A time-delayed acceleration feedback control is proposed to improve the vibration performance of a nonlinear vehicle suspension system. First, the harmonic balance method is applied to obtain the vertical acceleration amplitude of the system excited by simple harmonic road excitation. Then, taking the amplitude of the sprung mass acceleration and control force into account, the single-objective and multiple-objective optimization problems of time-delayed feedback control parameters, respectively, are discussed. Finally, the mathematical simulation is provided to verify the correctness of the optimization results. It is concluded that the nonlinear suspension with optimal time-delayed feedback control has better vibration control performance compared to passive one. The acceleration amplitude of the sprung mass is significantly reduced by the single-objective optimization of the control parameters. Moreover, when the optimal time delay is introduced, the active control force input is fewer than that without time delay. The phenomenon of energy transfer between the sprung mass and the unsprung mass is observed in some road-excitation frequencies.

为了提高非线性车辆悬架系统的振动性能，提出了一种时滞加速度反馈控制方法。首先，应用谐波平衡法获得通过简谐道路激励而激励的系统的垂直加速度幅度。然后，考虑簧载质量加速度和控制力的幅值，分别讨论了时滞反馈控制参数的单目标和多目标优化问题。最后，通过数学仿真验证了优化结果的正确性。结论是，具有最优时滞反馈控制的非线性悬架与被动悬架相比具有更好的振动控制性能。通过对控制参数进行单目标优化，可以显着减小簧载质量的加速度幅度。而且，当引入最佳时间延迟时，主动控制力输入要比没有时间延迟的主动控制力输入少。在某些道路激励频率中观察到了簧载质量与未簧载质量之间的能量传递现象。