线性定常系统特征模型的特征参量辨识

CHARACTERISTIC PARAMETERS IDENTIFICATION OF CHARACTERISTIC MODELS OF LINEAR TIME INVARIANT SYSTEMS

说明线性定常系统特征模型的特征参量是一组由高阶线性定常系统的相关信息压缩而成,于是不能简单的作为与状态无关的慢时变参数来处理.基于特征建模思想,建立了线性定常系统特征模型的特征参量与子空间方法之间的联系,给出了一种该特征模型的特征参量的合成辨识算法.同时证明了在用于子空间辨识的样本量充分大和用于状态估计的时间充分长的情况下,特征参量的估计值与真值之间的误差达到充分小.最后,对于一个六阶的单输入单输出线性定常系统的仿真例子,对投影的带遗忘因子最小二乘算法和合成辨识算法进行了比较,验证了合成辨识算法的有效性.

For the linear time invariant（LTI） systems,it is shown that the characteristic parameters of characteristic model are condensed by the system information of high order LTI form,therefore some tracking algorithms,which are used to deal with the slowly time varying parameters that are unrelated with system states,are not suitable in this case.This paper establishes the connection between the characteristic parameters of characteristic model for LTI systems and subspace method,and presents a composite identification algorithm to estimate these parameters.Furthermore,it is proved that when the sample number for subspace identification is sufficiently large and the time for state estimation is sufficiently long,the error between the estimated values and the true values of characteristic parameters can be sufficiently small.A simulation example of six order single input single output（SISO） model is considered, and the proposed method is compared with the projecting forgetting factor recursive least square（FFRLS） algorithm.The simulation results show that the proposed method in the paper has more advantage than FFRLS.