<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

A Novel Method for the Design of Switching Surfaces for Discretized MIMO Nonlinear Systems

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Designing variable structure control with sliding mode (VSC-SM) control schemes needs a switching function or a sliding surface which guarantees the global...

A Novel Method for the Design of Switching Surfaces for Discretized MIMO Nonlinear Systems

Publié en ligne: 04 mai 2017

Pages: 5 - 17

Reçu: 14 oct. 2015

Accepté: 31 oct. 2016

DOI: https://doi.org/10.1515/amcs-2017-0001

Mots clés
discrete sliding mode, variable structure control, nonlinear control, optimal control, MIMO systems

© by José Darío Luis-Delgado

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A Novel Method for the Design of Switching Surfaces for Discretized MIMO Nonlinear Systems

Publié en ligne: 04 mai 2017

Pages: 5 - 17

Reçu: 14 oct. 2015

Accepté: 31 oct. 2016

DOI: https://doi.org/10.1515/amcs-2017-0001

Mots clésdiscrete sliding mode, variable structure control, nonlinear control, optimal control, MIMO systems

© by José Darío Luis-Delgado

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
discrete sliding mode, variable structure control, nonlinear control, optimal control, MIMO systems