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Control of Neimark–Sacker bifurcation in a type of weak impulse excited centrifugal governor system
International Journal of Non-Linear Mechanics ( IF 2.8 ) Pub Date : 2020-10-08 , DOI: 10.1016/j.ijnonlinmec.2020.103624
Zengyao Lv , Huidong Xu , Zihao Bu

Centrifugal governors play an important role in rotating machinery such as diesel engines and steam engines. This paper considers two impulse excitations of the freewheel. The feedback control issue of the Neimark–Sacker bifurcation design of the centrifugal governor system is studied. A feedback control method is addressed to realize the control objectives of the existence, stability and the mean radius of cross section of the torus solution. An explicit criterion, without the use of eigenvalue calculations, including eigenvalue assignments and transversality conditions, is used to push the linear gain responsible for controlling the existence of bifurcation. Using the central manifold theory and the normal form reduction method, the nonlinear gain of the control torus stability is obtained. The expression of mean radius of cross section of the limit torus is developed to derive the linear gains, which are responsible for controls of torus. Numerical simulations of the centrifugal governor system show that the Neimark–Sacker​ torus with the desired characteristics can be produced at any of the pre-set parameter points.



中文翻译:

一类弱脉冲励磁离心调速器系统中Neimark-Sacker分叉的控制

离心式调速器在旋转机械(例如柴油机和蒸汽机)中扮演着重要角色。本文考虑了飞轮的两种脉冲激励。研究了离心调速器系统的Neimark-Sacker分叉设计的反馈控制问题。提出了一种反馈控制方法,以实现环解的存在性,稳定性和平均横截面半径的控制目标。使用不使用特征值计算(包括特征值分配和横向条件)的显式准则来推动负责控制分叉的存在的线性增益。利用中心流形理论和正规形式约简方法,获得了控制环面稳定性的非线性增益。极限圆环横截面的平均半径的表达式被开发出来,以得出线性增益,这是控制圆环的原因。离心式调速器系统的数值模拟表明,可以在任何预设参数点上产生具有所需特性的Neimark-Sacker环面。

更新日期:2020-10-11
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