通用型複合式質量阻尼器系統之時間延遲與去調諧效應交互影響研究

Interaction Effects of Detuning and Time-delay on Generalized Hybrid Mass Damper Systems

The vibration mitigation performance of a conventional tuned mass damper (TMD) system is very sensitive to the fluctuation in tuning of the designed frequency to the natural frequency of the main system. In view of the stochastic characteristics of external loading and the errors of identifying system parameters, a hybrid mass damper (HMD) system with optimal selection on control parameters can enhance the designed performance with the help of a supplementary active force acted between the main system and the mass damper. However, the control performance degradation induced by the control force application time delay should be considered and investigated before practical application. Having the best versatility in mind, the generalized hybrid mass damper (GHMD) systems are reclassified and investigated in this paper to examine diversifying needs. The variations in their modal properties and tuning effects with respect to delay time are addressed based on an explicit formula derived from a delayed exponential characteristic equation (DECE). It is found that the active control force with delay-time chosen as the natural period of the system in a HMD based on an uncompensated output feedback scheme will keep the robustness on response reduction performance. This advantage degrades for non-optimal systems with delayed control force due to the detuning effects. A detailed study is addressed to demonstrate the interaction effects of detuning and time-delay in this study. In addition to modal properties, a discrete-time state-space approach is applied to verify the control performance in time domain subjected to earthquake excitations. 由於外力形式之隨機特性與系統識別之誤差，傳統被動調諧質量阻尼器（TMD）系統對於頻率去調諧效應十分敏感，而藉由複合式調諧質量阻尼器（HMD）進行額外主動控制力施加輔助時，時間延遲效應勢必產生，預期將造成控制效果折減。實務上，由於被動系統之阻尼項參數掌握不易，本文提出通用型複合式質量阻尼器系統（GHMD），經由適度調整HMD系統主動控制力之比例，可藉以同時提供並置換被動系統之勁度項與阻尼項參數，或僅置換被動系統之阻尼項參數，以提供多樣性的控制需求。各類型系統的模態參數與調諧效應，可藉由考慮延遲時間之指數特徵方程式（DECE）進行探討與分析。本文結果顯示，對於採用最佳化輸出回饋控制之HMD系統，只要主動控制力之延遲時間選用為受控系統之自然振動週期，尚可保持控制效能的強健性。然而，此有效改善時間延遲之優點，將隨著控制系統逐步置換被動系統之阻尼項參數而遞減。本文除了探討各系統在頻率域上之控制成效，亦進一步利用離散時間狀態空間時域分析法來進行歷時控制效果之探討與驗證。