Strong stabilization of the SCOLE model using a tuned mass damper

We study the vibration reduction of the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) model representing a vertical beam clamped at the bottom, with a rigid body having a large mass on top, using a Tuned Mass Damper (TMD). The TMD is a heavy trolley mounted on top of the rigid body, connected to the rigid body via a spring and a damper. Such an arrangement is used to stabilize tall buildings. Using our recent well-posedness and strong stabilization results for coupled impedance passive linear time-invariant systems (possibly infinite-dimensional), we show the following: The SCOLE system with the trolley is well-posed and regular on the energy state space with the force or torque acting on the rigid body as input and with the speed or angular velocity of the rigid body as output, and this system is strongly stable on the energy state space.