Tracking through singularities using sliding mode differentiators

Bernardino Castillo-Toledo; Stefano Di Gennaro; Armando López-Cuevas

Kybernetika (2015)

  • Volume: 51, Issue: 1, page 20-35
  • ISSN: 0023-5954

Abstract

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In this work, an alternative solution to the tracking problem for a SISO nonlinear dynamical system exhibiting points of singularity is given. An inversion-based controller is synthesized using the Fliess generalized observability canonical form associated to the system. This form depends on the input and its derivatives. For this purpose, a robust exact differentiator is used for estimating the control derivatives signals with the aim of defining a control law depending on such control derivative estimates and on the system state variables. This control law is such that, when applied to the system, bounded tracking error near the singularities is guaranteed.

How to cite

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Castillo-Toledo, Bernardino, Di Gennaro, Stefano, and López-Cuevas, Armando. "Tracking through singularities using sliding mode differentiators." Kybernetika 51.1 (2015): 20-35. <http://eudml.org/doc/270046>.

@article{Castillo2015,
abstract = {In this work, an alternative solution to the tracking problem for a SISO nonlinear dynamical system exhibiting points of singularity is given. An inversion-based controller is synthesized using the Fliess generalized observability canonical form associated to the system. This form depends on the input and its derivatives. For this purpose, a robust exact differentiator is used for estimating the control derivatives signals with the aim of defining a control law depending on such control derivative estimates and on the system state variables. This control law is such that, when applied to the system, bounded tracking error near the singularities is guaranteed.},
author = {Castillo-Toledo, Bernardino, Di Gennaro, Stefano, López-Cuevas, Armando},
journal = {Kybernetika},
keywords = {singularities; sliding mode differentiator; tracking; singularities; sliding mode differentiator; tracking},
language = {eng},
number = {1},
pages = {20-35},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Tracking through singularities using sliding mode differentiators},
url = {http://eudml.org/doc/270046},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Castillo-Toledo, Bernardino
AU - Di Gennaro, Stefano
AU - López-Cuevas, Armando
TI - Tracking through singularities using sliding mode differentiators
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 1
SP - 20
EP - 35
AB - In this work, an alternative solution to the tracking problem for a SISO nonlinear dynamical system exhibiting points of singularity is given. An inversion-based controller is synthesized using the Fliess generalized observability canonical form associated to the system. This form depends on the input and its derivatives. For this purpose, a robust exact differentiator is used for estimating the control derivatives signals with the aim of defining a control law depending on such control derivative estimates and on the system state variables. This control law is such that, when applied to the system, bounded tracking error near the singularities is guaranteed.
LA - eng
KW - singularities; sliding mode differentiator; tracking; singularities; sliding mode differentiator; tracking
UR - http://eudml.org/doc/270046
ER -

