Design tradeoffs for a single degree of freedom structure

Abstract

This study demonstrates that a single degree-of-freedom structure's vibrations can be effectively suppressed by using either passive damping, a combination of passive damping and active control, or active control without any passive damping. There are several limitations to a controller's effectiveness, two of which are the absorber's mass and stroke length. If settling time is used as the criterion to determine an absorber's effectiveness, then the classical den Hartog solution does not yield the optimum settling time for a passive absorber. The best settling time occurs when the passive absorber is tuned to a natural frequency close to that obtained with the den Hartog solution, but with a damping ratio that is significantly greater. Three different closed-loop control schemes, namely, local velocity feedback (LVF), linear quadratic regulator (LQR), and linear quadratic Gaussian (LQG), are overlaid on a passively tuned absorber. Slightly faster settling times are achieved than with the passive absorber only, and the passive absorber's parameters differ from those used to obtain the best settling time using the passive absorber only. Without passive damping, the three control strategies yield settling times much smaller than that obtained using passive damping only. However, with LVF control the actuator's maximum stroke length is quite large, and after a disturbance the actuator drifts to a steady-state position far from its initial position. For LQR and LQG control schemes, the best settling times result when there is no weighting on the actuator's position and velocity and the ratio between theQ andR matrices is large. The observer in LQG control causes that controller to generate larger settling times when compared to LQR control.