This paper investigates the application of semi-active inerter in semi-active suspension. A semi-active inerter is defined as an inerter whose inertance can be adjusted within a finite bandwidth by on-line control actions. A force-tracking approach to designing semi-active suspension with a semi-active inerter and a semi-active damper is proposed, where the target active control force derived by LQR control in the 'Reciprocal State-Space' (RSS) framework is tracked by controlling the semi-active damping coefficient and semi-active inertance. One of the advantages of the proposed method is that it is straightforward to use the acceleration information in the controller design. Simulation results demonstrate that the semi-active suspension with a semi-active inerter and a semi-active damper can track the target active control force much better than the conventional semi-active suspension (which only contains a semi-active damper) does. As a consequence, the overall performance in ride comfort, suspension deflection and road holding is improved, which effectively demonstrates the necessity and the benefit of introducing semi-active inerter in vehicle suspension.preprin
