### Abstract

In this paper we derive a nonlinear control law for stabilization of the Furuta pendulum system with the pendulum in the upright position and the rotating rigid link at rest at the origin. The control law is derived by first applying feedback that makes the Furuta pendulum look like a planar pendulum on a cart plus a gyroscopic force. The planar pendulum on a cart is an example of a class of mechanical systems which can be stabilized in full state space using the method of controlled Lagrangians. We consider this class of systems as our normal form and for the case of the Furuta pendulum, we add to the first transforming feedback law, the energy-shaping control law for the planar pendulum system. The resulting system looks like a mechanical system plus feedback-controlled dissipation and an external force that is quadratic in velocity. Using energy as the Lyapunov function we prove local exponential stability and demonstrate a large region of attraction.

Original language | English (US) |
---|---|

Pages (from-to) | 516-521 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 1 |

State | Published - Dec 1 2002 |

Event | 41st IEEE Conference on Decision and Control - Las Vegas, NV, United States Duration: Dec 10 2002 → Dec 13 2002 |

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization