The study on a kind of control system with nonlinear parabolic distributed parameters
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 wordsdistributed parameter control system nonlinear moving boundary stability measurability controllability
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- Curry D M, Cox J E. Transient, compressible heat and mass transfer in porous media using the strongly implicit iteration procedure [Z] AIAA No 72-23, 1972.Google Scholar
- ZHOU Jian-jun, TONG Sheng, LIU Xing-dong, et al. One-dimensional model of fire spread on the crown of trees and its application [J].Journal of China University of Science and Technology, 1996,26(supplement):218–222. (in Chinese)Google Scholar
- WU Qing-song, TONG, Sheng, ZHOU Jian-jun, et al. Model of fire spread on the crown of trees and computational simulation [J].Fire Safety Science, 1996,5(2):29–34. (in Chinese)Google Scholar
- XU Yan-hou. Transpiration cooling system of controlling temperature rise of heat protection shield [J].Journal of Shanghai Institute of Building Materials, 1994,7(3):259–264. (in Chinese)Google Scholar
- Friedman A.Partial Differential Equations of Parabolic Type [M]. Prentice, Inc, 1964.Google Scholar
- XU Yan-hou, WU Guang-yu, GONG Guang-hui, et al. The analysis and numerical simulation of dynamical functions of the transpiration cooling control system with surface ablation [J].Chinese J System Engineering and Electronics, 1993,15(10):75–81 (in Chinese)Google Scholar
- XU Yan-hou, WU Guang-yu, GONG Guang-hui, et al. Control of transpiration cooling system with thermal shield on the body of revolution [J].Computational Physics, 1995,12(1):71–78. (in Chinese)Google Scholar
- YANG Zhao-ji, XU Yan-hou, YANG Xue-shi. The second-type Volterra integral equations of transpiration cooling system and its numerical solutions [J].Journal of China University of Science and Technology, 1993,23(3):100–107. (in Chinese)Google Scholar