磁悬浮控制系统的动力稳定性研究 Alternative Title Research on the Dynamical Stability of Maglev System 沈飞 Thesis Advisor 武建军 2009-05-31 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 磁悬浮 稳定性 Hopf分岔 反馈增益 时滞反馈控制 周期振动 Abstract 本学位论文针对两级磁悬浮控制系统分别讨论了反馈增益系数和时滞对系统稳定性的影响。主要内容如下： 1. 讨论了反馈增益系数对磁悬浮系统稳定性的影响。利用矩阵Bialternate积的性质，引入了Hopf分岔的检验函数，该方法克服了一般方法在确定系统Hopf分岔点时，对于参数的每一次变化都必须求解系统的所有特征根，并判定特征根实部是否为零的庞大计算量的缺陷，从而可以较方便地搜索出系统的Hopf分岔点。并以速度反馈增益为分岔参量，利用中心流形法和规范型法分析了在Hopf分岔点处系统的分岔方向及周期解的稳定性。 2. 讨论了控制回路中反馈信号存在的时滞对磁悬浮系统稳定性的影响。定量地给出了一些系统参数之间的稳定区域，并对不同参数下磁悬浮系统的动态响应进行了数值仿真。 3. 以时滞为分岔参数，得到系统出现Hopf分岔的条件，并运用中心流形法和规范型法，解析地确定出表征磁悬浮时滞系统中Hopf分岔方向及周期解的稳定性的特征量。然后通过数值模拟验证了主要结果的正确性。分析表明，当时滞量达到临界值时，系统将会经历一个超临界Hopf分岔而产生稳定的周期振动。若时滞固定且超过了临界值，则可将反馈增益作为分岔参数，且将反馈增益向分岔的反方向调节，能使系统重新进入渐近稳定状态。 Other Abstract In this dissertation, focusing on the second order model of a maglev vehicle, the influences of the feedback control gains and the delay time on the stability of the maglev system are investigated, respectively. The main achievements are as follows: 1. The influence of the feedback control gains on the stability of the maglev system is discussed. A test function for Hopf bifurcation is introduced to analyze the formation condition of the Hopf bifurcation. In this way, the time-consuming of eigenvalue computation in the process of analyzing system stability is avoided. With the velocity feedback control gains as the bifurcation parameter, the normal form theory and center manifold argument are applied to derive the explicit formulae, which determine the direction of Hopf bifurcation and the stability of periodic solutions bifurcating from trivial equilibrium. 2. The influence of the delay time on the stability of the maglev system with delayed feedback control is investigated. The stable regions of some system parameters are gained by numerical methods, and the dynamic responses of maglev system are numerically simulated by using various parameters. 3. Taking the time delay as the bifurcation parameter, the condition on which the Hopf bifurcation may occur is investigated. The explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the theory of normal form and center manifold. Meanwhile, the results of numerical simulations are given to support the above theoretical predictions. It can be seen obviously from the analysis that when the delay reaches the critical value, the maglev system will undergo a supercritical Hopf bifurcation and generate stable periodic oscillation. If the time delay is fixed and exceeds the critical value, then taking the feedback control gain as the bifurcation parameter, the asymptotically stable system can be regained by adjusting the feedback control gain in the direction opposite to that of the Hopf bifurcation. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/226630 Collection 土木工程与力学学院 Recommended CitationGB/T 7714 沈飞. 磁悬浮控制系统的动力稳定性研究[D]. 兰州. 兰州大学,2009.
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