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An inerter-based active vibration isolation system
Last modified: 2017-12-20
Abstract
In this paper a novel, inerter-based active vibration isolation system is presented. The methodology is studied on a simple two degree of freedom (dof) system, such that many conclusions can be drawn based on analytically derived expressions. The two dof system consists of two lumped masses connected by a coupling spring (the isolator spring). Both masses are also attached to a firm reference base by a mounting spring. A mass and the corresponding mounting spring are referred to as either a source body or a receiving body. Each uncoupled body is therefore characterised by a natural frequency so that the system can be seen as a reduced order model of a potentially more complicated structure. The source body is excited by a broadband force and the vibrations are transmitted to the receiving body. The objective of the active vibration isolation system is to minimise the receiving body vibrations. This is achieved through a vibration rejection scheme. The scheme is realised through direct velocity feedback. The receiving body velocity is used as an error signal. The control force is generated with a reactive actuator in parallel with the coupling spring.
It is shown in the paper that only with the inclusion of the inerter the active vibration isolation can be achieved on subcritical systems. This is because with such systems the direct velocity feedback becomes unstable. Subcritical systems are those which have the fundamental natural frequency of the uncoupled receiving body larger than the fundamental natural frequency of the uncoupled source body. Adding the inerter into the isolator effectively generates a sort of relative acceleration feedback that stabilises the control loop. In fact, it is analytically calculated in the paper that the minimum inertance to stabilise the loop is proportional to the stiffness of the isolator spring and inversely proportional to the squared natural frequency of the source body. It is important to mention that direct acceleration feedback is not possible in practice due to very pronounced stability problems.
It is shown in the paper that only with the inclusion of the inerter the active vibration isolation can be achieved on subcritical systems. This is because with such systems the direct velocity feedback becomes unstable. Subcritical systems are those which have the fundamental natural frequency of the uncoupled receiving body larger than the fundamental natural frequency of the uncoupled source body. Adding the inerter into the isolator effectively generates a sort of relative acceleration feedback that stabilises the control loop. In fact, it is analytically calculated in the paper that the minimum inertance to stabilise the loop is proportional to the stiffness of the isolator spring and inversely proportional to the squared natural frequency of the source body. It is important to mention that direct acceleration feedback is not possible in practice due to very pronounced stability problems.