近年來，以軟性板材為基底的電子產品逐漸興起，但就軟板可撓曲的特性，以捲繞式(Roll to Roll, R2R)製程進行大量生產的技術尚未完備。故本論文的目的在於提供捲繞式製程相關的學理基礎，針對其縱向與橫向動態進行數學模式推導，並藉由有效摩擦係數的求解，得以對多滾輪、多間距系統進行完整的分析。使用Simulink建立系統的模擬環境，以最佳化設計工具箱搜尋軟板系統的張力、速度以及橫向位置PID控制器之增益值，同時將上述的響應控制在一定的範圍內。並利用張力與速度變化時的橫向位置平均誤差值，設計出耦合縱向的橫向位置時變控制器。本論文也針對工研院研發的複合循邊(Compound Guider)進行數學模式的推導，利用模擬驗證了其中粗循邊(Coarse Guider)與細循邊(Fine Guider)複合控制的效能。

In recent years, the application of flexible substrate in electronic products is gradually on the rise. Based on its flexible features, the Roll to Roll (R2R) process can be used for mass production, but the technique is not well developed yet. The aims of this thesis are to provide the relevant theoretical foundations for the R2R system. The longitudinal and lateral dynamical model is derived, and by the introduction of the effective coefficient of friction, we are able to analyze the complete system, which contains multi-roll and multi-section. In the Simulink simulation environment, the optimization toolbox is used to search PID gains for the web tension, speed and lateral position control. So that they all can be controlled within a certain range. By calculating the average position error, which is varying with tension and speed, time-varying and auto-tuning PID controllers are designed in this thesis. We also derive the mathematical model for the compound guider, which was developed by ITRI, and prove its effectiveness.

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