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Vol. 15 No. 2 (2024)
Vol. 15 Núm. 2 (2024): Vol 15, Núm.2 (2024): Julio-Diciembre

Artículos de investigación / Research papers

Diseño de un controlador general basado en Lyapunov para el péndulo con rueda de reacción: Un caso de estudio en simulación

https://doi.org/10.19053/uptc.01217488.v15.n2.2024.17198

Published 2024-10-10

  • Oscar Danilo Montoya Giraldo
    • ,
  • Walter Gil-González
    • ,
  • Andrés Leonardo Jutinico-Alarcóm

Oscar Danilo Montoya Giraldo
a:1:{s:5:"es_ES";s:47:"Universidad Distrital Francisco José de Caldas";}

Walter Gil-González
Universidad Tecnológica de Pereira

Andrés Leonardo Jutinico-Alarcóm
Universidad Distrital Francisco José de Caldas

Abstract

This article addresses the control problem on a reaction wheel pendulum (RWP) using a control design supported by Lyapunov stability theory. Firstly, a stability analysis using the small signal theory (the linearization approach via Taylor's series) around the RWP equilibrium points considering the open-loop operation case. This analysis defines that the system has a sink unstable equilibrium point in the upright position, while the equilibrium point is a stable focus in the downright place. Secondly, a nonlinear controller is designed using a Lyapunov candidate function to obtain a stable focus on the upright position during its closed-loop operation. Numerical validations demonstrate that the proposed controller stabilizes the RWP system between 400~ms and 600~ms, which depends on the parametric uncertainties of the system parameters and variations in the control parameters. The main contribution of this article corresponds to the generalization of the control lay, which, as a function of the selected parameters, could result in an exact feedback linearization approach or a nonlinear generalized control approach for the RWP. Computational validations were made in MATLAB software using the discrete equivalent of the dynamic system via the ahead derivative method.

