Optimal Tracking VI Bration Suppression of Flexible Beams Subjected to Moving Dynamic Loads with Complex Motion Characteristics

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Project title

Code/計畫編號

NSC101-2221-E019-002

Translated Name/計畫中文名

承受具複雜運動特徵移動動態負載之撓性樑的最佳追蹤振動制抑

Project Coordinator/計畫主持人

Yih-Hwang Lin

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Mechanical and Mechatronic Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=2582564

Year

2012

Start date/計畫起

01-08-2012

Expected Completion/計畫迄

01-07-2013

Bugetid/研究經費

412千元

ResearchField/研究領域

機械工程

"本計畫考慮承受移動動態負載之撓性樑的最佳追踪振動制抑。與傳統以恆定的行進速度或加速度的移動荷載不同，本研究考慮的移動動態系統，係以一般化之運動形式移動。從靜止狀態開始，移動動態系統迅速移動到下一個位置，並保持靜止，以方便後續操作。這種類型的操作常見於精密定位平台或起重吊車。該操作通常應用最小時間策略，以取得最大生產量。一個典型的運動形式通常包括四個階段。前兩個階段為bang-bang 形式，具有一個快速加速的運動過程，隨後即迅速減速。第三個階段是移動的動態系統原地停息，使振動降至可接受的水平，以利第四個階段之實際加工或材料處理歷程。為了實現上述運動形式，我們須經由伺服機構施加bang-bang形式的外力，以對移動系統進行加速和減速。因此，此等操作可能誘發劇烈振動。本計畫考慮具有兩個自由度的移動動態系統於撓性支持結構上移動，作為進一步發展的原型。首先將建立此集成系統之有限元模型以適用於複雜的邊界條件。應用最佳追踪控制以抑制移動動態系統之過度振動，使停息時間可盡量縮短，而提升作業效率。控制動作係由兩個部分合成，一為狀態反饋，另一為與系統狀態無關之開路控制項。上述控制需解複雜的聯立非線性微分方程，以倒退時間之方式進行。由於實際的定位運動軌跡為預先設定，所以這是可行的。此龐大的計算可離線解決，避免主動控制時常遇到的線上計算壓力。由於目的是在移動動態系統到達操作位置時，盡量減少振動，最後時間加權矩陣於控制系統的性能至關重要。將就其影響進行檢驗，以提供適當的設計指導方針。最佳追踪控制策略應用於高精度定位平台或起重吊車，可確保操作的精確度，並提高生產力。" "This project considers optimal tracking vibration suppression of a flexible beam subjected to moving dynamic loads. The moving dynamic system considered in this work travels with a general movement profile, which is different from the traditional moving load analysis with a constant traveling speed or acceleration. Starting from rest, the moving dynamic system rapidly moves to the next position and remains stationary to facilitate subsequent operation. This type of operation is common in precision positioning platforms or weight lifting cranes. The operation usually applies a minimal time strategy to maximize the production. A typical movement profile usually involves four stages. The first two stages have a bang-bang type motion for rapid acceleration, followed by rapid deceleration. The third stage is for the moving dynamics system to settle such that vibration is within an acceptable level. The fourth stage is for actual machining or material handling. To realize the movement profile mentioned above, we have to apply a bang-bang type of force using a servo-mechanism to accelerate and to decelerate the moving dynamic system. Consequently, severe vibration can be induced by such an operation. In this project, a moving dynamic system with two degrees of freedom moving on a flexible support structure will be considered as a prototype for further development. The finite element model of the integrated system will first be developed to facilitate the treatment of a system with complex boundary conditions. Optimal tracking control will be applied in this study for suppressing excessive vibration of the moving dynamics system so that the settling time can be minimized for maximum production efficiency. The control action will be synthesized from two parts, one with state feedback and the other with an open loop control action being independent of the system states. The aforementioned control action requires solution of complex simultaneous nonlinear differential equations which must be integrated back in time. This is feasible because the motion profile is known in practice. The intense computation can be solved offline, avoiding the online computation pressure commonly encountered in active control. Because of the aim is to minimize vibration when the moving dynamic system reaches the position of operation, the weighting matrix at the final time plays a crucial role for performance of the control system. The influence of the final time weighting matrix will be examined to provide an appropriate design guideline. For high precision positioning platforms or weight lifting cranes, the optimal tracking control strategy can serve to ensure operation accuracy and to increase the productivity."

Keyword(s)

最佳追蹤控制
移動動態負載
有限元素分析
optimal tracking control
moving dynamic loads
finite element analysis

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Optimal Tracking VI Bration Suppression of Flexible Beams Subjected to Moving Dynamic Loads with Complex Motion Characteristics

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