Cascade Delayed Controller Design for a Class of Underactuated Systems
In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the clos...
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Series: | Complexity |
Online Access: | http://dx.doi.org/10.1155/2020/2160743 |
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doaj-8c8554832f034ee8b015a3c652cdd91f2020-11-25T03:44:06ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/21607432160743Cascade Delayed Controller Design for a Class of Underactuated SystemsG. Ochoa-Ortega0R. Villafuerte-Segura1A. Luviano-Juárez2M. Ramírez-Neria3N. Lozada-Castillo4Universidad Politécnica del Valle de México, Av. Mexiquense s/n Colonia Villa Esmeralda, Tultitlán 54910, MexicoUniversidad Autónoma del Estado de Hidalgo, CITIS, Carretera Pachuca-Tulancingo km. 4.5, Col. Carboneras, Mineral de la Reforma 42184, MexicoInstituto Politécnico Nacional-UPIITA, Av. IPN 2580 Colonia Barrio la Laguna Ticomán, Ciudad de México 07340, MexicoInIAT Universidad Iberoamericana Ciudad de México, Prolongación Paseo de la Reforma 880, Colonia Lomas de Santa Fé, Ciudad de México CP 01219, MexicoInstituto Politécnico Nacional-UPIITA, Av. IPN 2580 Colonia Barrio la Laguna Ticomán, Ciudad de México 07340, MexicoIn this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot.http://dx.doi.org/10.1155/2020/2160743 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
G. Ochoa-Ortega R. Villafuerte-Segura A. Luviano-Juárez M. Ramírez-Neria N. Lozada-Castillo |
spellingShingle |
G. Ochoa-Ortega R. Villafuerte-Segura A. Luviano-Juárez M. Ramírez-Neria N. Lozada-Castillo Cascade Delayed Controller Design for a Class of Underactuated Systems Complexity |
author_facet |
G. Ochoa-Ortega R. Villafuerte-Segura A. Luviano-Juárez M. Ramírez-Neria N. Lozada-Castillo |
author_sort |
G. Ochoa-Ortega |
title |
Cascade Delayed Controller Design for a Class of Underactuated Systems |
title_short |
Cascade Delayed Controller Design for a Class of Underactuated Systems |
title_full |
Cascade Delayed Controller Design for a Class of Underactuated Systems |
title_fullStr |
Cascade Delayed Controller Design for a Class of Underactuated Systems |
title_full_unstemmed |
Cascade Delayed Controller Design for a Class of Underactuated Systems |
title_sort |
cascade delayed controller design for a class of underactuated systems |
publisher |
Hindawi-Wiley |
series |
Complexity |
issn |
1076-2787 1099-0526 |
publishDate |
2020-01-01 |
description |
In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot. |
url |
http://dx.doi.org/10.1155/2020/2160743 |
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