Controlled Lagrangian systems with gyroscopic forcing and dissipation

Craig Woolsey, Chevva Konda Reddy, Anthony M. Bloch, Dong Eui Chang, Naomi Ehrich Leonard, Jerrold E. Marsden

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


This paper describes a procedure for incorporating artificial gyroscopic forces and physical dissipation in the method of controlled Lagrangians. Energy-conserving gyroscopic forces provide additional freedom to expand the basin of stability and tune closed-loop system performance. We also study the effect of physical dissipation on the closed-loop dynamics and discuss conditions for stability in the presence of natural damping. We apply the technique to the inverted pendulum on a cart, a case study from previous papers. We develop a controller that asymptotically stabilizes the inverted equilibrium at a specific cart position for the conservative dynamic model. The region of attraction contains all states for which the pendulum is elevated above the horizontal plane. We also develop conditions for asymptotic stability in the presence of linear damping.

Original languageEnglish (US)
Pages (from-to)478-496
Number of pages19
JournalEuropean Journal of Control
Issue number5
StatePublished - 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Engineering


  • Energy shaping
  • Gyroscopic forces
  • Nonlinear stabilization
  • Underactuated mechanical systems


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