This paper investigates the potential of utilizing frequency-varying negative stiffness properties of the inerter in vehicle suspensions to improve the comprehensive dynamic performance. Firstly, the dynamic characteristics of the air spring and the inerter are analyzed to evaluate the feasibility of integrating them into vehicle suspensions. Secondly, a quarter-vehicle model incorporating the nonlinear stiffness features of an air spring is established, and a vehicle semi-active control strategy for the air inerter–spring–damper (ISD) suspension based on the frequency-varying negative stiffness of the inerter is proposed. Thirdly, in order to implement this strategy effectively, this paper builds an uneven road surface estimator based on the discrete Kalman filter with unknown input (DKF-UI) and an uneven road surface frequency identifier based on the first order-zero crossing algorithm. Finally, the superiority of the proposed suspension system is verified by simulations, and the results reveal that with respect to the passive air suspension, the peak values of the gains of the body acceleration, the suspension working space and the dynamic tire load are reduced. The vehicle semi-active air ISD suspension exhibits reductions of 68.7%, 51.0%, 67.6% in the body frequency region and 5.1%, 9.9%, 7.9% in the wheel frequency region, respectively. Under a segment sinusoidal road input, the RMS values of the three performance indicators exhibit reductions of 79.2%, 57.8%, 77.7% at 1.4 Hz and 6.8%, 15.4%, 5.8% at 11 Hz, respectively. Consequently, the vehicle semi-active air ISD suspension proposed in this paper has significant performance improvement at both the vehicle body natural frequency and the wheel natural frequency region compared to the passive air suspension, which indicates that it has better ride comfort and road holding performance.
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