Model on a class of automatic control system with hysteresis

XU Wei

doi:10.13471/j.cnki.acta.snus.2018.06.018

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Model on a class of automatic control system with hysteresis

更新时间：2023-12-11

- Model on a class of automatic control system with hysteresis
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 57, Issue 6, Pages: 135-144(2018)
- 作者机构：
  
  1. ．南京航空航天大学经济与管理学院,江苏,南京,210016
  2.  2．南京审计大学会计学院,江苏,南京,211815
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2018.06.018
  CLC：
- Published：2018，
  
  Published Online：25 November 2018，
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XU Wei. Model on a class of automatic control system with hysteresis. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(6):135-144(2018)
DOI：

XU Wei. Model on a class of automatic control system with hysteresis. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(6):135-144(2018) DOI： 10.13471/j.cnki.acta.snus.2018.06.018.

摘要

很多自控系统都存在时滞效应，描述有害物质反应扩散过程的数学模型就是某种含时滞的微分方程。由于迟滞因子的非线性特性，如函数的许多优良性质被破坏，使得许多具有迟滞特性的模型几乎无法进行分析，因此在一般自控系统的建模中，人们都略去时滞因素。首先根据空气净化系统的功能原理引进了一类时滞算子，通过一系列细致分析给出了时滞算子的若干重要性质。然后主要利用不动点定理证明了含时滞的微分方程整体古典解存在唯一性，最后提出了精细地测算净化设备投资与效益的决策模型。

Abstract

There exists hysteresis effects in many automatic control systems. Models of mathematical describing harmful matter to reactdiffuse process are some kind of differential equations with hysteresis in air cleaning system. Due to the nonlinearity of hysteresis factors

such as the destruction of many excellent properties of functions

many models with hysteresis characteristics hardly can be analyzed. Therefore

in the modeling of general automatic control systems

hysteresis factors are omitted. First

a class of hysteresis operators are introduced according to the functional principle of air purification system

and some important properties of hysteresis operators are given through a series of detailed analysis. Then the existence and uniqueness of the global classical solution of differential equation with hysteresis are proved by using the fixed point theorem. Finally

a decision model for calculating the investment and benefit of purification equipment is proposed.

关键词

净化器时滞算子映射不动点决策模型

Keywords

purifierhysteresis operatormappingfixed pointdecision model

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Related Author

WANG Jinhua

XIANG Hongjun

ZHAO Yulin

PIAO Yongjie

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Related Institution

College of Mathematics and Finance, Xiangnan University



Department of Mathematics, College of Science, Yanbian University, Yanji

School of Mathematics and Information, China West Normal University, Nanchong

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