References

  1. H. Khalil, Nonlinear Systems (Always learning).Pearson Education, Limited, 2013, ISBN: 9781292039213.
  2. E. N. Sanchez y F. Ornelas-Tellez, Discrete-Time Inverse Optimal Control for Nonlinear Systems. CRC Press Taylor y Francis Group, mayo de 2017, ISBN: 1138073814.
  3. S. J. Lee y T.-C. Tsao, “Repetitive learning of backstepping controlled nonlinear electrohydraulic material testing system,” Control Eng. Pract., vol. 12, n.o 11, págs. 1393-1408, nov. de 2004. DOI: 10.1016/j.conengprac.2004.02.011.
  4. O. D. Montoya,W. Gil-González y F. Martin Serra, “Discrete-time inverse optimal control for a reaction wheel pendulum: a passivity-based control approach,” Revista UIS Ingenierías, vol. 19, n.o 4, págs. 123-132, mayo de 2020, ISSN: 1657-4583. DOI: 10.18273/revuin.v19n4-2020011.
  5. M. W. Spong, P. Corke y R. Lozano, “Nonlinear control of the Reaction Wheel Pendulum,” Automatica, vol. 37, n.o 11, págs. 1845-1851, 2001, ISSN: 0005-1098. DOI: https://doi.org/10.1016/S00051098(01)00145-5.
  6. O. D. Montoya, L. F. Grisales-Noreña, V. D. Correa-Ramírez y D. Giraldo-Buitrago, “Global control of reaction wheel pendulum through energy regulation and extended linearization of the state variables,” Tecno Lógicas, vol. 17, n.o 32, págs. 33-46, jun. de 2014, ISSN: 2256-5337.
  7. O. D. Montoya y W. Gil-González, “Nonlinear analysis and control of a reaction wheel pendulum: Lyapunov-based approach,” Engineering Science and Technology, an International Journal, vol. 23, n.o 1, págs. 21-29, feb. de 2020. DOI: 10.1016/j.jestch.2019.03.004.
  8. D. J. Block, K. J. Åström y M. W. Spong, “The reaction wheel pendulum,” Synthesis Lectures on Control and mechatronics, vol. 1, n.o 1, págs. 1-105, 2007.
  9. O. D. Montoya, C. A. Ramírez y L. F. Grisales, “Global Control of Reaction Wheel Pendulum Using Artificial Neural Networks and Extended Linearization,” Scientia et technica, vol. 22, n.o 20, págs. 130-140, jun. de 2017.
  10. K. Srinivas y L. Behera, “Swing-up control strategies for a reaction wheel pendulum,” Int. J. Syst. Sci., vol. 39, n.o 12, págs. 1165-1177, 2008. DOI: 10.1080/00207720802095137. eprint: https: //doi.org/10.1080/00207720802095137.
  11. B. Bapiraju, K. N. Srinivas, P. P. Kumar y L. Behera, “On balancing control strategies for a reaction wheel pendulum,” en Proceedings of the IEEE INDICON 2004. First India Annual Conference, 2004., dic. de 2004, págs. 199-204. DOI: 10.1109/
  12. INDICO.2004.1497738.
  13. J. G. Valenzuela, O. D. Montoya y D. Giraldo- Buitrago, “Local Control of Reaction Wheel Pendulum Using Fuzzy Logic,” Scientia et Technica, vol. 18, n.o 4, págs. 623-632, dic. de 2013, ISSN:0122-1701.
  14. V. D. Correa y D. G. A. Escobar, “Fuzzy control of an inverted pendulum Driven by a reaction wheel using a trajectory tracking scheme,” TecnoLogicas, vol. 20, n.o 39, págs. 1-13, mayo de 2017.
  15. O. D. Montoya, V. M. Garrido, W. Gil-González y C. Orozco-Henao, “Passivity-Based Control Applied of a Reaction Wheel Pendulum: an IDA-PBC Approach,” en 2019 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), 2019, págs. 1-6.
  16. T. U. E. Faculty of Automatics, “Feedback Linearization Control of the Inertia Wheel Pendulum,” Cybernetics and Information Technologies, vol. 14, n.o 3, págs. 96-109, sep. de 2014. DOI: 10.2478/cait-2014-0036.
  17. S. Irfan, A. Mehmood, M. T. Razzaq y J. Iqbal, “Advanced sliding mode control techniques for Inverted Pendulum: Modelling and simulation,” Engineering Science and Technology, an International Journal, vol. 21, n.o 4, págs. 753-759, 2018, ISSN: 2215-0986. DOI: https://doi.org/10.1016/j. jestch.2018.06.010.
  18. A. M. El-Nagar, M. El-Bardini y N. M. EL-Rabaie, “Intelligent control for nonlinear inverted pendulum based on interval type-2 fuzzy PD controller,” Alexandria Engineering Journal, vol. 53, n.o 1, págs. 23-32, 2014.
  19. F. M. Escalante, A. L. Jutinico, M. H. Terra y A. A. Siqueira, “Robust linear quadratic regulator applied to an inverted pendulum,” Asian Journal of Control, vol. 25, n.o 4, págs. 2564-2576, 2023. DOI: https://doi.org/10.1002/asjc.2978.
  20. O. D. Montoya, W. Gil-González, J. A. Dominguez-Jimenez, A. Molina-Cabrera y D. A. Giral-Ramírez, “Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function,” Symmetry, vol. 12, n.o 11, pág. 1771, oct. de 2020, ISSN: 2073-8994. DOI: 10.3390/sym12111771.
  21. S. Kharuf Gutiérrez, A. Ferreira de Loza, L. Aguilar y L. Coria, “Output-Feedback Stabilization of the Reaction Wheel Pendulum Via Active Disturbance Rejection Control,” Memorias del Congreso Nacional de Control Automático, vol. 6, n.o 1, págs. 223-228, oct. de 2023, ISSN: 2594-2492. DOI: 10.58571/cnca.amca.2023.049.
  22. D. Zaborniak, K. Patan y M. Witczak, “Design, Implementation, and Control of a Wheel-Based Inverted Pendulum,” Electronics, vol. 13, n.o 3, pág. 514, ene. de 2024, ISSN: 2079-9292. DOI: 10.3390/electronics13030514.
  23. D. Giraldo Buitrago y V. D. Correa R., “Control local de un sistema no lineal: el péndulo con rueda de reacción,” Scientia et Technica, vol. 1, n.o 34, págs. 55-60, mayo de 2007. dirección: https : / / revistas.utp.edu.co/index.php/revistaciencia/article/view/5533.
  24. L. Perko, Differential Equations and Dynamical Systems. Springer New York, 2001, ISBN: 9781461300038. DOI: 10.1007/978- 1- 4613-
  25. -8.
  26. A. Garcés-Ruiz, W. J. Gil-González y O. D. Montoya-Giraldo, Introducción a la estabilidad de sistemas eléctricos de potencia. Universidad Tecnológica de Pereira - UTP, 2023, ISBN: 9789587228960. DOI: 10 . 22517 / 9789587228960.
  27. W. M. Haddad y V. Chellaboina, Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach. Princeton University Press, sep. de 2011, ISBN: 9780691133294. DOI: 10.2307/ j ctvcm4hws.
  28. D. J. Block, K. J. Åström y M. W. Spong, The Reaction Wheel Pendulum. Springer International Publishing, 2008, ISBN: 9783031018275. DOI: 10.1007/978-3-031-01827-5.

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