VSS Vibration Control for a Double Pendulum System with a Vertically Movable Pivot

An active vibration control technique for a double pendulum system, the pivot of which is mounted on a motorized cart and vertically transferred, is developed using a VSS control scheme, in which the Lyapunov function is characterized by a switching function that is weighted by all of the pendulum’s state variables. The designed control system, including a linear observer for estimating the cart velocity and a nonlinear observer for estimating the angular velocities, is actively effective in suppressing vibrations of double pendulum, although the control effect is slightly better for the first link than for the second for both the in-phase and out-of-phase modes.