Abstract

In this paper, based on the original friction-induced oscillation, we propose a new friction-induced mathematical model associated with moving belt of particle supply device. Two delay feedback control methods are provided to make the new model be stable. Linear stability analysis is carried out to obtain the stability of equilibrium and the stability boundary, corresponding to the critical value of Hopf bifurcation, dividing stable and unstable regimes of equilibrium. Next, we derive explicit formulae for determining the stability of Hopf bifurcating periodic solutions and the direction of Hopf bifurcation. Finally, detailed numerical simulations using MATLAB software are presented to demonstrate the application of the theoretical results, and we also compare the efficacy of the two control forces in new friction-induced models.

中文翻译：

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改进的摩擦诱导模型的时滞反馈控制：在颗粒供给装置运动带中的应用

摘要

本文在原始的摩擦引起的振动的基础上，提出了一种与颗粒供给装置运动带相关的新的摩擦引起的数学模型。提供了两种延迟反馈控制方法以使新模型稳定。进行线性稳定性分析，以获得平衡的稳定性和稳定性边界，对应于Hopf分叉的临界值，划分平衡的稳定和不稳定状态。接下来，我们导出用于确定Hopf分支周期解的稳定性和Hopf分支方向的显式。最后，使用MATLAB软件进行了详细的数值模拟，以证明理论结果的应用，并且我们还比较了两种控制力在新的摩擦诱导模型中的功效。