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研究生： 連怡華
Lian, Yi-Hua
論文名稱： LQR控制結合系統識別應用於結構物地震反應之研究
Research on LQR control combined with system identification applied to the seismic response of structures
指導教授： 朱聖浩
Ju, Shen-Haw
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2021
畢業學年度： 109
語文別： 英文
論文頁數： 101
中文關鍵詞： 系統識別 、線性二次調節器 、Riccati方程 、有限元素模型 、最優線性控制
外文關鍵詞： System identification, Linear quadratic regulator, Riccati equation, Finite element model, Optimal linear control
相關次數： 點閱：116  下載：23 
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    • 本論文旨在利用遞迴子空間之系統識別方法以及二次線性調節器(LQR控制器)應用到結構物受到地震的反應。建立有限元模型並透過電腦輔助分析程式獲取結構物上加速度反應歷時資料來得到系統參數，將已知的結構質量矩陣以及結構參數推估勁度矩陣，再由LQR控制器進一步控制結構位移以及速度反應，並由控制前後的結果來討論此方法的有效性。
    本研究將不同自由度大小以及不同情況的有限元模型施加人工地震，進行每一時間步的遞迴子空間識別，並將識別結果分別與有限元模型計算的結果以及降階的狀態空間方程推算的結果做比較，藉此了解此系統識別方法的準確性。一旦有了結構參數並決定LQR控制的權重矩陣大小後，就能計算出在結構物上要額外施加的力大小，透過結構物最頂層上的一組LQR控制器給予控制力達到降低結構反應的效果。此外，本文亦施加不同最大地表加速度(PGA)以及不同主要頻率(Ts)的人工地震於模型，並在結構物上安裝兩組控制器，了解此控制方法對於不同地震情況下的適用性，也討論了不同數量控制器的有效性。
    由研究分析結果來看，LQR控制方法在各種不同建築結構以及在不同地震激勵下的結構都能有良好的控制結果，且僅一組控制器就有不錯的控制能力。而系統識別應用在大部分結構物也都能良好的識別結構參數。電腦輔助分析程式由朱聖浩教授研究團隊所開發，分析程式以及研究成果皆為公開資源。

    This paper aims to apply the recursive subspace system identification (RSI) method and the linear quadratic regulator (LQR) to the finite element model under seismic excitation. The acceleration response time data on the structure is obtained through the computer-aided analysis program, thereby obtaining the system parameters. Then the LQR controller further controls the structure response and discusses the effectiveness of the LQR method.
    In this research, artificial earthquakes are applied to structures under different conditions. The RSI method is performed at each time step, and the recognition results are compared with the calculation results of the finite element model and the reduced-order state space equation to understand the accuracy of the system recognition method. After obtaining the structural parameters and determining the weighting matrix of the LQR control, the control force can be calculated. The force given by the LQR controller at the top of the structure can reduce the response of the structure. In addition, this paper also applies artificial earthquakes with different PGA and different main periods to the model to understand the applicability of the control method to different earthquake situations.
    According to the research and analysis results, the LQR control method has a good control effect when applied to various building structures. System identification can also identify most structural parameters well. The computer-aided analysis programs are developed by Shen-Haw Ju’s research team, which are open source.

    摘要 I Abstract II Acknowledgement III Contents IV List of Tables VI List of Figures VIII Chapter 1 Introduction 1 1.1 Background and research purposes 1 1.2 Literature review 2 1.2.1 Study of the tuned mass dampers (TMD) 2 1.2.2 Study of the semi-active and active tuned mass dampers 3 1.2.3 Study of the linear quadratic regulator (LQR) 4 1.3 Overview 6 Chapter 2 Theories and Methods 7 2.1 Theories of system identification 7 2.2 Subspace Identification 7 2.2.1 Theory of subspace identification 7 2.2.2 Parameter confirmation 13 2.3 Recursive Subspace Identification (RSI) Algorithms 14 2.4 Equation of motion of the structure 17 2.5 Optimal linear control 18 2.5.1 Limited time state controller 18 2.5.2 Infinite time state controller (Infinite horizon LQR) 19 2.6 Solution of the Riccati equation 23 2.6.1 The continuous time algebraic Riccati equation 23 2.6.2 The discrete time algebraic Riccati equation 24 2.6.3 Description of the program 25 Chapter 3 Modeling Procedure 27 3.1 Introducing the execution file 27 3.2 Operation procedure of element model 28 3.3 Artificial earthquake 36 3.3.1 SIMQKE 36 3.3.2 The process of generating seismic acceleration 37 Chapter 4 Simulation and Cases Study 41 4.1 System identification with RSI method 41 4.1.1 Low-floor building 42 4.1.2 High-floor building 47 4.1.3 Asymmetric structure 55 4.1.4 Section summary 63 4.2 LQR control applied to structures 64 4.2.1 Symmetric structure 64 4.2.2 Asymmetric structure 77 4.2.3 Section summary 84 4.3 LQR control of the structure under different artificial earthquake excitations 85 4.3.1 Section summary 94 Chapter 5 Conclusions and Future Work 95 5.1 Conclusions 95 5.2 Future work 97 reference 98

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    劉豹,現代控制理論,台北市科技圖書股份有限公司,1992年2月
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