基于部分可控性矩阵的模型降阶方法及误差分析

Model Reduction Based on Partial Block Controllability Matrix and Its Error Analysis

针对单输入单输出系统,利用部分可控性矩阵的M-P广义逆作为集结矩阵,提出了一种新的近似集结法模型降阶方法。首先给出了当系统可控与不可控时的2种降阶模型,然后通过误差最小分析归结为一种降阶模型,并利用向量到子空间的距离给出了不同阶降阶模型误差的一个简单计算方法。以此误差作为标准,可以方便地选择满足需要的降阶阶数及降阶模型。最后以实例表明了该方法的有效性和应用性。

For the single input and single output linear system,a new method of approximately aggregated model reduction is presented by using the Moore-Penrose generalized inverse of a partial block controllability matrix as an aggregation matrix.Two aggregated order reduction models are presented firstly under the condition that the system is controllable and uncontrollable,and then a unique least error reduced model is integrated no matter whether the system is controllable or not.A simple method is deduced to compute the errors of all order reduced models,which are the distances from some known vectors to some certain subspaces.The errors of all order reduced models can be used as a model reduced order selection criterion and according to this the best order reduced model can be chosen easily.Some examples are shown to verify the validity and feasibility of this method.