一类机电系统的谐波分析与微分几何控制
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:国家自然科学基金资助项目(61473237);陕西省自然科学基础研究计划项目(2016JM1024);陕西省教育厅科研计划项目(15JK2181);西京学院科研基金项目(XJ130114)


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    摘要:

    耦合系统动力学分析研究对现代机电系统的设计,故障诊断,振动等有着重要的意义.针对一类自激非线性机电耦合系统,利用谐波平衡法对系统主谐波解进行了计算,并运用Floquet理论对主谐波解的稳定性进行了分析,给出主谐波解的稳定区域.同时,运用微分几何控制理论,分析并设计了精确线性化控制器.研究结果表明,该机电系统随着谐波解频率的减小,振幅增大,当谐波解频率到达主频率时,振幅达到最大,进而振幅减小,而且振幅会发生跳跃,系统会产生混沌现象.同时给系统添加控制器后,系统关系度为4,使得控制系统在所有的状态点处可以准确线性化.最后数值验证了所提控制方法的有效性和可实现性.

    Abstract:

    The primary harmonic of a self-sustained nonlinear electromechanical coupled system is computed by using the harmonic balance method. Based on the theory of Floquet, the stability of primary harmonic was analyzed. Also, the exact linearization controller for this electromechanical coupled system was designed based on the theory of differential geometry. The research results show that the amplitude of the harmonic solutions for this electromechanical system increase along with the decreasing of frequency, and the amplitude reached the maximum when the frequency reaches the main frequency. Meanwhile, the amplitude will jump and the system will emerge chaos. Furthermore, the relative degree of the system is 4 after adding a feedback controller to this system, and so that the control system can be linearized at all the state points. Finally, the numerical simulation results demonstrate the effectiveness and realizableness of the proposed method.

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李永新,王震,张善文.一类机电系统的谐波分析与微分几何控制[J].湖南科技大学学报(自然科学版),2016,31(4):77-82

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  • 在线发布日期: 2016-10-18