【作者】 刘班；

【导师】 王洪滨；

【作者基本信息】 哈尔滨工业大学 ， 应用数学， 2009， 硕士

【摘要】 摩擦是一种复杂的非线性物理现象,产生于具有相对运动的接触面之间。在机械机电系统的摩擦模型的研究方面,以往的学者们比较注重系统的控制策略及其实现方法的研究,而对系统动力学方面的探讨尚不多见。具时滞反馈控制的Stribeck摩擦模型是一个非线性控制系统,反馈控制力是被控对象位移的线性函数,Stribeck摩擦力则为速度的非线性函数,当系统参数位于某些区域时,反馈控制力会使滑块产生相当大的振动,所以分析系统的振动特性、稳定性等动力学性质是具时滞反馈控制的摩擦模型的重要研究课题。另外,反馈控制系统中不可避免地带有时滞,考虑时滞的影响,一方面可以更客观、更准确地反应系统的实际工作情况,另一方面可以通过时滞反馈去控制动力学系统,以实现理想的控制策略。通过对具有时滞反馈控制的摩擦模型的研究,可以最大程度地消除和减少摩擦引起的不利因素,提高系统的动力学性能。因此,对具时滞反馈控制的Stribeck摩擦模型的研究有重要的理论和实际意义。在本文中,我们首先引入了一类具时滞反馈控制的Stribeck摩擦模型系统。然后利用线性稳定性方法对此系统的平衡点进行稳定性分析,当系统的线性部分对应的特征方程的特征根为纯虚根时,算出相应的时滞τ,得到了平衡点的稳定性在时滞τ取某些值时发生翻转,并且在平衡点处系统经历Hopf分支,而且我们发现当时滞量发生变化时系统产生了“稳定性开关”的现象。接着利用规范型理论和中心流形定理讨论了系统Hopf分支的分支方向和分支周期解的稳定性,给出了关于分支方向和分支周期解稳定性的计算公式。最后利用MATLAB软件进行相应的数值模拟,数值模拟结果与所得理论分析结果具有一致性。更多还原

【Abstract】 Friction is one complicated kind of non-linear physics phenomena, which is produced between the interfaces with rightabout movement. In the study of mechanism system of friction model, former researchers have paid more attention to the controlling tactics and the realization methods, but few explorations were made in terms of the dynamical behavior of the system. As time-delayed feedback control of friction system is a non-linear control system, the feedback control force is a linear function for the displacement of the object and the Stribeck friction is a non-linear function for the velocity, the effects of the control will make rotor produce considerable vibrations when the parameters belong to certain domain. Taking the effect of time delay into consideration, we can understand the practical performance of the system more objectively and accurately; on the other hand we can control the dynamical system by delayed feedback and realize an ideal strategy. Thus investigating the Stribeck friction system with time-delayed feedback control is of great theoretical and practical significance.In this thesis, in the first, we introduce one kind of Stribeck friction system with time-delayed feedback control. Secondly, we analyze the stability of the equilibrium by using linearizing stability method. When the engenvalues of the linear part are pure imaginary numbers, we obtain the corresponding delay value. The stability of the steady state is lost when the delay passes through the critical value, as well as there will be a family periodic solutions bifurcate from the steady states, and we find that the stability switch occurs when delay varies. Then, we derive the explicit formulae for determining the direction of the Hopf bifurcation and the stability of these periodic solutions bifurcating from the steady states, by using the normal form method and center manifold theorem. Finally, some numerical simulations are carried out by using MATLAB, and the results are consistent with our analysis results.更多还原