Delayed acceleration feedback (DAF) is known to have a positive impact on the stability properties of dynamical models in several applications. Motivated by this, we study the impact of DAF on the classical car-following model (CCFM). First, we show that DAF shrinks the locally stable region. We then show that the resulting model, similar to the CCFM, loses local stability via a Hopf bifurcation. However, DAF decreases the amplitude and increases the frequency of the resulting limit cycles. Additionally, we show that DAF is detrimental to the CCFM due to |$(i)$| destruction of the non-oscillatory property of its solutions, |$(ii)$| increased risk of string instability and |$(iii)$| reduced resilience towards parametric uncertainty. Thus, we report a relevant application wherein DAF degrades the performance across several metrics of practical interest. Thus, our work motivates a systematic study of controllers that can guarantee performance enhancement. We complement our analytical results with stability charts and a bifurcation diagram.

中文翻译：

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延迟加速度反馈对经典跟随模型的影响

已知延迟加速度反馈（DAF）在某些应用中会对动力学模型的稳定性产生积极影响。因此，我们研究了DAF对经典汽车跟随模型（CCFM）的影响。首先，我们证明DAF缩小了本地稳定区域。然后，我们表明，所得模型类似于CCFM，通过Hopf分支失去了局部稳定性。但是，DAF会降低幅度，并增加最终极限循环的频率。此外，我们表明，由于| $（i）$ |，DAF不利于CCFM 。销毁其解决方案的非振荡特性，| $（ii）$ | 字符串不稳定和| $（iii）$ |的风险增加降低了对参数不确定性的适应力。因此，我们报告了一个相关的应用程序，其中DAF降低了多个具有实际意义的指标的性能。因此，我们的工作激发了对可以保证性能提升的控制器的系统研究。我们用稳定性图和分叉图来补充分析结果。