Lyapunov-Based PD Linear Control of the Oscillatory Behavior of a Nonlinear Mechanical System : The Inverted Physical Pendulum with Moving Mass Case

Abstract EN

This paper concerns active vibration damping of a frictionless physical inverted pendulum with a radially moving mass.

The motion of the inverted pendulum is restricted to an admissible set.

The proposed Proportional Derivative linear controller damps the inverted pendulum (which is anchored by a torsion spring to keep it in a stable upright position), exerting a force on the radially moving mass.

The controller design procedure, which follows a traditional Lyapunov-based approach, tailors the energy behavior of the system described in Euler-Lagrange terms.