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.
@article{bwmeta1.element.bwnjournal-article-amcv16i3p345bwm,
author = {Siong Chin, Cheng and Wai Shing Lau, Micheal and Low, Eicher and Gim Lee Seet, Gerald},
title = {A robust controller design method and stability analysis of an underactuated underwater vehicle},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {16},
year = {2006},
pages = {345-356},
zbl = {1139.93339},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv16i3p345bwm}
}
Siong Chin, Cheng; Wai Shing Lau, Micheal; Low, Eicher; Gim Lee Seet, Gerald. A robust controller design method and stability analysis of an underactuated underwater vehicle. International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) pp. 345-356. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv16i3p345bwm/
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