References

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  1. Becerra, H. M., López-Nicolás, G., Sagués, C., 10.1109/tro.2010.2091750, IEEE Trans. Robotics 27 (2011), 1, 175-183. DOI10.1109/tro.2010.2091750
  2. Benosman, M., Vey, G. Le, 10.1109/tcst.2003.813372, IEEE Trans. Control Systems Technol. 11 (2003), 4, 588-597. DOI10.1109/tcst.2003.813372
  3. Castillo, B., Output tracking through singular points for a class of nonlinear SISO systems, In: Proc. First European Control Conference 1991, pp. 1496-1498. 
  4. Devasia, S., Chen, D., Paden, B., 10.1109/9.508898, IEEE Trans. Automat. Control 41 (1996), 7, 930-942. Zbl0859.93006MR1398777DOI10.1109/9.508898
  5. Devasia, S., 10.1109/tac.2002.804478, IEEE Trans. Automat. Control 47 (2002), 11, 1865-1871. MR1937698DOI10.1109/tac.2002.804478
  6. Fliess, M., 10.1109/9.58527, IEEE Trans. Automat. Control 35 (1990), 9, 994-1001. MR1065035DOI10.1109/9.58527
  7. Hauser, J., Sastry, S., Kokotovic, P., 10.1109/cdc.1989.70513, In: Proc. 28th Conference on Decision and Control 1989, pp. 1987-1993. MR1148727DOI10.1109/cdc.1989.70513
  8. Hauser, J., Sastry, S., Kokotovic, P., 10.1109/cdc.1989.70513, IEEE Trans. Automat. Control 35 (1992), 3, 392-398. MR1148727DOI10.1109/cdc.1989.70513
  9. Herrero, P., Jaulin, L., Vehí, J., Sainz, M. A., 10.1007/s12555-010-0101-3, Int. J. Control Automat. Systems 8 (2010), 1, 1-7. DOI10.1007/s12555-010-0101-3
  10. Hirschorn, R. M., 10.1109/tac.2002.803538, IEEE Trans. Automat. Control 47 (2002), 10, 1696-1700. MR1929943DOI10.1109/tac.2002.803538
  11. Hirschorn, R., Davis, J., 10.1137/0325030, SIAM J. Control Optim. 25 (1987), 3, 547-557. Zbl0624.93008MR0885184DOI10.1137/0325030
  12. Isidori, A., 10.1007/978-3-662-02581-9, Springer Verlag, Berlin 1989. DOI10.1007/978-3-662-02581-9
  13. Krener, A., Approximate linearization by state feedback., SIAM J. Control Optim. 25 (1987), 3, 547-557. Zbl0555.93027
  14. Lamnabhi-Lagarrigue, F., Crouch, P. E., Ighneiwa, I., 10.1007/bfb0043016, In: New Trends in Control Theory, Lect. Notes in Control and Inform. Sci. Springer Berlin Heidelberg 122 (1989), pp. 44-53. Zbl0718.93023MR1229764DOI10.1007/bfb0043016
  15. Levant, A., 10.1016/s0005-1098(97)00209-4, Automatica 34 (1998), 3, 379-384. Zbl0915.93013MR1623077DOI10.1016/s0005-1098(97)00209-4
  16. Levant, A., 10.1080/0020717031000099029, Int. J. Control 76 (2003), 9/10, 924-945. Zbl1049.93014MR1999375DOI10.1080/0020717031000099029
  17. Levant, A., 10.1016/j.automatica.2004.11.029, Automatica 41 (2005), 5, 823-830. Zbl1093.93003MR2157713DOI10.1016/j.automatica.2004.11.029
  18. Márton, L., Hodel, A. S., Lantos, B., Hung, J., 10.1109/tie.2008.923285, IEEE Trans. Industr. Electron. 55 (2008), 10, 3724-3730. DOI10.1109/tie.2008.923285
  19. Perruquetti, W., Floquet, T., 10.1109/cdc.2007.4434702, In: Proc. 46th IEEE Conference on Decision and Control, New Orleans 2007, pp. 12-14. DOI10.1109/cdc.2007.4434702
  20. Saif, M., Chen, W., Wu, Q., 10.1007/978-3-540-79016-7_15, In: Modern Sliding Mode Control Theory, Lect. Notes in Control and Inform. Sci. Springer, Berlin - Heidelgerg 375 (2008) pp. 321-344. Zbl1145.93315MR2454142DOI10.1007/978-3-540-79016-7_15
  21. Sira-Ramirez, H., 10.1109/9.126590, IEEE Trans. Automat. Control 37 (1992), 4, 518-524. MR1153118DOI10.1109/9.126590
  22. Tomlin, C., Sastry, S., 10.1016/s0167-6911(98)00046-2, Systems Control Lett. 35 (1998), 145-154. Zbl0909.93032MR1749610DOI10.1016/s0167-6911(98)00046-2
  23. Utkin, V., Gulden, J., Shi, J., Sliding Modes in Electromechanical Systems., Taylor and Francis, London 1999. 
  24. Yu, Z., Fan, G., 10.1109/icma.2009.5246179, In: Proc. 2009 IEEE International Conference on Mechatronics and Automation 2009, pp. 3787-3792. DOI10.1109/icma.2009.5246179

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