A novel method for the design of switching surfaces for discretized MIMO nonlinear systems

José Darío Luis-Delgado; Basil Mohammed Al-Hadithi; Agustín Jiménez

International Journal of Applied Mathematics and Computer Science (2017)

  • Volume: 27, Issue: 1, page 5-17
  • ISSN: 1641-876X

Abstract

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Designing variable structure control with sliding mode (VSC-SM) control schemes needs a switching function or a sliding surface which guarantees the global stability of the closed-loop system. Despite the fact that a wide range of design approaches has been proposed for solving this mathematical problem, the number of proposed methodologies for nonlinear systems is not very extensive, especially for discrete time nonlinear MIMO systems, and most of them require some coordinate system transformation. Therefore, it is not an easy task to find a design scheme that can be applied to discrete time nonlinear MIMO systems. The proposed methodology introduces a mathematical tool: a switching surface equation for a class of MIMO nonlinear systems through an explicit equation without any coordinate transformation. This equation makes use of an implicit linearizing process via the Taylor expansion that allows the use of linear procedures for the design of switching surfaces and the forward Euler method to obtain a discrete time dynamics representation. An illustrative example is included to show the advantages of the proposed design methodology.

How to cite

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José Darío Luis-Delgado, Basil Mohammed Al-Hadithi, and Agustín Jiménez. "A novel method for the design of switching surfaces for discretized MIMO nonlinear systems." International Journal of Applied Mathematics and Computer Science 27.1 (2017): 5-17. <http://eudml.org/doc/288100>.

@article{JoséDaríoLuis2017,
abstract = {Designing variable structure control with sliding mode (VSC-SM) control schemes needs a switching function or a sliding surface which guarantees the global stability of the closed-loop system. Despite the fact that a wide range of design approaches has been proposed for solving this mathematical problem, the number of proposed methodologies for nonlinear systems is not very extensive, especially for discrete time nonlinear MIMO systems, and most of them require some coordinate system transformation. Therefore, it is not an easy task to find a design scheme that can be applied to discrete time nonlinear MIMO systems. The proposed methodology introduces a mathematical tool: a switching surface equation for a class of MIMO nonlinear systems through an explicit equation without any coordinate transformation. This equation makes use of an implicit linearizing process via the Taylor expansion that allows the use of linear procedures for the design of switching surfaces and the forward Euler method to obtain a discrete time dynamics representation. An illustrative example is included to show the advantages of the proposed design methodology.},
author = {José Darío Luis-Delgado, Basil Mohammed Al-Hadithi, Agustín Jiménez},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {discrete sliding mode; variable structure control; nonlinear control; optimal control; MIMO systems},
language = {eng},
number = {1},
pages = {5-17},
title = {A novel method for the design of switching surfaces for discretized MIMO nonlinear systems},
url = {http://eudml.org/doc/288100},
volume = {27},
year = {2017},
}

TY - JOUR
AU - José Darío Luis-Delgado
AU - Basil Mohammed Al-Hadithi
AU - Agustín Jiménez
TI - A novel method for the design of switching surfaces for discretized MIMO nonlinear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2017
VL - 27
IS - 1
SP - 5
EP - 17
AB - Designing variable structure control with sliding mode (VSC-SM) control schemes needs a switching function or a sliding surface which guarantees the global stability of the closed-loop system. Despite the fact that a wide range of design approaches has been proposed for solving this mathematical problem, the number of proposed methodologies for nonlinear systems is not very extensive, especially for discrete time nonlinear MIMO systems, and most of them require some coordinate system transformation. Therefore, it is not an easy task to find a design scheme that can be applied to discrete time nonlinear MIMO systems. The proposed methodology introduces a mathematical tool: a switching surface equation for a class of MIMO nonlinear systems through an explicit equation without any coordinate transformation. This equation makes use of an implicit linearizing process via the Taylor expansion that allows the use of linear procedures for the design of switching surfaces and the forward Euler method to obtain a discrete time dynamics representation. An illustrative example is included to show the advantages of the proposed design methodology.
LA - eng
KW - discrete sliding mode; variable structure control; nonlinear control; optimal control; MIMO systems
UR - http://eudml.org/doc/288100
ER -

References

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