設備物應用衝程考量天鉤主動隔震系統之數值模擬分析及實驗驗證

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Title:	設備物應用衝程考量天鉤主動隔震系統之數值模擬分析及實驗驗證
Authors:	蔡元峰;Tsai, Yuan-Feng
Contributors:	土木工程學系
Keywords:	天鉤控制;主動隔震;基底加速度積分前饋;直接輸出回饋;振動台實驗;衝程限制;增益規劃;skyhook control;active isolation;base acceleration integral feedforward;direct output feedback;shaking table experiment;stroke restraint;gain scheduling
Date:	2023-07-26
Issue Date:	2024-09-19 14:37:44 (UTC+8)
Publisher:	國立中央大學
Abstract:	對於高科技廠中之設備物，一般其自然頻率較高，可視為剛體設備物；如需降低微振影響，對其下加裝一被動隔絕微振裝置，整體則可視為非剛體設備物。本研究分別以剛體及非剛體設備物應用天鉤(Skyhook)主動控制技術，形成單自由度及二自由度天鉤主動隔震系統，並同時考量隔震衝程限制，進行運動方程式之推導、天鉤隔震及衝程限制控制律設計、數值模擬分析以及實驗驗證，確保所提控制律之可行性。首先，傳統天鉤控制理論中之天鉤阻尼係數越大，系統可有越小之絕對加速度反應，其控制力以隔震平台之絕對速度回饋計算。透過改良傳統天鉤控制理論，將控制力調整為隔震平台相對地表速度回饋以及地表加速度積分濾波之地表速度前饋，進行主動控制力之計算。不僅可充分考量隔震平台固有阻尼之影響，更可提升訊號量測之便利性及穩定性。積分濾波器為自行引入，其內部參數可充分掌握及調整，可將天鉤主動隔震系統擴展為包含積分濾波器之型式，以便於最佳化設計時能夠充分考量積分濾波器之影響。主動控制力之計算並非全狀態回饋，因此利用連續時間直接輸出回饋，以設備物之絕對加速度最小化為設計目標，搭配參數迭代更新方法設計最佳化增益參數。此外，考量隔震衝程之限制，可透過增益規劃(Gain Scheduling)折減地表速度增益參數，限縮隔震衝程達到保護之效果。為了解剛體設備物應用天鉤主動隔震系統之特性，將考量控制力影響之系統進行特徵分析，可見施加控制力後將調整系統極點位置，使其遠離地震主要作用頻率範圍，藉此減少地震力引起共振之可能性。相對地表速度增益參數可直接提升隔震平台阻尼比，使主動隔震系統為高度過阻尼系統，非地震外力作用下不易激發隔震平台，可維持常時之穩定狀態。於頻率反應函數分析及地震歷時分析中，天鉤主動隔震系統皆較被動隔震系統具有良好之隔震效果。考量實際應用設備物質量可能變動之情形，進行質量敏感度分析，僅控制力與非剛體設備物變位對於質量變化具有較敏感之反應。於穩定性分析中證實系統於相對地表速度增益參數更改時，將改變其極點位置，因此需考量系統之穩定性；地表速度增益參數更改時並未改變系統極點位置，因此不影響系統之穩定性，並可驗證先前提出地表速度增益參數之增益規劃實為可行。而一主動控制系統將必定具有時間延遲之影響，透過將時間延遲加入控制系統並計算其模態阻尼比，分析出系統可接受之時間延遲時長，確保控制系統對於時間延遲之穩定性。依照隔震衝程之容量上限進行衝程限制控制律之設計，於地震歷時分析中可得到系統具有降低隔震衝程峰值之效果，並同時保有部分隔震功能。非剛體設備物應用天鉤主動隔震系統於前述各項數值模擬分析中，具有與剛體設備物相同之結論。為證實所提控制律具有目標隔震及衝程保護之效果，分別於線性伺服滑台上固定質量塊作為剛體設備物；固定小型隔絕微振裝置及質量塊作為非剛體設備物，並以振動台實驗驗證天鉤主動隔震及衝程限制控制律之可行性。實驗結果顯示，天鉤主動隔震系統於所使用之震波作用下，皆具有隔震效果，而考量衝程限制之系統大部分皆具有衝程保護之效果。關鍵字：天鉤控制、主動隔震、基底加速度積分前饋、直接輸出回饋、振動台實驗、衝程限制、增益規劃 ;In high-tech factories, the equipment is generally characterized by higher natural frequencies and be considered as rigid equipment. To reduce the impact of micro-vibrations, passive isolator is installed underneath. This transforms the system into non-rigid equipment. This study explores the application of skyhook active control to both rigid and non-rigid equipment to form Single-Degree-of-Freedom and Two-Degree-of-Freedom skyhook active isolation systems. This study derives the motion equations and designs skyhook isolation algorithm. It also considers the restraint of isolation stroke to build the stroke limiting control law. Through conducting numerical simulations and performing experimental verification, the feasibility of the proposed algorithms is ensured. In traditional skyhook control theory, control force is calculated by the absolute velocity feedback of isolation platform and skyhook damping coefficient. Moreover, greater skyhook damping coefficient could get smaller absolute acceleration response. To improve the theory, control force is adjusted to be calculated by the relative velocity feedback between isolation platform and ground, along with the ground acceleration integrated and filtered to obtain ground velocity feedforward. This modification not only considers the influence by inherent damping of isolation platform but also enhances the convenience and stability of signal