Formularization Method for Calculating the Breakaway and Break-in Points and the Corresponding Gain of Root Locus Graphs

Q3 Engineering

Advances in Systems Science and Applications Pub Date : 2021-03-31 DOI:10.25728/ASSA.2021.21.1.1012

H. Shibly, Orwah H. Shibly

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引用次数: 0

Abstract

Break points, break-away and break-in points, are an essential part in root locus technique for single input single output linear invariant control systems. The importance of Break points comes from the fact that at the Break points at least two roots of the characteristic equation of the closed loop control system change their type from real to a complex at the break away point, and from complex to real at break-in point. This change affects the response of the system which can be crucial for some of systems’ applications. The conditions for being a Break point are analysed and a new formulated systematic method for finding the Break points and their corresponding gains is presented. An efficient algorithm was developed and can be solved analytically. There is no mathematical differentiation during calculation, and the algorithm can be programmed easily. The developed algorithm is applicable for any order of transfer function of a linear invariant control system. This method is compared with other common methods to show its merits and effectiveness.

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计算根轨迹图的断点、断点及相应增益的公式化方法

在单输入单输出线性不变控制系统的根轨迹技术中，断点、断点和断点是一个重要的组成部分。断点的重要性来自于这样一个事实，即在断点处，闭环控制系统的特征方程的至少两个根在断点处从实数变为复数，在断点处由复数变为实数。这种变化会影响系统的响应，这对某些系统的应用程序来说至关重要。分析了成为断点的条件，并提出了一种新的系统方法来寻找断点及其相应的增益。开发了一种有效的算法，该算法可以解析求解。在计算过程中没有数学微分，并且算法可以很容易地编程。该算法适用于线性不变控制系统的任意阶传递函数。将该方法与其他常用方法进行了比较，以表明其优点和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Systems Science and Applications Engineering-Engineering (all)

CiteScore

1.20

自引率

0.00%

发文量

期刊介绍： Advances in Systems Science and Applications (ASSA) is an international peer-reviewed open-source online academic journal. Its scope covers all major aspects of systems (and processes) analysis, modeling, simulation, and control, ranging from theoretical and methodological developments to a large variety of application areas. Survey articles and innovative results are also welcome. ASSA is aimed at the audience of scientists, engineers and researchers working in the framework of these problems. ASSA should be a platform on which researchers will be able to communicate and discuss both their specialized issues and interdisciplinary problems of systems analysis and its applications in science and industry, including data science, artificial intelligence, material science, manufacturing, transportation, power and energy, ecology, corporate management, public governance, finance, and many others.