本文關(guān)鍵詞：基于PDE模型的空間柔性曲梁無窮維Kalman濾波器設(shè)計(jì)　出處：《中國(guó)科學(xué):物理學(xué) 力學(xué) 天文學(xué)》2017年10期 　論文類型：期刊論文

  更多相關(guān)文章： 柔性曲梁 PDE模型 狀態(tài)估計(jì) 觀測(cè)溢出

【摘要】：狀態(tài)觀測(cè)器設(shè)計(jì)是大型空間結(jié)構(gòu)主動(dòng)控制設(shè)計(jì)中的一項(xiàng)重要內(nèi)容.由于大型空間結(jié)構(gòu)頻率低、模態(tài)密集且阻尼小,傳統(tǒng)的基于模態(tài)截?cái)嗄Ｐ偷挠^測(cè)器設(shè)計(jì)方法容易導(dǎo)致觀測(cè)溢出問題.直接基于結(jié)構(gòu)的偏微分方程(PDE)模型進(jìn)行狀態(tài)觀測(cè)器設(shè)計(jì)可以避免上述問題,目前正成為該領(lǐng)域的研究熱點(diǎn).針對(duì)具有弱阻尼的空間柔性曲梁,對(duì)曲梁在懸臂狀態(tài)下的面內(nèi)振動(dòng)進(jìn)行狀態(tài)估計(jì).首先建立考慮剪切變形和轉(zhuǎn)動(dòng)慣量的曲梁面內(nèi)振動(dòng)PDE模型,并通過變量替換將PDE模型轉(zhuǎn)化為Hilbert空間中的抽象狀態(tài)方程,然后基于Kalman濾波理論構(gòu)建曲梁的無窮維狀態(tài)觀測(cè)器模型,并采用頻域下的譜分解方法得到無窮維Kalman濾波器增益函數(shù)的解析解.最后通過數(shù)值算例對(duì)無窮維Kalman濾波器的觀測(cè)效果進(jìn)行了驗(yàn)證,并揭示了該方法在防止觀測(cè)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.

【作者單位】： 南京航空航天大學(xué)機(jī)械結(jié)構(gòu)力學(xué)及控制國(guó)家重點(diǎn)實(shí)驗(yàn)室;南京林業(yè)大學(xué)土木工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金重大項(xiàng)目(編號(hào):11290153) 裝備預(yù)研基金資助項(xiàng)目(編號(hào):6140210010202) 江蘇高校優(yōu)勢(shì)學(xué)科建設(shè)工程資助
【分類號(hào)】：TN713
【正文快照】： 引用格式:劉福壽,金棟平,文浩.基于P D E模型的空間柔性曲梁無窮維K a l m a n濾波器設(shè)計(jì).中國(guó)科學(xué):物理學(xué)力學(xué)天文學(xué),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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