The use of active vibration control may induce a delay leading to detrimental degradation of the performance of active vibration control. This is particularly true in the case of mechanical systems subjected to friction-induced vibration and noise for which such time-delays can lead to the appearance of undesirable instability. Furthermore, conducting a stability analysis of time-delay systems and estimation of the critical time delay are challenging, due to the infinite nature of the characteristic (quasi) polynomial of the associated closed-loop system, having an infinite number of roots.

The objective of this paper is to discuss a strategy for the estimation of the critical time delay for the problem of Friction-Induced Vibration and noisE (FIVE). To achieve such an objective, the prediction of the stability analysis of time delay systems and the estimation of the associated critical time delay are first performed by applying the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term. In a second time, a mixed approach is proposed to predict effectively the real critical time delay of autonomous controlled systems subjected to friction-induced vibration. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological model with two degrees of freedom for which it is possible to provide a clear understanding and illustration of the phenomena involved and observed.

主动振动控制的使用可能会导致延迟，从而导致主动振动控制性能的不利降低。在遭受摩擦引起的振动和噪声的机械系统的情况下尤其如此，因为这种时间延迟会导致出现不希望的不稳定性。此外，由于相关联的闭环系统的特征（准）多项式具有无限的根，因此进行时滞系统的稳定性分析和估计关键的时延是具有挑战性的。

本文的目的是讨论一种用于估计摩擦引起的振动和噪声（FIVE）问题的关键时间延迟的策略。为了实现该目的，首先通过应用频率扫描测试和使用延迟项的泰勒级数展开的特征值问题近似来执行时滞系统稳定性分析的预测和相关的关键时延的估计。第二次，提出了一种混合方法来有效预测受到摩擦引起的振动的自主控制系统的实际临界时间延迟。