Most of the physical structures may be described in terms of mathematical models. The mathematical methods of system modelling also lead to a thorough explanation of the mechanism in the form of mathematical equations, which are often difficult to use for both analysis and controller synthesis. Consequently, it is useful and very important to determine the likelihood of different calculations of the same type, but in a lower-order representation, which can be assumed to correctly represent almost all the basic features of the system under examination. In this article, the proposed method is based on the modified balanced truncation method (BTM) by which the steady-state value from the problem of the BTM has been circumvented. This weakness has been eliminated by using a modified BTM to narrow the deviations by incorporating a gain factor into the response transfer matrix of the reduced-order model (ROM) to adjust the steady-state value of the ROM, without affecting the variations in dynamical behaviour as compared to the original system. To illustrate the proposed method, a real-time application model has been reduced where the ROM retains all the essential characteristics of the original system. In order to analyse the effectiveness, accuracy and validation with the other existing reduction methods, two standard numerical test systems have been taken from the literature and been tested also.

中文翻译：

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使用改进的平衡截断方法的线性降阶系统

大多数物理结构可以用数学模型来描述。系统建模的数学方法也以数学方程的形式对机制进行了彻底的解释，这通常很难用于分析和控制器综合。因此，确定相同类型的不同计算的似然性是有用且非常重要的，但采用低阶表示，可以假设它可以正确表示所检查系统的几乎所有基本特征。在本文中，所提出的方法基于改进的平衡截断方法 (BTM)，通过该方法避免了 BTM 问题中的稳态值。通过使用改进的 BTM 通过将增益因子纳入降阶模型 (ROM) 的响应传递矩阵以调整 ROM 的稳态值来缩小偏差，从而消除了这一弱点，而不会影响动力学的变化。与原始系统相比的行为。为了说明所提出的方法，一个实时应用模型已经被简化，其中 ROM 保留了原始系统的所有基本特征。为了分析与其他现有缩减方法的有效性、准确性和有效性，从文献中提取了两个标准数值测试系统并进行了测试。与原始系统相比，不会影响动态行为的变化。为了说明所提出的方法，一个实时应用模型已经被简化，其中 ROM 保留了原始系统的所有基本特征。为了分析与其他现有缩减方法的有效性、准确性和有效性，从文献中提取了两个标准数值测试系统并进行了测试。与原始系统相比，不会影响动态行为的变化。为了说明所提出的方法，一个实时应用模型已经被简化，其中 ROM 保留了原始系统的所有基本特征。为了分析与其他现有缩减方法的有效性、准确性和有效性，从文献中提取了两个标准数值测试系统并进行了测试。