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一种多输入多输出振动系统状态空间建模方法

State space modeling method for multi-input and multi-output vibration system
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摘要 状态空间方法在多输入多输出(MIMO)振动系统中有着较为广泛的应用,文中结合现代控制理论中最小实现和降阶法的思想建立了多输入多输出振动系统的状态空间模型。该方法基于测试得的离散频响函数(传递函数)矩阵,经向量拟合得到频响函数有理分式模型,依据该模型首先建立可控(可观)的状态空间,然后从中分离出可观(可控)部分,最终得到的状态空间模型既可控又可观,利用MATLAB悬臂梁仿真以及三轴向振动台实验频响数据分别得到了对应的状态空间模型。将上述状态空间模型生成的频响数据与原始频响数据进行比较发现基本吻合,误差值均在可接受范围内,因此认为该方法准确可靠。 The state space method has a wide range of applications in multiple-input multiple-output(MIMO)vibration systems.In this paper,a state space modeling method for MIMO vibration system based on the idea of minimum realization and reduced order in modern control theory is proposed.The method is based on the measured frequency response function(transfer function)matrix.The rational fraction model of frequency response function is obtained by vector fitting.According to the model,the controllable(observable)state space is first established,and then the observable(controllable)part is separated from it.The resulted state space model is both controllable and observable.The state space models are obtained from frequency response functions by cantilever beam simulation with MATLAB and three-axis vibration table experiment respectively.By comparing the frequency response functions generated by the state space model with the original data,it is found that the analyzed results are basically consistent and the error values are within the acceptable tolerances,which demonstrates the validity and accuracy of the proposed method.
作者 牟杭 陈怀海 Mou Hang,Chen Huaihai(State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210001, China)
出处 《国外电子测量技术》 2018年第4期1-6,共6页 Foreign Electronic Measurement Technology
基金 江苏高校优势学科建设工程基金资助
关键词 多输入多输出振动系统 状态空间 最小实现 降阶法 频响函数矩阵 multiple-input multiple-output(MIMO) system state space minimum realization method of the reduction of order frequency response function matrix
作者简介 牟杭,1993年出生,硕士研究生,主要研究方向为振动及其控制。E—mail:2651260213@qq.com;陈怀海(通信作者),1965年出生,教授,博士生导师,主要研究方向为振动环境实验、振动疲劳。E-mail:chhnuaa@nuaa.edu.cn
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