Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians

Anthony M. Bloch; Naomi Ehrich Leonard; Jerrold E. Marsden

Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians

Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden

Research output: Contribution to journal › Conference article › peer-review

Abstract

This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the 'method of controlled Lagrangians'. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or 'controlled' Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy 'matching' conditions. The pendulum on a rotor arm requires an interesting generalization of our earlier approach which was used for systems such as a pendulum on a cart.

Original language	English (US)
Pages (from-to)	500-505
Number of pages	6
Journal	Proceedings - IEEE International Conference on Robotics and Automation
Volume	1
State	Published - 1999
Externally published	Yes
Event	Proceedings of the 1999 IEEE International Conference on Robotics and Automation, ICRA99 - Detroit, MI, USA Duration: May 10 1999 → May 15 1999

All Science Journal Classification (ASJC) codes

Software
Control and Systems Engineering
Artificial Intelligence
Electrical and Electronic Engineering

Cite this

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title = "Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians",

abstract = "This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the 'method of controlled Lagrangians'. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or 'controlled' Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy 'matching' conditions. The pendulum on a rotor arm requires an interesting generalization of our earlier approach which was used for systems such as a pendulum on a cart.",

author = "Bloch, {Anthony M.} and Leonard, {Naomi Ehrich} and Marsden, {Jerrold E.}",

year = "1999",

language = "English (US)",

volume = "1",

pages = "500--505",

journal = "Proceedings - IEEE International Conference on Robotics and Automation",

issn = "1050-4729",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "Proceedings of the 1999 IEEE International Conference on Robotics and Automation, ICRA99 ; Conference date: 10-05-1999 Through 15-05-1999",

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TY - JOUR

T1 - Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians

AU - Bloch, Anthony M.

AU - Leonard, Naomi Ehrich

AU - Marsden, Jerrold E.

PY - 1999

Y1 - 1999

N2 - This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the 'method of controlled Lagrangians'. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or 'controlled' Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy 'matching' conditions. The pendulum on a rotor arm requires an interesting generalization of our earlier approach which was used for systems such as a pendulum on a cart.

AB - This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the 'method of controlled Lagrangians'. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or 'controlled' Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy 'matching' conditions. The pendulum on a rotor arm requires an interesting generalization of our earlier approach which was used for systems such as a pendulum on a cart.

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UR - http://www.scopus.com/inward/citedby.url?scp=0032644080&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0032644080

SN - 1050-4729

VL - 1

SP - 500

EP - 505

JO - Proceedings - IEEE International Conference on Robotics and Automation

JF - Proceedings - IEEE International Conference on Robotics and Automation

T2 - Proceedings of the 1999 IEEE International Conference on Robotics and Automation, ICRA99

Y2 - 10 May 1999 through 15 May 1999

ER -

Stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians

Abstract

All Science Journal Classification (ASJC) codes

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