Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties

Paweł Latosiński and Andrzej Bartoszewicz
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Paweł Latosiński: Institute of Automatic Control, Lodz University of Technology, 18/22 Bohdana Stefanowskiego St., 90-924 Łódź, Poland
Andrzej Bartoszewicz: Institute of Automatic Control, Lodz University of Technology, 18/22 Bohdana Stefanowskiego St., 90-924 Łódź, Poland

Energies, 2021, vol. 14, issue 11, 1-16

Abstract: 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.

Keywords: robust control; discrete-time systems; sliding mode control (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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