This paper is concerned with Inerter-Spring-Damper(ISD) suspension design with semi-active inerter and semi-active damper configuration. First, a quarter vehicle model with semi-active suspension is established, and three control laws, named Sky-Hook (SH) control, Acceleration-Driven-Damping (ADD) control and Power-Driven-Damper (PDD) control, are derived to control the inertance and damper in the semi-active part. Hybrid control of semi-active inerter and damper is carried out, in which, switch and continuous control are used in the process of SH control, the combinations of different control algorithms are simulated as well. The simulation results show that the RMS of the car body acceleration with the proposed semi-active suspension can be greatly improved. And in the frequency domain, body vibration can also be restrained in wide frequency range, the proposed semi-active suspension has a good ability to attenuate the body vibration and improve the ride comfort. The proposed control strategy can compensate the inaction of inerter, and even benefit the suspension performance at a little higher frequency range.
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