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Browse Journals & Magazines > Automatic Control, IEEE Trans ...> Volume:55 Issue:8 Help

Stabilizability of Controlled Lagrangian Systems of Two Degrees of Freedom and One Degree of Under-Actuation by the Energy-Shaping Method

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1 Author(s)
Dong Eui Chang ; Dept. of Appl. Math., Univ. of Waterloo, Waterloo, ON, Canada

We provide some criteria for stabilizability by the energy-shaping method for the class of all controlled Lagrangian systems of two degrees of freedom and one degree of under-actuation: a necessary and sufficient condition for Lyapunov stabilizability, two sufficient conditions for asymptotic stabilizability, and a necessary and sufficient condition for exponential stabilizability. As a corollary, we show that some of the asymptotically stabilizing controllers that were designed in old literatures with the energy-shaping method are actually exponentially stabilizing controllers. Examples of such systems are the inverted pendulum on a cart, the Furuta pendulum, the ball and beam system, and the Pendubot.

Published in:
Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 8 )

Date of Publication: Aug. 2010

Page(s):
1888 - 1893
ISSN :
0018-9286
INSPEC Accession Number:
11447124
Digital Object Identifier :
10.1109/TAC.2010.2049279
Product Type:
Journals & Magazines
Date of Publication :
29 April 2010
Date of Current Version :
29 July 2010
Issue Date :
Aug. 2010
Sponsored by :
IEEE Control Systems Society

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