北京航空航天大学学报 ›› 2020, Vol. 46 ›› Issue (6): 1169-1176.doi: 10.13700/j.bh.1001-5965.2019.0402

• 论文 • 上一篇    下一篇

六自由度压电隔振平台面向控制的模态分析与动力学建模

于帅彪1, 张臻1, 周克敏2   

  1. 1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100083;
    2. 山东科技大学 电气与自动化工程学院, 青岛 266590
  • 收稿日期:2019-07-19 发布日期:2020-07-02
  • 通讯作者: 张臻 E-mail:zhangzhen@buaa.edu.cn
  • 作者简介:于帅彪 男,硕士研究生。主要研究方向:智能结构建模控制;张臻 男,博士,讲师,硕士生导师。主要研究方向:智能结构动力学与控制、迟滞非线性系统建模与控制;周克敏 男,博士,教授,博士生导师。主要研究方向:鲁棒控制、多目标优化、故障诊断与容错控制、迟滞非线性控制等。
  • 基金资助:
    国家自然科学基金(61433011)

Control-oriented modal analysis and dynamic modeling for six-degree-of-freedom piezoelectric vibration isolation platform

YU Shuaibiao1, ZHANG Zhen1, ZHOU Kemin2   

  1. 1. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100083, China;
    2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
  • Received:2019-07-19 Published:2020-07-02
  • Supported by:
    National Natural Science Foundation of China (61433011)National Natural Science Foundation of China (61873021); Aeronautical Science Foundation of China (20185651020);the Fundamental Research Funds for the Central Universities-Top Program of Young Talents Funding of Beihang University; Key Topics of the Ministry of Education of National Education Science Planning (DHA160356); National Key Scientific Instrument and Equipment Development Project (2014YQ350461)

摘要: 六自由度压电隔振平台各通道之间存在的强耦合性以及压电作动器固有的迟滞非线性都对系统动力学建模提出了挑战。为此,基于模态分析技术对六自由度压电隔振平台开展面向控制的非线性动力学建模研究。在充分考虑压电作动器的迟滞非线性后,采用模态坐标变换方法建立了隔振平台Hammerstein非线性动力学模型,包含了输入端的静态迟滞非线性子系统、解耦的模态方程组以及模态正/反变换矩阵。通过实验测量方法辨识得到模态方程中的参数,采用MPI模型辨识得到静态迟滞非线性子系统,并经过逆补偿控制实验验证了迟滞模型的正确性。基于迟滞逆补偿策略辨识得到模态反变换矩阵。最终建立了平台的动力学模型,为后续的控制奠定了良好的基础。

关键词: 解耦, 模态分析, 迟滞非线性, 逆补偿, 六自由度压电隔振平台

Abstract: The strong coupling between the channels of the six-degree-of-freedom piezoelectric vibration isolation platform and the inherent hysteresis nonlinearity of the piezoelectric actuator pose challenges to the system dynamic modeling. In this paper, based on modal analysis technology, the control-oriented nonlinear dynamic modeling of six-degree-of-freedom piezoelectric vibration isolation platform is studied. After fully considering the hysteresis nonlinearity of the piezoelectric actuator, the Hammerstein nonlinear dynamic model of the vibration isolation platform is established by the modal coordinate transformation method, including the hysteresis nonlinearity subsystem at the input end, the decoupled modal equations and the modal positive/inverse transformation matrix. The parameters in the modal equation are identified by experimental measurement method. The static hysteresis nonlinear subsystem of the piezoelectric actuator is obtained by MPI model. The correctness of the hysteresis model is verified by inverse compensation control experiment. The modal inverse transformation matrix is obtained based on the hysteresis inverse compensation strategy. Finally, a dynamic model of the platform was established, which laid a good foundation for subsequent control.

Key words: decoupling, modal analysis, hysteresis nonlinearity, inverse compensation, six-degree-of-freedom piezoelectric vibration isolation platform

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