非线性系统参数识别的频域方法

系统识别是现代控制过程的关键环节．本文提出了一种识别弱非线性振动系统参数的方法．本方法中，参数识别的数学模型是系统的一阶近似频率响应函数．首先，用多尺度法导出弱非线性强迫激励系统的频率响应函数．接着，利用非线性参数变换将此频率响应函数变换为系统参数的线性函数，在此基础上用最小二乘法识别系统的参数．最后，通过数值模拟检验了方法的精度．

Frequency Method of Parameter Identification of Nonlinear Systems

System identification is the key step for controlling the vibration. The frequency method of identifying parameters of weakly nonlinear vibrating system is presented in this paper. In the method, the mathematic model of parameter identification is frequency response function. Firstly, by means of multiple scale method the frequency response function of weakly nonlinear vibration system is derived. Next, a parameter transformation is made and the frequency response function becomes a linear function of the new parameters. Then, based on the frequency response function and with the least square method, the parameters of the system are identified. Finally, a numerical simulation is made to check the precision of the method.