Motivated by improving performance of a bi-stable vibration energy harvester (VEH) from the viewpoint of vibration control, the time-delayed feedback control of displacement and velocity are constructively proposed into an electromechanical coupled VEH mounted on a rotational automobile tire, which is subject to colored noise and the periodic excitation. Using the improved stochastic averaging procedure based on energy-dependent frequency, the expressions of stationary probability density (SPD) and signal-to-noise ratio (SNR) are obtained analytically. Then, the efficiency of time-delayed feedback control on the stationary response and stochastic resonance (SR) for the delay-controlled VEH is explored in detail theoretically. Results show that both noise-induced SR and delay-induced SR can occur. Time delay is able to not only enhance the SR behavior but also weaken it. Furthermore, a larger negative feedback gain of displacement and a larger positive feedback gain of velocity are more beneficial for VEH. Interesting finding is that the optimal combination of time delay in maximizing the harvested performance, such as the harvest power, the output voltage and the power conversion efficiency, is almost perfectly consistent with that in maximizing SNR. Compared with the uncontrolled VEH, the delay-controlled VEH can achieve certain desirable optimization in harvesting energy by choosing the appropriate combination of time delays and feedback gains.

从振动控制的角度出发，通过提高双稳态振动能量收集器（VEH）的性能，将位移和速度的时滞反馈控制建设性地提出到搭载在旋转汽车轮胎上的机电耦合VEH中。对有色噪声和周期性激励。使用基于能量依赖频率的改进的随机平均程序，可以解析地获得平稳概率密度（SPD）和信噪比（SNR）的表达式。然后，从理论上详细探讨了时滞反馈控制对延迟控制的VEH的平稳响应和随机共振（SR）的效率。结果表明，噪声引起的SR和延迟引起的SR都可能发生。时间延迟不仅可以增强SR行为，而且可以减弱SR行为。此外，较大的位移负反馈增益和较大的速度正反馈增益对VEH更有利。有趣的发现是，在最大化采集性能（例如采集功率，输出电压和功率转换效率）方面，时间延迟的最佳组合几乎与最大化SNR完全一致。与不受控制的VEH相比，通过选择时间延迟和反馈增益的适当组合，延迟控制的VEH可以在收集能量时实现某些理想的优化。有趣的发现是，在最大化采集性能（例如采集功率，输出电压和功率转换效率）方面，时间延迟的最佳组合几乎与最大化SNR完全一致。与不受控制的VEH相比，通过选择时间延迟和反馈增益的适当组合，延迟控制的VEH可以在收集能量时实现某些理想的优化。有趣的发现是，在最大化采集性能（例如采集功率，输出电压和功率转换效率）方面，时间延迟的最佳组合几乎与最大化SNR完全一致。与不受控制的VEH相比，通过选择时间延迟和反馈增益的适当组合，延迟控制的VEH可以在收集能量时实现某些理想的优化。