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標題: H∞ 直接輸出回饋之結構控制策略
On Control Strategies of H∞ Direct Output Feedback Control of Structures
作者: 張長菁
Chang, Chang-Ching
關鍵字: H-infinite direct output feedback control;H∞ 直接輸出回饋控制理論;Time delay;Active control;Earthquake Engineering;時間延遲;主動控制;地震工程
出版社: 土木工程學系
本文探討主動控制系統中考慮外力擾動且具強健性之 控制法則,應用滿足最小熵數之H∞直接輸出回饋控制理論於建築結構受地震作用之減振。分別考量層間變位及系統能量兩種不同控制輸出形式所設計之最佳預力鋼鍵控制裝置,分析比較在相同的控制條件下降低結構動態反應之效用。理論分析結果發現採用直接速度回饋僅需使用單一控制裝置及少量速度感應器便能增加結構系統阻尼比,達到良好的減震效果。由於本文發展之控制理論係由線外計算常數回饋增益矩陣值,當實際應用時,只需將此增益矩陣值乘以輸出量測,即可得知需施加的控制力大小,為相當可行之結構振動控制方式。此外,在H∞ 控制理論中,能藉由調整兩控制參數α與γ以增加結構系統主要模態阻尼比,在控制設計上具有較大彈性及較佳的減振效果,選擇γ值愈小或α值愈大,控制效果愈佳,但對任一結構系統而言,γ值必須滿足一下限值且α也必須滿足一上限值,否則將造成整體控制系統不穩定,本文針對單自由度結構,推導得知控制參數α上限與γ下限臨界值之解析式,以作為控制參數選擇之參考。另一方面,為克服控制力施加時間延遲效應,以單層建築結構裝設預力鋼鍵控制裝置為例,進一步推導具時間延遲時,臨界控制參數值之解析式,使得能夠藉由選擇適當的控制參數將時間延遲效應降至最低,不但可確保控制系統穩定,且可達到預期減振目標。

In this paper, a H∞ direct output feedback control algorithm through minimizing the entropy is developed to reduce the structural responses due to dynamic loads such as earthquakes. Two kinds of controlled outputs, named “interstory drift controlled output” and “system energy controlled output” are presented to design the optimal controller for a structure equipped with active tendon systems. Their merits are evaluated based on the control effectiveness under the same control efforts. It is concluded that direct velocity feedback control is effective in reducing structural responses with much fewer sensors and controllers than the degrees of freedom of the controlled structure. The control forces are obtained from the multiplication of direct output measurements by a pre-calculated time-invariant feedback gain matrix. Thus, it is quite feasible for real implementation. To achieve optimal control performance and assure control system stability, the strategy to select both control parameters α and γ is extensively investigated considering the control force execution time delay. It is found that the selection of smaller γ or larger α will result in better control effectiveness, but larger control forces requirement. However, a lower bounded of γ and an upper bound α exist. The selection beyond these values will cause the system instability. In this paper, the analytical expressions of the upper and lower bounds of γ and α are derived for the design of a stable control system. Moreover, in real active control, 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. In this study, explicit formulas of the maximum allowable delay time and critical control parameters are derived for reference in avoiding the control system instability. Some solutions are also proposed to increase the maximum allowable delay time.
Appears in Collections:土木工程學系所

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