Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function

This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can b...

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Autores:
Gil-González, Walter
Molina-Cabrera, Alexander
Giral-Ramírez, Diego Armando
Domínguez Jiménez, Juan Antonio
Montoya Giraldo, Oscar Danilo
Tipo de recurso:
Article of journal
Fecha de publicación:
2020
Institución:
Universidad Tecnológica de Bolívar
Repositorio:
Repositorio Institucional UTB
Idioma:
eng
OAI Identifier:
oai:repositorio.utb.edu.co:20.500.12585/9544
Acceso en línea:
https://hdl.handle.net/20.500.12585/9544
https://www.mdpi.com/2073-8994/12/11/1771
Palabra clave:
Discrete-inverse optimal control
Global exponential stabilization
Reaction wheel pendulum
Parametric uncertainties
Discrete-affine systems
Cost functional
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-nd/4.0/
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network_acronym_str UTB2
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dc.title.spa.fl_str_mv Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function
title Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function
spellingShingle Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function
Discrete-inverse optimal control
Global exponential stabilization
Reaction wheel pendulum
Parametric uncertainties
Discrete-affine systems
Cost functional
title_short Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function
title_full Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function
title_fullStr Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function
title_full_unstemmed Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function
title_sort Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function
dc.creator.fl_str_mv Gil-González, Walter
Molina-Cabrera, Alexander
Giral-Ramírez, Diego Armando
Domínguez Jiménez, Juan Antonio
Montoya Giraldo, Oscar Danilo
dc.contributor.author.none.fl_str_mv Gil-González, Walter
Molina-Cabrera, Alexander
Giral-Ramírez, Diego Armando
Domínguez Jiménez, Juan Antonio
Montoya Giraldo, Oscar Danilo
dc.subject.keywords.spa.fl_str_mv Discrete-inverse optimal control
Global exponential stabilization
Reaction wheel pendulum
Parametric uncertainties
Discrete-affine systems
Cost functional
topic Discrete-inverse optimal control
Global exponential stabilization
Reaction wheel pendulum
Parametric uncertainties
Discrete-affine systems
Cost functional
description This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software.
publishDate 2020
dc.date.accessioned.none.fl_str_mv 2020-11-04T21:34:22Z
dc.date.available.none.fl_str_mv 2020-11-04T21:34:22Z
dc.date.issued.none.fl_str_mv 2020-10-26
dc.date.submitted.none.fl_str_mv 2020-11-03
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.citation.spa.fl_str_mv Montoya, O.D.; Gil-González, W.; Dominguez-Jimenez, J.A.; Molina-Cabrera, A.; Giral-Ramírez, D.A. Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function. Symmetry 2020, 12, 1771.
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/9544
dc.identifier.url.none.fl_str_mv https://www.mdpi.com/2073-8994/12/11/1771
dc.identifier.doi.none.fl_str_mv 10.3390/sym12111771
dc.identifier.instname.spa.fl_str_mv Universidad Tecnológica de Bolívar
dc.identifier.reponame.spa.fl_str_mv Repositorio Universidad Tecnológica de Bolívar
identifier_str_mv Montoya, O.D.; Gil-González, W.; Dominguez-Jimenez, J.A.; Molina-Cabrera, A.; Giral-Ramírez, D.A. Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function. Symmetry 2020, 12, 1771.
