Advertisement

IDA-PBC Controller Tuning Using Steepest Descent

  • J. A. Morales
  • M. A. Castro
  • D. Garcia
  • C. Higuera
  • J. Sandoval
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 785)

Abstract

The optimization of controller parameters or gains is a challenge usually approached using empirical methods that consume valuable time, without the certainty that the obtained gains actually produce the desired behaviour of the controlled plant. There are several analytical and numerical methodologies to find the parameters for PID controllers, however currently there is not enough available information regarding the application of optimization methods for nonlinear controllers. The present work describes the application of the maximum descent method to find the gains of IDA-PBC controller for a ball and beam system. The proposed methodology involves implementing a mathematical model to describe the system’s dynamics, the design of a objective function to measure how closely the plant follows the desired behaviour, and finally the evaluation of a set of gains obtained by the numerical method. The dynamic model and the optimization algorithm were implemented in C language in order to reduce the computer time compared to the use of frameworks such as MATLAB. Numerical simulations to validate the effectiveness of the proposed methodology are included.

Keywords

Ball and beam system Controller tuning Nonlinear control system Steepest descent IDA-PBC 

References

  1. 1.
    Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, Harlow (2002)zbMATHGoogle Scholar
  2. 2.
    Zúñiga, J.: Control de un Robot SCARA Basado en Pasividad. Maestría en ciencias en ingeniería electrónica, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, México (2016)Google Scholar
  3. 3.
    García, D., Sandoval, J., Gutiérrez-Jagüey, J., Bugarin, E.: Control IDA-PBC de un Vehículo Submarino Subactuado. Revista Iberoamericana de Automática e Informática industrial 15, 36 (2017)CrossRefGoogle Scholar
  4. 4.
    González-Cabezas, H.A., Duarte-Mermoud, M.A.: Control de velocidad para motores de inducción usando IDA-PBC. Revista Chilena de Ingeniería 446, 81–90 (2005)Google Scholar
  5. 5.
    Ortega, R., Spong, M.W., Gómez-Estern, F., Blankenstein, G.: Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Autom. Control 47(8), 1218–1233 (2002)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Acosta, J.Á., Ortega, R., Astolfi, A., Mahindrakar, A.D.: Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one. IEEE Trans. Autom. Control 50(12), 1936–1955 (2005)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gómez-Estern, F., Van der Schaft, A.: Physical damping in IDA-PBC controlled underactuated mechanical systems. Eur. J. Control 10(5), 451–468 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    De-León-Gómez, V., Santibañez, V., Sandoval, J.: Interconnection and damping assignment passivity-based control for a compass-like biped robot. Int. J. Adv. Rob. Syst. 14(4), 1–18 (2017).  https://doi.org/10.1177/1729881417716593CrossRefGoogle Scholar
  9. 9.
    Wang, W.: Control of a ball and beam system. Ph.D. thesis (2007)Google Scholar
  10. 10.
    López, F., Monroy, P., Rairán, J.D.: Control de posición de un sistema bola y viga con actuadores magnéticos. Tecnura 15, 12–23 (2011)CrossRefGoogle Scholar
  11. 11.
    Ortiz, E., Liu, W.Y.: Modelado y control PD-Difuso en tiempo real para el sistema barra-esfera. In: Congreso anual de la AMCA, pp. 1–6 (2004)Google Scholar
  12. 12.
    Meneses Morales, P., Zafra Siancas, H. D.: Diseño e implementación de un módulo educativo para el control de sistema Bola y Varilla. PhD thesis, Pontificia Universidad Católica del Perú (2013)Google Scholar
  13. 13.
    Muralidharan, V., Anantharaman, S., Mahindrakar, A.D.: Asymptotic stabilisation of the ball and beam system: design of energy-based control law and experimental results. Int. J. Control 83(6), 1193–1198 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Higuera, C., Chargoy, A., Sandoval, J., Bugarin, E., Coria, L.N.: IDA-PBC en Voltaje para la Regulación de un Sistema Barra-Bola Experimental. In: Congreso Nacional de Control Automático, Monterrey, Nuevo León, Mexico, pp. 1–6 (2017)Google Scholar
  15. 15.
    Morales Viscaya, J.A., Rochín Ramírez, A., Castro Liera, M.A., Sandoval Galarza, J.A.: AG y PSO como métodos de sintonía de un PID para el control de velocidad de un motor CD. In: Castro Liera, I., Cortés Larrinaga, M. (eds.) Nuevos avances en robótica y computación, 1st edn. pp. 81–87. ITLP, La Paz (2015)Google Scholar
  16. 16.
    Wu, H., Su, W., Liu, Z.: PID controllers: design and tuning methods. In: Proceedings of the 2014 9th IEEE Conference on Industrial Electronics and Applications, ICIEA 2014 (2014)Google Scholar
  17. 17.
    Ogata, K.: Modern Control Engineering, 5th edn. Pearson, New York (2016)zbMATHGoogle Scholar
  18. 18.
    Schultz, W.C., Rideout, V.C.: Control system performance measures: past, present, and future. IRE Trans. Autom. Control AC–6, 22–35 (1961)CrossRefGoogle Scholar
  19. 19.
    Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)zbMATHGoogle Scholar
  20. 20.
    Nieves Hurtado, A., Domínguez Sánchez, F.C.: Métodos numéricos: aplicados a la ingeniería. 4th edn. Grupo Editorial Patria (2012)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • J. A. Morales
    • 1
  • M. A. Castro
    • 1
  • D. Garcia
    • 1
  • C. Higuera
    • 1
  • J. Sandoval
    • 1
  1. 1.Tecnólogico Nacional de MéxicoInstituto Tecnológico de La PazLa PazMexico

Personalised recommendations