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System Approximation via Restructured Hankel Matrix
Circuits, Systems, and Signal Processing ( IF 2.3 ) Pub Date : 2021-06-02 , DOI: 10.1007/s00034-021-01745-2
Ramveer Singh Sengar , Kalyan Chatterjee , Jay Singh

This paper presents a modified minimal realization technique to reduce single input single output (SISO) systems from higher-order SISO systems. The reduction process is based on restructuring the Hankel matrix, which consists of two major elements, i.e., Time Moments and Markov parameters. The system transformation is executed to reduce the order of the system by maintaining the desired system properties. The modified Hankel Matrix is proposed to obtain an expected reduce order model, i.e., kth order reduced model by selecting \(\left[ {k \times k} \right]\) order square matrix and using Silverman’s algorithm. This paper presents a simple solution of model order reduction with the advantages of minimizing the steady-state error, fast convergence of steady-state behavior, better approximation in terms of rise time, peak time, and settling time at higher frequencies. Three different cases have been taken from the literature to validate the proposed technique with the comparisons of performance in terms of a quality check through performance indices and response matching between original and reduced-order models.



中文翻译:

通过重组 Hankel 矩阵的系统逼近

本文提出了一种改进的最小实现技术,以从高阶 SISO 系统中减少单输入单输出 (SISO) 系统。归约过程基于对 Hankel 矩阵的重构,该矩阵由两个主要元素组成,即时间矩和马尔可夫参数。执行系统转换以通过维护所需的系统属性来降低系统的阶数。提出修改后的Hankel矩阵,通过选择\(\left[ {k \times k} \right]\)获得一个预期的降阶模型,即k阶降阶模型排序方阵并使用 Silverman 算法。本文提出了一种模型降阶的简单解决方案,其优点是稳态误差最小,稳态行为收敛速度快,在较高频率下的上升时间、峰值时间和稳定时间方面具有更好的近似性。已经从文献中提取了三个不同的案例来验证所提出的技术,并通过性能指标和原始模型和降阶模型之间的响应匹配在质量检查方面进行性能比较。

更新日期:2021-06-02
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