用李群微分代數方程做結構的滑模控制

By using the LGDAE to solve the Sliding Mode Control problems of Structures

田偉樂(Wei-Le Tian)

指導教授 ： 劉進賢

國立臺灣大學/工學院/土木工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.00515

摘要

在土木建築中，地震是必然會遇到的問題，如何將地震影響力降低是每個建築工程師所追求的目標。
在劉教授於2013年時所推導出來的李群微分代數方程法，對於地震問題有了新的方向。將李群微分代數方程法與二階線性最佳控制法及滑模控制相結合後，對於結構物起到了快速收斂控制的效果。透過此法我們不但有效的控制住了結構物，與傳統方法比較起來，此法具有更快速的收斂效果與更佳的收束效果，對於控制方法上展開到了新的一面。
在本文中，除了會介紹李群微分代數方程法與上述所提到的方法的基本理論外，還會將其歸納與應用於多層樓的結構物中，模擬其在不同類型的地震力下的振盪情形，並予以總結。

關鍵字

地震問題 ； 李群 ； 微分代數方程 ； 滑模控制 ； 結構動力

並列摘要

There are a lot of important problems you need to face in civil and structure engineering science. One of them is earthquake. How to reduce the influence of the earthquake is every civil engineer want to seek for.
In 2013, Professor Liu had derived the Lie-group differential algebraic equations(LGDAE), which had a great effectiveness in controlling the effect of the earthquake. When we combine LGDAE with the linear quadratic(LQ) optimal control methodologies and the Sliding Mode Control(SMC), we have the fast convergence effect in controlling the structures. Not only we can effectively control the structures by using this method but also the faster and better control effect than the traditional method can be seen in this method.
In this thesis, we will describe the theory of LGDAE, LQ method and SMC. Furthermore, we use this method in multiple structures. We write a program to simulate the response of the structures under different earthquakes. After that, there are some conclusions and future works at last.

並列關鍵字

Lie-group ； differential algebra equation ； sliding mode control ； dynamics of structures ； earthquake problems

參考文獻

[3] M.Kubicek, V.Hlavacek, Numerical solution of nonlinear boundary value problems with applications. Prentice-Hall, New York .(1983)

[22] C.-S.Liu, A Lie-group shooting method for simultaneously estimating the time-dependent damping and stiffness coefficients. CMES: Computer Modeling in Engineering & Sciences, Vol. 27, pp. 137-149. (2008)

[1] Anil K.Chopra, Dynamics of Structures theory and applications to earthquake engineering, Fourth edition. (2012)

[4] J.Vlassenbroeck, R.Van Dooren, A Chebyshev technique for solving nonlinear optimal control problems. IEEE Trans Auto , Vol. 33,pp. 333-40(1988).

[6] M.J.Mahmoodabadi, S.Momennejad , A.I.Bagher , Online optimal decoupled sliding mode control based on moving least squares and particle swarm optimization. Information Science, Vol. 268,1, pp. 342-356.(2014)