基于Normal Form方法的电机系统分岔控制
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TM331; TM271; O231. 2

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国家自然科学基金资助项目(51275081);沈阳市科技攻关计划资助项目(F13-01-21-00);辽宁省科技创新重大专项资助项目(201303004)


Bifurcation Control in a Motor System Based on Normal Form
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    摘要:

    研究了无刷直流电机系统等效非线性数学模型,分析了系统的Hopf分岔行为,并设计了washout滤波器,对系统产生的分岔行为进行控制。引入直接Normal Form(规范型)计算方法,求出系统的Hopf分岔规范式。通过规范式系数讨论控制参数的选择原则以及对Hopf分岔类型及极限环幅值的影响。理论和仿真结果表明:在施加控制器之前,系统发生亚临界Hopf分岔,极限环不稳定,系统进入混沌状态;在施加控制器之后,当受控系统规范式系数实部小于零时,系统发生超临界Hopf分岔,原系统不稳定极限环被控制为稳定极限环,从而抑制了混沌的产生,保证了电机运行性能的稳定性。

    Abstract:

    In this paper, the equal effective non-linear mathematical model of the brushless DC motor system is studied, the Hopf bifurcation behavior of system is investigated, and the washout filter is adopted to control the Hopf bifurcation behavior of the system. Then, the Hopf bifurcation normal form of the controlled system is obtained using the direct normal form method. According to the normal form coefficient, the selection criteria of the parameter and its effect on the periodic solution′s amplitude and Hopf bifurcation type of system are discussed. Theories and simulation results show that without the controller, the subcritical Hopf bifurcation occurs and unstable limit cycles appear, which leads to chaos. However, with the controller, supercritical Hopf bifurcation occurs, and the cycles of the original system become stable when the real part of coefficient of normal form is less than zero. Thus, the chaotic behavior of the system is controlled, and the stability of the motor′s running performance is ensured.

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  • 在线发布日期: 2015-01-06
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