Pd Control For Active Vibration Damping In An Underactuated Nonlinear System

A Lyapunov based control approach is proposed for the specification of the constant gains of an asymptotically stabilizing Proportional‐Derivative (PD) controller, devised to damp the oscillations of an underactuated nonlinear mechanical system. The system consists of a rigid beam, sliding on the interior of a spherical surface, and an actuated cart, located over the beam, which acts as an active vibration damping element.