10.3390/sym12111771
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/9544
https://www.mdpi.com/2073-8994/12/11/1771
dc.language.iso.spa.fl_str_mv eng
language eng
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dc.rights.cc.*.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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dc.format.extent.none.fl_str_mv 13 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.place.spa.fl_str_mv Cartagena de Indias
dc.source.spa.fl_str_mv Symmetry 2020 , 12 (11), 1771, Vol 12 no 11
institution Universidad Tecnológica de Bolívar
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spelling Gil-González, Walterce1f5078-74c6-4b5c-b56a-784f85e52a08Molina-Cabrera, Alexander01b29f76-a1f3-4151-a070-ce883ba39849Giral-Ramírez, Diego Armando8926006f-c361-4505-9219-92565a6b4de4Domínguez Jiménez, Juan Antoniovirtual::5671-1Montoya Giraldo, Oscar Danilovirtual::6235-12020-11-04T21:34:22Z2020-11-04T21:34:22Z2020-10-262020-11-03Montoya, O.D.; Gil-González, W.; Dominguez-Jimenez, J.A.; Molina-Cabrera, A.; Giral-Ramírez, D.A. Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function. Symmetry 2020, 12, 1771.https://hdl.handle.net/20.500.12585/9544https://www.mdpi.com/2073-8994/12/11/177110.3390/sym12111771Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software.13 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Symmetry 2020 , 12 (11), 1771, Vol 12 no 11Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov functionArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Discrete-inverse optimal controlGlobal exponential stabilizationReaction wheel pendulumParametric uncertaintiesDiscrete-affine systemsCost functionalCartagena de IndiasPúblico generalIsidori, A. Nonlinear Control Systems; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013.Iqbal, J.; Ullah, M.; Khan, S.G.; Khelifa, B.; Cukovi´c, S. Nonlinear control systems-A brief overview of ´ historical and recent advances. Nonlinear Eng. 2017, 6, 301–312.Lu, Q.; Sun, Y.; Mei, S. Nonlinear Control Systems and Power System Dynamics; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013; Volume 10.Montoya, O.D.; Gil-González, W. Nonlinear analysis and control of a reaction wheel pendulum: Lyapunov-based approach. Eng. Sci. Technol. Int. J. 2020, 23, 21–29Montoya, O.D.; Garrido, V.M.; Gil-González, W.; Orozco-Henao, C. Passivity-Based Control Applied of a Reaction Wheel Pendulum: An IDA-PBC Approach. In Proceedings of the 2019 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), Ixtapa, Mexico, 13–15 November 2019; pp. 1–6Olivares, M.; Albertos, P. Linear control of the flywheel inverted pendulum. ISA Trans. 2014, 53, 1396–1403.Correa-Ramírez, V.D.; Giraldo-Buitrago, D.; Escobar-Mejía, A. Fuzzy control of an inverted pendulum Driven by a reaction wheel using a trajectory tracking scheme. TecnoLogicas 2017, 20, 57–69.Spong, M.W.; Corke, P.; Lozano, R. Nonlinear control of the Reaction Wheel Pendulum. Automatica 2001, 37, 1845–1851.Baimukashev, D.; Sandibay, N.; Rakhim, B.; Varol, H.A.; Rubagotti, M. Deep Learning-Based Approximate Optimal Control of a Reaction-Wheel-Actuated Spherical Inverted Pendulum. In Proceedings of the 2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Boston, MA, USA, 6–9 July 2020; pp. 1322–1328.Montoya, O.D.; Gil-González, W.; Ramírez-Vanegas, C. Discrete-Inverse Optimal Control Applied to the Ball and Beam Dynamical System: A Passivity-Based Control Approach. Symmetry 2020, 12, 1359.Sanchez, E.N.; Ornelas-Tellez, F. Discrete-Time Inverse Optimal Control for Nonlinear Systems; CRC Press Taylor and Francis Group: Boca Raton, FL, USA, 2017.Ornelas, F.; Sanchez, E.N.; Loukianov, A.G. Discrete-time inverse optimal control for nonlinear systems trajectory tracking. In Proceedings of the 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, USA, 15–17 December 2010Montoya, O.D.; Gil-González, W.; Serra, F.M. Discrete-time inverse optimal control for a reaction wheel pendulum: a passivity-based control approach. Rev. UIS Ing. 2020, 19, 123–132.Ohsawa, T.; Bloch, A.M.; Leok, M. Discrete Hamilton-Jacobi Theory. SIAM J. Control Optim. 2011, 49, 1829–1856.Block, D.J.; Åström, K.J.; Spong, M.W. The reaction wheel pendulum. Synth. Lect. Control Mechatron. 2007, 1, 1–105.Atkinson, C.; Osseiran, A. Discrete-space time-fractional processes. Fract. Calc. Appl. Anal. 2011, 14Owolabi, K.M.; Atangana, A. Finite Difference Approximations. In Numerical Methods for Fractional Differentiation; Springer: Singapore, 2019; pp. 83–137.Sun, J.; liang Cheng, X. Iterative methods for a forward-backward heat equation in two-dimension. Appl. Math.-A J. Chin. Univ. 2010, 25, 101–111.Keadnarmol, P.; Rojsiraphisal, T. Globally exponential stability of a certain neutral differential equation with time-varying delays. Adv. Differ. Equ. 2014, 2014.Teel, A.R.; Forni, F.; Zaccarian, L. Lyapunov-Based Sufficient Conditions for Exponential Stability in Hybrid Systems. IEEE Trans. Autom. Control 2013, 58, 1591–1596.Valenzuela, J.G.; Montoya, O.D.; Giraldo-Buitrago, D. Local Control of Reaction Wheel Pendulum Using Fuzzy Logic. Sci. Tech. 2013, 18, 623–632.Sanfelice, R.G. On the Existence of Control Lyapunov Functions and State-Feedback Laws for Hybrid Systems. IEEE Trans. Autom. 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