Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem
Top Cited Papers
- 1 December 2000
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 45 (12) , 2253-2270
- https://doi.org/10.1109/9.895562
Abstract
We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler-Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in these equations are identified with control forces. Since the controlled system is Lagrangian by construction, energy methods can be used to find control gains that yield closed-loop stability. We use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group. The procedure is demonstrated for several underactuated balance problems, including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane.Keywords
This publication has 27 references indexed in Scilit:
- The energy-momentum method for the stability of non-holonomic systemsDynamics and Stability of Systems, 1998
- Configuration Controllability of Simple Mechanical Control SystemsSIAM Journal on Control and Optimization, 1997
- Feedback Stabilization of Relative Equilibria for Mechanical Systems with SymmetryPublished by Springer Nature ,1997
- On passivity‐based output feedback global stabilization of euler‐lagrange systemsInternational Journal of Robust and Nonlinear Control, 1995
- Lagrangian reduction and the double spherical pendulumZeitschrift für angewandte Mathematik und Physik, 1993
- Gyroscopic control and stabilizationJournal of Nonlinear Science, 1992
- Lectures on MechanicsPublished by Cambridge University Press (CUP) ,1992
- Stability of relative equilibria. Part I: The reduced energy-momentum methodArchive for Rational Mechanics and Analysis, 1991
- Stabilization of Hamiltonian systemsNonlinear Analysis, 1986
- Hamiltonian dynamics with external forces and observationsTheory of Computing Systems, 1981