A robust controller design method and stability analysis of an underactuated underwater vehicle

Cheng Siong Chin; Micheal Wai Shing Lau; Eicher Low; Gerald Gim Lee Seet

International Journal of Applied Mathematics and Computer Science (2006)

  • Volume: 16, Issue: 3, page 345-356
  • ISSN: 1641-876X

Abstract

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The problem of designing a stabilizing feedback controller for an underactuated system is a challenging one since a nonlinear system is not stabilizable by a smooth static state feedback law. A necessary condition for the asymptotical stabilization of an underactuated vehicle to a single equilibrium is that its gravitational field has nonzero elements corresponding to unactuated dynamics. However, global asymptotical stability (GAS) cannot be guaranteed. In this paper, a robust proportional-integral-derivative (PID) controller on actuated dynamics is proposed and unactuated dynamics are shown to be global exponentially bounded by the Sordalen lemma. This gives a necessary and sufficient condition to guarantee the global asymptotic stability (GAS) of the URV system. The proposed method is first adopted on a remotely-operated vehicle RRC ROV II designed by the Robotic Research Centre in the Nanyang Technological University (NTU). Through the simulation using the ROV Design and Analysis toolbox (RDA) written at the NTU in the MATLAB/SIMULINK environment, the RRC ROV II is robust against parameter perturbations.

How to cite

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Siong Chin, Cheng, et al. "A robust controller design method and stability analysis of an underactuated underwater vehicle." International Journal of Applied Mathematics and Computer Science 16.3 (2006): 345-356. <http://eudml.org/doc/207798>.

@article{SiongChin2006,
abstract = {The problem of designing a stabilizing feedback controller for an underactuated system is a challenging one since a nonlinear system is not stabilizable by a smooth static state feedback law. A necessary condition for the asymptotical stabilization of an underactuated vehicle to a single equilibrium is that its gravitational field has nonzero elements corresponding to unactuated dynamics. However, global asymptotical stability (GAS) cannot be guaranteed. In this paper, a robust proportional-integral-derivative (PID) controller on actuated dynamics is proposed and unactuated dynamics are shown to be global exponentially bounded by the Sordalen lemma. This gives a necessary and sufficient condition to guarantee the global asymptotic stability (GAS) of the URV system. The proposed method is first adopted on a remotely-operated vehicle RRC ROV II designed by the Robotic Research Centre in the Nanyang Technological University (NTU). Through the simulation using the ROV Design and Analysis toolbox (RDA) written at the NTU in the MATLAB/SIMULINK environment, the RRC ROV II is robust against parameter perturbations.},
author = {Siong Chin, Cheng, Wai Shing Lau, Micheal, Low, Eicher, Gim Lee Seet, Gerald},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {simulation; underactuated; stabilizable; underwater vehicle; robust controller},
language = {eng},
number = {3},
pages = {345-356},
title = {A robust controller design method and stability analysis of an underactuated underwater vehicle},
url = {http://eudml.org/doc/207798},
volume = {16},
year = {2006},
}

TY - JOUR
AU - Siong Chin, Cheng
AU - Wai Shing Lau, Micheal
AU - Low, Eicher
AU - Gim Lee Seet, Gerald
TI - A robust controller design method and stability analysis of an underactuated underwater vehicle
JO - International Journal of Applied Mathematics and Computer Science
PY - 2006
VL - 16
IS - 3
SP - 345
EP - 356
AB - The problem of designing a stabilizing feedback controller for an underactuated system is a challenging one since a nonlinear system is not stabilizable by a smooth static state feedback law. A necessary condition for the asymptotical stabilization of an underactuated vehicle to a single equilibrium is that its gravitational field has nonzero elements corresponding to unactuated dynamics. However, global asymptotical stability (GAS) cannot be guaranteed. In this paper, a robust proportional-integral-derivative (PID) controller on actuated dynamics is proposed and unactuated dynamics are shown to be global exponentially bounded by the Sordalen lemma. This gives a necessary and sufficient condition to guarantee the global asymptotic stability (GAS) of the URV system. The proposed method is first adopted on a remotely-operated vehicle RRC ROV II designed by the Robotic Research Centre in the Nanyang Technological University (NTU). Through the simulation using the ROV Design and Analysis toolbox (RDA) written at the NTU in the MATLAB/SIMULINK environment, the RRC ROV II is robust against parameter perturbations.
LA - eng
KW - simulation; underactuated; stabilizable; underwater vehicle; robust controller
UR - http://eudml.org/doc/207798
ER -

References

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  5. Koh T.H., Lau M.W.S., Low E., Seet G., Swei S. and Cheng P.L. (2002b): Development and improvement of an underactuated remotely operated vehicle (ROV) . - Proc. MTSIEEE Int. Conf.s Oceans, Biloxi, MS, pp. 2039-2044. 
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  8. Soodalen O.J. and Egeland O. (1993): Exponential stabilization of chained nonholonomic systems. - Proc. 2-nd European Control Conf., Groningen, The Netherlands, pp. 1438-1443. 
  9. Sodalen O.J. and Egeland O. (1995): Exponential stabilization of nonholonomic chained systems. - IEEE Trans. Automat.Contr., Vol. 40, No. 1, pp. 35-49. Zbl0828.93055
  10. Sordalen O.J., Dalsmo M. and Egeland O. (1993): An exponentially convergent control law for a nonholonomic underwater vehicle. - Proc. 3-rd Conf. Robotics and Automation, ICRA, Atlanta, Georgia, USA, pp. 790-795. 
  11. Wichlund K.Y., Sordalen O.J. and Egeland O. (1995): Control of vehicles with second-order nonholonomic constraints: Underactuated vehicles. - Proc. European Control Conf., Rome, Italy, pp. 3086-3091. 
  12. Yuh J. (1990): Modeling and control of underwater robotic vehicles. - IEEE Trans. Syst. Man Cybern., Vol. 20, No. 6, pp. 1475-1483. 

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