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標題: H∞直接輸出回饋之結構控制
H∞ Direct Output Feedback in Structural Control
作者: 潘銘棋
Pan, Ming-Chi
關鍵字: Earthquake Engineering
Active Control
H-infinite Control
Time Delay
Direct Output Feedback
出版社: 土木工程學系
摘要: 本文探討滿足最小熵數之H∞直接輸出回饋控制理論於建築結構受地震作用之減振,熵數為一個藉由參數γ在H∞範數及H2範數之間作取捨的性能指標,當γ值趨近無限大時,熵數即等於H2範數,此時滿足最小熵數的控制器即為最佳H2控制器。H∞控制理論中可選擇的控制參數有α及γ,選擇γ值愈小或α值愈大控制效果愈佳。 對於單自由度結構,本文推導出在特定參數下直接輸出回饋增益解析解,並藉由控制後模態參數的改變、頻域及時域的動態反應分析,得知採用直接速度回饋可產生與狀態回饋相當的控制效果,由於直接速度回饋係由線外計算常數回饋增益值,對於實際應用而言,此增益值直接乘以輸出量測即可得知需施加的控制力大小,不但計算簡單且可大量減少感應器數目,所以H∞直接速度回饋為可行的結構振動控制方式。對於相同原始模態阻尼比之結構,越堅硬結構需選擇較大的α值方能得到相同的控制後阻尼比,也才能產生相近的減振效果。 當控制力施加具時間延遲時,將使得控制後系統阻尼比降低,甚至造成整體控制系統不穩定。若藉由增加系統高頻原始阻尼比或選擇較小的α值,可使控制模態轉為較低模態,增加容許時間延遲量。同時,增加高頻原始阻尼比可選擇較大的α值以增大控制效果。
In this study, a H∞ direct output feedback control algorithm, through minimizing the entropy, a performance index measuring the tradeoff between the H∞ optimality and the H2 optimality, is applied to reduce the structural responses under seismic loads. The values of control parameters γ and α are selected based on the desired control efficiency. The decrease of γ or increase of α will result in better effectiveness in reducing structural responses, but larger control forces required to be applied. Larger α has to be selected for stiff structures to achieve the same control effectiveness than flexible structures. For a SDOF damped structure, exact output feedback gains are derived. From the modal parameters, frequency domain and time domain analysis of the controlled system, we found that the control effectiveness of direct velocity output feedback control is similar to state feedback control. The control forces are then calculated from the multiplication of output measurements by time-invariant feedback gain matrix. Small number of sensors and simple on-line calculation made the proposed control algorithm favorable to real implementation. 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 are obtained to calculate the maximum allowable delay time to avoid system instability. In addition, a formula is also derived to determine the critical control weighting factor so as to make the system stability dominated by the lower mode, and hence the allowable delay time is significantly lengthened. In addition, the maximum delay, (td)max, for system instability can be increased with increasing structural original damping ratios or selecting small α in which the stability of control system are dominated by lower modes.
Appears in Collections:土木工程學系所



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