Research Article | OPEN ACCESS
The Development of Mathematical Modeling for Solving Problem of Assessment of the Stability of Nonlinear Systems with Slowly Changing Parameters
1Khaled Batiha and 2Khaldoun Batiha
1Prince Hussein Bin Abdullah Faculty of Information Technology, Al al-Bayt University
2Faculty of Information Technology, Philadelphia University, Amman, Jordan
Research Journal of Applied Sciences, Engineering and Technology 2016 6:638-641
Received: June 8, 2015 | Accepted: August 22, 2015 | Published: March 15, 2016
Abstract
The major objective of this study is to obtain mathematical models for evaluation behavior of non-linear system, parameters non-linear elements are taken to be time change. The problem is solved by transaction from description at non-linear non-stationary system in space of variable states to description of its behavior in space of parameter increments by means of apparatus of Sensitivity functions. Using this apparatus, we transit from non-linear differential equation, to describing behavior system as a space of variable states to linear description at the systems increment change at these parameters. For overcoming the generalized functions which appear invariably during obtaining the sensitivity function, we used describing function. The main study also is to develop a mathematical model to estimate the stability of electric drive relay action and to identify areas of its robust stability when exposed to uncontrolled parametric perturbations described by harmonic laws.
Keywords:
Describing function, harmonic linearization, nonlinear non-stationary systems, stability, sensitivity functions,
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Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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