Vibration suppression of multi-modal translational motion using a rotational actuator

In recent the work of Wan et al. it was shown that a rotational torque actuator with attached eccentric mass can be used to globally stabilize a one-mode translational oscillator. A family of globally stabilizing nonlinear feedback control laws was derived by using partial feedback linearization and integrator backstepping. These control laws accounted for the strongly nonlinear coupling between the rotational motion of the eccentric mass and the translational motion of the oscillator. In the present paper, we extend these results to address the problem of stabilizing the translational motion of multi-mode systems with a rotational actuator. The controller synthesis methodology extends the previous work to address a system involving six state variables. Detailed numerical simulation of the closed-loop system illustrates the angular position of the eccentric mass and the harmonic content of its motion in suppressing both modal frequencies