臺灣博碩士論文加值系統

本文探討應用H-infinite控制理論於樓房結構受地震作用之減振，分別考量控制系統位移與能量兩種控制輸出形式，設計最佳預力鋼鍵控制裝置。根據預期控制效用需求決定參數alpha及gamma之值，alpha愈小、gamma愈大，控制後系統阻尼增加愈大，表示要求愈高的控制效果，結構振動反應降低量愈大。針對相同原始阻尼之不同頻率結構，愈高頻結構必須選擇較大 值以達到相同的控制效果。依此參數選擇評估控制效果，確實能達到減振之功效。
文中並探討主結構模態參數誤差對評估控制後系統頻率及阻尼比之精確度的影響。得知基本周期誤差對位移控制輸出影響較大；原始阻尼比誤差對能量控制輸出影響較大。
針對時間延遲效應，分析顯示當控制力施加具時間延遲時，將使得控制系統阻尼比降低，若予忽略，將會降低控制效果，甚至造成系統不穩定。藉由增加系統原始阻尼比或選擇較小的alpha值，將使控制模態轉為較低模態，增加容許時間延遲量。同時，若增加原始阻尼比可選用較大alpha值以增大控制效果。最後，考慮時間延遲作最佳化設計，可確保控制系統的穩定性並達到與無延遲時相當的控制效果。

In this study,H-infinite control algorithm is applied to reduce the structural responses under seismic loads. Two kinds of controlled outputs, named “displacement controlled output” and “energy controlled output” are presented to design the optimal controller for structures equipped with active tendon systems. The value of parameters alpha and gamma are selected based on the desired control efficiency. The decrease of alpha or increase of gamma will result in larger control forces and better effectiveness in reducing structural responses. Larger has to be selected for stiff structures to achieve the same control effectiveness than flexible structures.
The influence of structural modeling error on the accuracy of estimating controlled frequencies and damping ratios was also investigated. It is found that control system with displacement controlled output are primarily affected by the errors of structural fundamental period, whereas the “energy controlled output” systems are more sensitive to the errors of structural original damping ratio.
In active control systems, control force execution time delay cannot be avoided. Small delay time not only can render the control ineffective, but also may cause the system instability. The maximum delay time for system instability increased with increasing structural original damping ratios or selecting smaller alpha in which the stability of control system are dominated by lower modes. In the final part of this thesis, an optimal time-delayed H-infinite control algorithm is developed for discrete-time systems. According to the proposed control algorithm, the structural system is assured to remain stable and the control effectiveness is not degraded even with the presence of time delay.

目 錄
誌謝..........................................i
中文摘要.....................................ii
英文摘要.....................................iii
目錄.........................................iv
表格目錄......................................vii
圖形目錄......................................viii
第一章 緒論...................................1
1.1 研究動機與目的............................1
1.2 文獻回顧..................................2
1.3 本文內容..................................4
第二章 連續時間H-infinite控制理論.............5
2.1 範數.....................................6
2.2 H-infinite控制理論推導....................7
2.3 樓房結構地震反應之H-infinite控制..........12
2.3.1 位移控制輸出............................12
2.3.2 能量控制輸出............................14
第三章 連續時間H-infinite控制系統數值驗證.....16
3.1 單自由度結構控制系統......................16
3.1.1 固定頻率結構之控制參數選擇..............17
3.1.1.1 位移控制輸出..........................17
3.1.1.2 能量控制輸出..........................20
3.1.2 變化頻率結構之控制參數選擇..............22
3.1.2.1 位移控制輸出..........................22
3.1.2.2 能量控制輸出..........................23
3.1.3 系統參數誤差之敏感度分析................24
3.1.3.1 位移控制輸出..........................24
3.1.3.2 能量控制輸出..........................27
3.1.4 控制效果評估............................29
3.1.5 系統能量................................30
3.1.6 部分量測輸出控制........................33
3.2 多自由度結構控制系統......................36
3.2.1 控制權重參數之選擇......................36
3.2.2 控制效果評估............................37
3.2.3 系統能量................................38
3.2.3 部分量測輸出控制........................39
第四章 時間延遲系統穩定分析...................40
4.1 時間延遲與系統模態特性....................40
4.1.1 單自由度系統............................40
4.1.2 多自由度系統............................43
4.2 時間延遲對轉換函數與動態歷時的影響........44
4.2.1 單自由度系統............................44
4.2.2 多自由度系統............................45
4.3 最大延遲時間..............................46
4.3.1 單自由度系統............................46
4.3.2 多自由度系統............................48
4.4 最大控制參數..............................50
4.4.1 單自由度系統............................50
4.4.2 多自由度系統............................51
第五章 離散時間H-infinite 控制理論與數值驗證..52
5.1 連續時間狀態方程式之離散化................52
5.1.1 無時間延遲之離散時間系統................53
5.1.2 具時間延遲之離散時間系統................54
5.2 離散時間之 控制理論.......................56
5.3 離散時間 數值模擬.........................59
5.3.1 單自由度系統............................59
5.3.2 多自由度系統............................60
第六章 結論與建議.............................62
參考文獻......................................64
表格..........................................67
圖形..........................................72

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