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In this paper, the vehicle ISD (inerter-spring-damper) suspension and power-driven-damper control strategy are combined to the suspension design, and the power-driven-damper semiactive ISD suspension is proposed. The dynamic models of the passive suspension S1 and two semiactive ISD suspensions S2 and S3 are established. Based on the port-controlled Hamiltonian theory, the power-driven-damper semiactive control strategy is designed by analyzing the power transfer of suspension S3. Then, the parameters of the two models are optimized by the particle swarm optimization algorithm, and the optimization results show that the suspension S3 has better performance. The influence of the semiactive damping coefficient, the spring stiffness, and the inertance on the vibration suppression performance is investigated based on the suspension S3. The effect of parameter perturbation on power-driven-damper semiactive vehicle ISD suspension illustrates that the designed semiactive vehicle ISD suspension has better ride comfort in a wider range frequency and good robust performance. [ABSTRACT FROM AUTHOR]