基于PDE模型的空间柔性曲梁无穷维Kalman滤波器设计

发布时间：2018-01-08 01:27

本文关键词：基于PDE模型的空间柔性曲梁无穷维Kalman滤波器设计　出处：《中国科学:物理学力学天文学》2017年10期 　论文类型：期刊论文

【摘要】：状态观测器设计是大型空间结构主动控制设计中的一项重要内容.由于大型空间结构频率低、模态密集且阻尼小,传统的基于模态截断模型的观测器设计方法容易导致观测溢出问题.直接基于结构的偏微分方程(PDE)模型进行状态观测器设计可以避免上述问题,目前正成为该领域的研究热点.针对具有弱阻尼的空间柔性曲梁,对曲梁在悬臂状态下的面内振动进行状态估计.首先建立考虑剪切变形和转动惯量的曲梁面内振动PDE模型,并通过变量替换将PDE模型转化为Hilbert空间中的抽象状态方程,然后基于Kalman滤波理论构建曲梁的无穷维状态观测器模型,并采用频域下的谱分解方法得到无穷维Kalman滤波器增益函数的解析解.最后通过数值算例对无穷维Kalman滤波器的观测效果进行了验证,并揭示了该方法在防止观测溢出方面的有效性
[Abstract]:The observer is an important content in the design of active control of large space structure. Due to the large space structure of low frequency, modal density and small damping, the traditional observer design method based on modal truncation model is easy to cause the overflow problem. Direct observation based on the partial differential equation of the structure (PDE) model for the state observer is designed to be able to avoid the at present, it become a research hotspot in the field. For the flexible space of weakly damped beam, the state estimation of the vibration of curved beam in cantilever state plane. Firstly, considering the shear deformation and rotary inertia of the beam vibration in plane PDE model, and introducing substitution variables PDE model into abstract the state equation in Hilbert space, and then construct the infinite dimensional state observer model of curved beam based on Kalman filter theory, and obtained by the spectral decomposition method of frequency domain The analytic solution of the gain function of infinite dimensional Kalman filter is obtained. Finally, the observational effect of infinite dimensional Kalman filter is verified by numerical examples, and the effectiveness of the method in preventing observation overflow is revealed.

【作者单位】：南京航空航天大学机械结构力学及控制国家重点实验室;南京林业大学土木工程学院;
【基金】：国家自然科学基金重大项目(编号:11290153) 装备预研基金资助项目(编号:6140210010202) 江苏高校优势学科建设工程资助
【分类号】：TN713
【正文快照】： 引用格式:刘福寿,金栋平,文浩.基于P D E模型的空间柔性曲梁无穷维K a l m a n滤波器设计.中国科学:物理学力学天文学,2 0 1 7,4 7:1 0 4 6 1 1L i u F S,J i n D P,W e n H.I n fi n i t e-d i m e n s i o n a l K a l m a n fi l t e r d e s i g n f o r fl e x i b l e c

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