基于主导能量最优逼近的模型降阶方法

本文从能量最优逼近的角度论述了一种新的模型降阶方法。首先根据系统输出的主导能量分布确定系统的主导极点,以此确定降阶模型的维数和分母系数;然后按照使系统主导能量与降阶模型主导能量之差为极小的最优准则,同时通过选择“能量因子”的数值来确定降阶模型的分子系数,从而获得连续系统和离散系统均可适用的统一降阶模式。本文提出的模型降阶方法,可以确保降阶模型的稳定性,具有良好的暂态和稳态拟合精度,并且简便实用。本中举倒说明了这一模型降阶方法的应用,并与其他模型降阶方法进行了对比,结果是令人满意的。

A Model Reduction Method Based on Optimal Approximation to the Dominent Energy

In this paper, a new model reduction method is developed from the viewpoint of optimal approximation to the energy. First, the dominent poles of the system are determined according to the dominent energy distribution of the system output, and the dimension and the denominator of the reduced model are obtained. Then, the parameters of the numerator are determined by using the method of minimizing the difference between the dominent energy of the system and that of the reduced model and by choosing the "energy factor" . So a united reduced mode is gained and applied to both the continued system and the discrete one. The model reduction method can guarantee the reduced model to be stable and to hava a good approximation to the original system in both the transient and the steady-state responses. The explanations of the practicability of the model reduction method are made by an example given at the end of this paper.