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Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (2): 178-186.

• 论文 • 上一篇    下一篇

THE STUDY ON A KIND OF CONTROL SYSTEM WITH NONLINEAR PARABOLIC DISTRIBUTED PARAMETERS

周建军1, 徐燕侯2   

  1. 1. State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, P R China;
    2. Department of Mechanic Engineering, University of Science and Technology of China, Hefei 230026, P R China
  • 收稿日期:2000-12-12 修回日期:2001-10-30 出版日期:2002-02-18 发布日期:2002-02-18
  • 基金资助:
    the National Natural Science Foundation of China(59936140)

THE STUDY ON A KIND OF CONTROL SYSTEM WITH NONLINEAR PARABOLIC DISTRIBUTED PARAMETERS

ZHOU Jian-jun1, XU Yan-hou2   

  1. 1. State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, P R China;
    2. Department of Mechanic Engineering, University of Science and Technology of China, Hefei 230026, P R China
  • Received:2000-12-12 Revised:2001-10-30 Online:2002-02-18 Published:2002-02-18
  • Supported by:
    the National Natural Science Foundation of China(59936140)

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摘要： 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.

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.

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