修正的ARMA模型在微悬臂系统辨识中的应用

在力学显微镜和光力学的研究中,微悬臂是一种被广泛使用的微机械器件。为了了解微悬臂的模态信息,采用ARMA模型对微悬臂进行系统辨识和模态参数识别。针对观测噪声会使时间序列模型辨识精度变低的问题,研究如何将带有观测噪声的ARMA模型转化为无观测噪声的ARMA模型。得到微悬臂的ARMA模型后将其转化为连续系统的传递函数,再从传递函数中求出微悬臂的各模态参数。为了减小微悬臂对外力的延迟响应时间,根据系统辨识得到的模型,构造一个复原滤波器,微悬臂的位移信号通过这个复原滤波器后得到作用力信号。仿真及实验结果证明了所用的系统辨识、模态参数识别及信号复原方法的有效性。

Application of Modified ARMA Model in System Identification for Micro-cantilevers

Micro-cantilever is a kind of micromechanical device which is widely used in the research of force microscope and optomechanics. We employ system identification and modal parameters identification to micro-cantilever via ARMA model in order to knowing the modal information of micro-cantilever. Aiming at the problem that observing noise will decrease the identification accuracy of time series model, we studied the problem of converting the ARMA model with observing noise to the ARMA model without observing noise. After obtained micro-cantilever’s ARMA model, this model was converted to a transfer function of continual system, then micro-cantilever’s modal parameters were calculated from the transfer function. A recovery filter was constructed on the basis of the model obtained by system identification in order to decrease the delay time of micro-cantilever response to external force. The applied force signal was output by inputting displacement signal into the recovery filter. Simulation result and experimental result show the effectiveness of system identification, modal parameter identification and signal recovery method presented by this paper.