Rotary inverted pendulum: trajectory tracking via nonlinear control techniques

Luis E. Ramos-Velasco; Javier Ruiz; Sergej Čelikovský

Kybernetika (2002)

  • Volume: 38, Issue: 2, page [217]-232
  • ISSN: 0023-5954

Abstract

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The nonlinear control techniques are applied to the model of rotary inverted pendulum. The model has two degrees of freedom and is not exactly linearizable. The goal is to control output trajectory of the rotary inverted pendulum asymptotically along a desired reference. Moreover, the designed controller should be robust with respect to specified perturbations and parameters uncertainties. A combination of techniques based on nonlinear normal forms, output regulation and sliding mode approach is used here. As a specific feature, the approximate solution of the so-called regulator equation is used. The reason is that its exact analytic solution can not be, in general, expressed in the closed form. Though the approximate solution does not give asymptotically decaying tracking error, it provides reasonable bounded error. The performance of the designed feedback regulator is successfully tested via computer simulations.

How to cite

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Ramos-Velasco, Luis E., Ruiz, Javier, and Čelikovský, Sergej. "Rotary inverted pendulum: trajectory tracking via nonlinear control techniques." Kybernetika 38.2 (2002): [217]-232. <http://eudml.org/doc/33577>.

@article{Ramos2002,
abstract = {The nonlinear control techniques are applied to the model of rotary inverted pendulum. The model has two degrees of freedom and is not exactly linearizable. The goal is to control output trajectory of the rotary inverted pendulum asymptotically along a desired reference. Moreover, the designed controller should be robust with respect to specified perturbations and parameters uncertainties. A combination of techniques based on nonlinear normal forms, output regulation and sliding mode approach is used here. As a specific feature, the approximate solution of the so-called regulator equation is used. The reason is that its exact analytic solution can not be, in general, expressed in the closed form. Though the approximate solution does not give asymptotically decaying tracking error, it provides reasonable bounded error. The performance of the designed feedback regulator is successfully tested via computer simulations.},
author = {Ramos-Velasco, Luis E., Ruiz, Javier, Čelikovský, Sergej},
journal = {Kybernetika},
keywords = {rotary inverted pendulum; nonlinear control; trajectory tracking; rotary inverted pendulum; nonlinear control; trajectory tracking},
language = {eng},
number = {2},
pages = {[217]-232},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Rotary inverted pendulum: trajectory tracking via nonlinear control techniques},
url = {http://eudml.org/doc/33577},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Ramos-Velasco, Luis E.
AU - Ruiz, Javier
AU - Čelikovský, Sergej
TI - Rotary inverted pendulum: trajectory tracking via nonlinear control techniques
JO - Kybernetika
PY - 2002
PB - Institute of Information Theory and Automation AS CR
VL - 38
IS - 2
SP - [217]
EP - 232
AB - The nonlinear control techniques are applied to the model of rotary inverted pendulum. The model has two degrees of freedom and is not exactly linearizable. The goal is to control output trajectory of the rotary inverted pendulum asymptotically along a desired reference. Moreover, the designed controller should be robust with respect to specified perturbations and parameters uncertainties. A combination of techniques based on nonlinear normal forms, output regulation and sliding mode approach is used here. As a specific feature, the approximate solution of the so-called regulator equation is used. The reason is that its exact analytic solution can not be, in general, expressed in the closed form. Though the approximate solution does not give asymptotically decaying tracking error, it provides reasonable bounded error. The performance of the designed feedback regulator is successfully tested via computer simulations.
LA - eng
KW - rotary inverted pendulum; nonlinear control; trajectory tracking; rotary inverted pendulum; nonlinear control; trajectory tracking
UR - http://eudml.org/doc/33577
ER -

References

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  1. Castillo B., Castro–Linares, 10.1016/0167-6911(94)00039-X, Systems Control Lett. 24 (1995), 361–371 (1995) MR1325676DOI10.1016/0167-6911(94)00039-X
  2. Čelikovský S., Huang, Jie, Continuous feedback asymptotic output regulation for a class of nonlinear systems having nonstabilizable linearization, In: Proc. 37th IEEE Conference on Decision and Control, Tampa 1998, pp. 3087–3092 (1998) 
  3. Priscoli F. Delli, Isidori A., Robust tracking for a class on nonlinear systems, In: 1st European Control Conference, Grenoble 1991, pp. 1814–1818 (1991) 
  4. Huang J., Rugh W. J., 10.1016/0005-1098(90)90081-R, Automatica 26 (1990), 963–972 (1990) Zbl0717.93019MR1080983DOI10.1016/0005-1098(90)90081-R
  5. Huang J., Rugh W. J., 10.1109/9.159580, IEEE Trans. Automat. Control 37 (1992), 1395–1398 (1992) Zbl0767.93034MR1183102DOI10.1109/9.159580
  6. Isidori A., Byrnes C. I., 10.1109/9.45168, IEEE Trans. Automat. Control 35 (1990), 131–140 (1990) Zbl0704.93034MR1038409DOI10.1109/9.45168
  7. Krener A. J., The construction of optimal linear and nonlinear regulators, In: Systems, Models and Feedback (A. Isidori and T. J. Tarn, eds.), Birkhäuser, Basel 1992, pp. 301–322 (1992) Zbl0778.49024MR1169953
  8. Kwatny H. G., Kim H., 10.1016/0167-6911(90)90046-W, Systems Control Lett. 10 (1990), 67–80 (1990) Zbl0704.93009MR1065350DOI10.1016/0167-6911(90)90046-W
  9. Sira–Ramírez H., 10.1109/9.250533, IEEE Trans. Automat. Control 38 (1993), 615–620 (1993) Zbl0782.93026MR1220746DOI10.1109/9.250533
  10. Slotine J. J., Hedrick K., 10.1080/00207179308934435, Internat. J. Control 57 (1993), 1133–1139 (1993) Zbl0772.93033MR1216952DOI10.1080/00207179308934435
  11. Spong M. W., Vidyasagar M., Robot Dynamics and Control, Wiley, New York 1989 
  12. Utkin V. I., Sliding Modes in Control and Optimization, Springer–Verlag, Berlin 1992 Zbl0748.93044MR1295845

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