measurement. Parameters of preselected integral filter are introduced and integrated into skyhook active isolation system, so the performance and concern of the stability issue can be ensured during optimization design. The control force is not full-state feedback, so it utilizes continuous-time direct output feedback and parameter iteration to obtain the optimal gain parameter which minimizes the absolute acceleration of equipment. Furthermore, considering the restraint on isolation stroke, the ground velocity gain parameter can be arranged according to gain scheduling to limit the stroke. To understand the characteristics of skyhook active isolation system applied to rigid equipment, the control effect is discussed through various simulation analysis. The characteristic analysis show that the system pole positions can move away from the primary seismic excitation frequencies after applying the control force, thereby reducing the possibility of resonance due to earthquake. The relative velocity gain parameter can raise the damping ratio of isolation platform and make the system highly over-damped. The over-damped system is less likely to be excited by non-seismic forces and highly likely to maintain stationary during peacetime. In frequency response and time history analysis, skyhook active isolation system outperforms passive isolation system in terms of reducing the absolute acceleration of equipment. Regarding the sensitivity analysis of equipment mass variation, the results show that the control force and movement of non-rigid equipment are sensitive to mass variation. The stability analysis confirms that changing the relative velocity gain parameter will change the system poles position. It requires to consider the stability of the system when the relative velocity gain is changed. However, changing the ground velocity gain parameter does not affect stability that verifies the feasibility of the proposed ground velocity gain scheduling. To consider the time delay effect, various time delays are incorporating into the system to calculate the modal damping ratio, the duration of maximum time delay of the system can be analyzed. By designing stroke restraint control law based on the limitation of the stroke, skyhook active isolation system exhibits reduced isolation stroke while retaining partial isolation functionality in time history analysis. Skyhook active isolation system for non-rigid equipment reaches similar conclusions as with rigid equipment in all simulation analyses. To demonstrate the effectiveness and feasibility of proposed algorithms for achieving both isolation and stroke protection, shaking table experiments are conducted on linear servo slider with rigid and non-rigid equipment. The experimental results show that skyhook active isolation system exhibits excellent isolation effects under the seismic waves, especially the stroke is protected by considering the stroke restraint control law. Keywords: skyhook control, active isolation, base acceleration integral feedforward, direct output feedback, shaking table experiment, stroke restraint, gain scheduling.
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