论文标题
型号降低带零零位置和高阶力矩匹配
Model reduction with pole-zero placement and high order moment matching
论文作者
论文摘要
在本文中，我们计算了一个大订单$ n $系统的低订单近似值，该系统与$ν$订单的订单$ j_i $ j_i $相匹配，以$ν$插值点为$ \ ell $ poles和$ k $ zeros和$ k $ zeros固定和$ n $ n-插值点。我们在自由参数中得出显式线性系统，以同时实现所需的极点零位置并匹配所需的高阶矩。我们计算满足约束的自由参数的封闭形式，作为$ν$订单线性系统的解决方案。此外，对于数据驱动的模型降低，我们将Loewner矩阵的构建概括为包括数据以及施加的极点和高阶矩约束。由此产生的近似值实现了良好的规范近似值和在感兴趣区域中原始系统动态的保存之间的权衡。
In this paper, we compute a low order approximation of a system of large order $n$ that matches $ν$ moments of order $j_i$ of the transfer function, at $ν$ interpolation points, has $\ell$ poles and $k$ zeros fixed and also matches $ν-(\ell +k)$ moments of order $j_i+1$, where $j_i+1$ is the multiplicity of the $i$-th interpolation point. We derive explicit linear systems in the free parameters to simultaneously achieve the required pole-zero placement and match the desired high order moments. We compute the closed form of the free parameters that meet the constraints, as the solution of a $ν$ order linear system. Furthermore, for data-driven model reduction, we generalize the construction of the Loewner matrices to include the data and the imposed pole and higher order moment constraints. The resulting approximations achieve a trade-off between the good norm approximation and the preservation of the dynamics of the original system in a region of interest.
