中山大学学报自然科学版 ›› 2018, Vol. 57 ›› Issue (6): 135-144.doi: 10.13471/j.cnki.acta.snus.2018.06.018

• 论文 • 上一篇    下一篇

一类含hysteresis的自控系统模型

徐伟1,2,孙涛1   

  1. 1.南京航空航天大学经济与管理学院,江苏 南京 210016;
    2.南京审计大学会计学院,江苏 南京211815
  • 收稿日期:2017-12-17 出版日期:2018-11-25 发布日期:2018-11-25

Model on a class of automatic control system with hysteresis

XU Wei1,2, SUN Tao1   

  1. 1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
     2. School of International Audit, Nanjing Audit University, Nanjing 211815, China
  • Received:2017-12-17 Online:2018-11-25 Published:2018-11-25

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。

关键词: 净化器, 时滞算子, 映射, 不动点, 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.

Key words: purifier, hysteresis operator, mapping, fixed point, decision model

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