On the Mathematical Background of Sliding Mode-Based Friction Compensation of a Micro-Telemanipulation System

Péter Korondi, Nándor Fink, Róbert Mikuska, Péter Tamás Szemes, Csaba Kézi and Imre Kocsis ()
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Péter Korondi: Department of Electrical Engineering and Mechatronics, Vehicles and Mechatronics Institute, Faculty of Engineering, University of Debrecen, 4028 Debrecen, Hungary
Nándor Fink: Department of Electrical Engineering and Mechatronics, Vehicles and Mechatronics Institute, Faculty of Engineering, University of Debrecen, 4028 Debrecen, Hungary
Róbert Mikuska: Department of Electrical Engineering and Mechatronics, Vehicles and Mechatronics Institute, Faculty of Engineering, University of Debrecen, 4028 Debrecen, Hungary
Péter Tamás Szemes: Department of Vehicles Engineering, Vehicles and Mechatronics Institute, Faculty of Engineering, University of Debrecen, 4028 Debrecen, Hungary
Csaba Kézi: Department of Basic Technical Studies, Faculty of Engineering, University of Debrecen, 4028 Debrecen, Hungary
Imre Kocsis: Department of Basic Technical Studies, Faculty of Engineering, University of Debrecen, 4028 Debrecen, Hungary

Mathematics, 2024, vol. 12, issue 20, 1-26

Abstract: Modeling of various phenomena in engineering work is always a kind of simplification of real processes, aiming at a model where a certain level of mathematical theory and computational procedures is sufficient. If the complexity of the required theory corresponds to the general mathematical competence of engineers, then technical problems can be treated separately in engineering (or physical) models without regard to the mathematical background. However, in some advanced engineering fields, the harmonized development of engineering and mathematical models and toolboxes is necessary to find efficient solutions. For example, modeling variable structure systems in ideal sliding mode requires a mathematical toolbox that goes far beyond general engineering competence through the theory of discontinuous right-hand-side differential equations. Although sliding mode control is popular in practice and the concept of sliding mode allows a significant reduction of model complexity, its exact mathematical description is rarely encountered. The problem of friction compensation of a micro-telemanipulator using sliding mode control demonstrates a harmonized application of the mathematical and engineering approaches. Based on Filippov’s theory, the ideal sliding mode can be discussed. Although an ideal system cannot be implemented in reality, the real systems can be kept close enough to it; therefore, the discussion of the solution of the ideal model is important for practical applications. Although several elements of the topic are available in the literature, in this paper a unique complex approach is given for users of sliding mode control with experimental considerations, different engineering models, and codes. The paper concludes that sliding mode control is a case where engineering and mathematical modeling are inseparable and requires the competence of both fields.

Keywords: modeling; micro-telemanipulation; sliding mode control; mechatronics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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