闭环系统辨识的模型结构检验

Model Structure Validity in Closed Loop System Identification

对于闭环系统辨识的模型结构检验问题,在预测误差辨识法的前提下,从参数估计的统计特性中推导出两概率模型不确定性边界及最优的输入滤波器形式。概率边界及输入滤波器是基于参数估计的渐近正态分布的方差矩阵,该方差矩阵由采样数据估计而得。根据未知参数的渐近方差矩阵内积形式从概率统计意义上构造模型参数及互相关函数的不确定性边界,从优化的角度推导输入滤波器的选取形式。最后用仿真算例验证本文辨识方法的有效性。

Aiming at the problem of the model structure validity in closed loop system identification, this paper derives two probabilistic model uncertainties and optimum input filter from statistical properties of the parameter estimation with the prediction error identification method. The probabilistic bounds and optimum input filter are based on an asymptotic normal distribution of the parameter estimator, accompanied by a covariance matrix, which has to be estimated from sampled data. The uncertainties bounds about the model parameter and cross-correlation function are constructed in the probability sense by using the inner product form of the asymptotic covariance matrix. And the input filter is derived from the point of optimization. Finally the simulation results verify the effectiveness of the proposed identification method.