弹性结构有限元控制系统
Finite Element Control Systems of Elastic Structures
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摘要: 本文讨论了经有限元方法处理后的弹性结构系统的可控、可观测、镇定等问题.所得的结论与用分布参量系统模型所得的结论一致,但却便于用计算机计算且方法简单.在一、中研究了系统的可控与可观测的问题,给出了易于用计算机判别的条件.在二、中对于采用线性反馈镇定弹性体的问题进行了仔细的讨论,指出对弹性结构系统而言,若系统完全可控仅用位移反馈可以任意配置振动频率但却无法镇定系统,而仅用速度反馈虽可以进行镇定但镇定能力是有限的,对于在系统运动方程中包含刚体运动成分的情形也作了研究.在三、中对梁的控制问题用有限元进行了处理,指出直梁作为一个系统可以分解为拉压、扭转和两个方向弯曲这四个互不关联的子系统,它们的可控与可观测问题可以分别进行讨论.最后对折线型刚架的可控与可观测的问题也作了探讨.Abstract: The article deals with the problems of controllability,observability and stabilizability of an elastic-structural system treated by the finite element method. The results obtained here agree with that obtained in distributed parameter-system model, nevertheless, they are more convenient than those in carrying out the computation with a computer, at the same time the method appears much easier than the conventional one. In section one,the system's controllability and observability are studied and some conditions which are easier to be justified by computer are given. In section two, the problem of stabilizing an elastic object by the use of linear feedback is fully discussed. As the attained results there show that, so far as an elastic-structural system is concerned, it is possible to assign arbitrary frequencies of vibration only by the use of displacement feedback, however, it is impossible to stabilize the system while the system is completely controllable. While the velocity feedback can stabilize the system, but its ability is limited. The case of rigid body motion involved in the system equation has also been discussed. In section three, the control of a straight beam is treated by the finite element method. The whole system of a beam can be decomposed into four irrelevant subsystems of tension-compression, torsion, bending in two directions, their controllability and observability are also analyzed respectively. The controllability and observability of segment-shaped beam are discussed in the end.
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[1] 王康宁,关望直,弹性振动的镇定I,中国科学,17(1974). [2] 王康宁,关于弹性振动的镇定Ⅱ,数学学报,18 (1975). [3] 王康宁,关肇直,弹性振动的镇定Ⅲ,中国科学,19(1976). [4] 宋健,于景元,带有反馈控制器的分布系统,中国科学,18(1975). [5] 宋健,于景元,点测量点控制的分布参数系统,中国科学,22(1979). [6] 冯康,基于变分原理的差分格式,应用数学与计算数学,2, 4 (1965). [7] 冯康,《数值分析》,国防工业出版社,北京,(1979). [8] Batha, K.J.and Wilson, E.L., Numerical method in finite element analysis, Pretice-Hall Inc.Englewood,Cliffs.New Jersey. [9] Ray, W.H.and Lainientis, D.G., Distributed parameter systems identification estimation and control, Marcel Dekker Inc., New York and Basel,(1978). [10] Likins, P.W.and Yoshiaki Ohkami,Altitude control concepts for precision-pointing nonrigid spacecraft (final report) prepared for George C.Marshall Space Flight Center Marshall Space Flight Center, Alabama.35812 Contract No NASS-28358 Mod 4 Contract Type CR, (1975). [11] Gabasov, R.and Kirillora, F., The Qualitative Theory of Optimal Processes, Marcel Dekker Inc.New York and Basel, (1976). [12] Rosenbrock, H.H., State-Space and Multivariable Theory, Nelson, London,(1970). [13] Wonham, W.M., Linear Multivariable Control.A Geometric Approach, Springer,Berlin, (1974). [14] Aziz, A.K., Wingate,J.W.and Balas,M.J., Control Theory of Systems Governed by Partial Differential Equations, Academic Press Inc., New York, San Francisco, London.(1977). [15] Колесников, К, С, и Сухов, В, Н., Упругий Аппарат Как Обвект Автоматического Упрвлсния, Мсшцносмроенне,(1974). [16] Гантмахер, Ф. Р., Теорцв Мамрцц, Изд, Наука, москва, (1966). [17] Wilkinson, J.H.Reinsch.C.(Editors), Handbook for Automatic Computation, Vol.II.Linear Algebra Springer-Verlag.Berlin, (1971). [18] 黄琳,郑应平,张迪,李雅普诺夫第二方法与最优控制器分析设计问题,自动化学报,2,(1964). -
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