Applied Mathematics and Mechanics

, Volume 23, Issue 2, pp 178–186 | Cite as

The study on a kind of control system with nonlinear parabolic distributed parameters

  • Zhou Jian-jun
  • Xu Yan-hou
Article
  • 33 Downloads

Abstract

The modelling of one kind of nonlinear parabolic distributed parameter control system with moving boundary, which had extensive applications was presented. Two methods were used to investigate the basic characteristics of the system: 1) transforming the system in the variable domain into that in the fixed domain; 2) transforming the distributed parameter system into the lumped parameter system. It is found that there are two critical values for the control variable: the larger one determines whether or not the boundary would move, while the smaller one determines whether or not the boundary would stop automatically. For one-dimensional system of planar, cylindrical and spherical cases the definite solution problem can be expressed as a unified form. By means of the computer simulation the open-loop control system and close-cycle feedback control system have been investigated. Numerical results agree well with theoretical results. The computer simulation shows that the system is well posed, stable, measurable and controllable.

Key words

distributed parameter control system nonlinear moving boundary stability measurability controllability 

CLC number

O302 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Zhou Jian-jun
    • 1
  • Xu Yan-hou
    • 2
  1. 1.State Key Laboratory of Fire ScienceUniversity of Science and Technology of ChinaHefeiP R China
  2. 2.Department of Mechanic EngineeringUniversity of Science and Technology of ChinaHefeiP R China

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