022693822102 |
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| Keywords | Implicit discretization Super-twisting algorithm Conditioning technique Actuator saturation |
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| SubjectTerms | Actuator saturation Conditioning technique Implicit discretization Super-twisting algorithm |
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| Title | Proper implicit discretization of the super-twisting controller—without and with actuator saturation |
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