engleski

Stabilisation of a non-collocated velocity feedback system by the use of inerter

In active vibration isolation systems direct velocity feedback may be used. A particular approach in this framework is known as “skyhook damping”. Skyhook damping is implemented by using a velocity sensor mounted on the receiving body whose output is used to drive a force actuator reacting between the source and the receiving bodies through a feedback gain. In such an arrangement the velocity sensor is collocated with the component of the actuator force acting on the receiving body. The other component reacting against the source body lacks a collocated sensor. If the fundamental natural frequency of the receiving body is lower than the fundamental natural frequency of the source body, the feedback loop exhibits unconditional stability and can generate significant vibration isolation effects in a broad band of frequencies. If the situation is opposite, the feedback loop becomes conditionally stable and only limited feedback gains can be implemented. This results in poor vibration isolation effects. However, if an inerter with a large enough inertance is used in the isolator suspension, the feedback loop becomes unconditionally stable and performant again. In this paper it is calculated using a lumped parameter model of the general vibration isolation problem that the minimum inertance to stabilise the feedback loop equals the stiffness of the isolator spring times the squared natural frequency of the source body. Furthermore, it is shown that time-averaged kinetic energy of the receiving body monotonically reduces with the increase of the feedback gain.

Vibration isolation Inerter Active vibration control Direct velocity feedback Stability of active control systems Optimisation of vibration control systems

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