In this study the use of an inerter is considered for active vibration control of a structure excited by white noise. The structure is modelled as a single degree of freedom system and the control system consists of a vibration absorber with a mass suspended on a spring, a damper and an inerter. The absorber is equipped with a reactive force transducer in parallel with the passive suspension which is driven with a signal proportional to the velocity of the structure under control measured by an ideal collocated sensor. The effect of the inerter on the control stability and performance of the control system is investigated. It is shown that the effect of the inerter is to reduce the natural frequency of the inertial actuator, improving the stability of the feedback loop and thus its performance. The optimisation of the physical and control parameters of the control system such as the internal damping of the actuator, its natural frequency, its inertance and the feedback gain are considered such that either the kinetic energy of the host structure is minimised or the power dissipated by the control system is maximised.
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