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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Bibliographic Details
Published inAutomatica (Oxford) Vol. 173; p. 112027
Main Authors Seeber, Richard, Andritsch, Benedikt
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2025
Subjects
Actuator saturation
Conditioning technique
Implicit discretization
Super-twisting algorithm
Implicit discretization
Super-twisting algorithm
Conditioning technique
Actuator saturation
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ISSN0005-1098
DOI10.1016/j.automatica.2024.112027

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Summary: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.
ISSN:0005-1098
DOI:10.1016/j.automatica.2024.112027