應用相位控制原理於調諧質塊阻尼器最佳化結構控制設計

Application of Phase Control for Optimal Design of Tuned Mass Dampers

賴勇安(Yong-An Lai)

指導教授 ： 鍾立來 ； 吳賴雲

國立臺灣大學/工學院/土木工程學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.01630

摘要

本文旨在探討線性被動式調諧質塊阻尼器(被動式TMD)之最佳化設計，以及相位控制之控制律，於半主動式調諧質塊阻尼器(半主動式TMD)與主動式調諧質塊阻尼器(主動式TMD)之減振效益研究。首先，以單自由度結構位移之均方為最小，提出線性被動式TMD之最佳設計方法-迭代法、圖表法與最佳化設計公式。接著，對於半主動式TMD及主動式TMD；半主動式TMD之模型為被動式TMD加裝半主動式摩擦機構，以可變之正向力調整摩擦機構之摩擦力；主動式TMD之模型為被動式TMD加裝主動式噴射機構，以噴射力之方式施加主動控制力於質塊上；本文以相位控制為控制原理，提出一組控制律，使半主動式TMD及主動式TMD盡量維持-90度相位差之控制律，以達最佳之減振效果。以0.5Hz單自由度結構於強迫振動及數值模擬之結果顯示，結構加裝半主動式TMD或主動式TMD後，可有較大之減振頻率帶寬；於隨機振動之數值模擬結果顯示，其結構反應都優於最佳化被動式TMD，且由頻率比敏感度及TMD阻尼比敏感度分析，半主動式TMD及主動式TMD對於頻率比及TMD阻尼比皆不敏感，可解決被動式TMD適應性之問題；經由三維圖進行頻率比及TMD阻尼比最佳化設計後，可再增加半主動式TMD及主動式TMD之減振效益。最後以台北101結構轉換為單自由度系統作為案例分析，在台北101半年回歸期風力下，分析結果顯示，加裝被動式TMD，三種最佳化設計方式與實際最佳值之減振效果相若，皆可達減振目的；加裝半主動式TMD與主動式TMD不僅均可達減振目的，且減振效果更較最佳化被動式TMD為佳；並且，由於無適應性之問題，可不需進行最佳化設計即可有優於被動式TMD之減振效果，驗證此控制律作用之半主動式TMD與主動式TMD確實可行並有其優點。

關鍵字

調諧質塊阻尼器 ； 最佳化設計公式 ； 結構控制 ； 半主動控制 ； 主動控制 ； 相位控制

並列摘要

The present study aims at developing an optimal design of linear passive tuned mass dampers (PTMD) and proposing the phase control algorithm for semi-active tuned mass dampers (SATMD) and active tuned mass dampers (ATMD). At first, by minimizing the sum of square of structural displacement response, three kinds of optimal design methods are proposed for PTMD - the iteration method, the diagram method and the optimal design formulae. Then, phase control algorithm for SATMD and ATMD is proposed. The principle of phase control algorithm is to keep the TMD response to maintain 90° phase lag to the structure. Finally the PTMD, SATMD and ATMD are, respectively, implemented on the structure of Taipei 101 which is simplified to single degree of freedom and subjected to the design wind forces. The numerical simulation result shows that three kinds of optimal design methods for PTMD may suppress the vibration of structure. Moreover, by the phase control algorithm, SATMD and ATMD not only have better performance than the optimal PTMD, but also improve the robustness. Therefore, even without the optimal design procedure, SATMD and ATMD both are more effective than the optimal PTMD.

並列關鍵字

Tuned Mass Damper (TMD) ； optimal design formulae ； structural control ； sem-acitve control ； active control ； phase control

參考文獻

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