非織物棉網成型機(non-woven cross-lapper machine)主要是利用滑輪組機構帶動滑動架(carriage)，以滑輪做往復運動，摺疊出非織物產品所需要棉網厚度(thickness)及寬度(width)。在非織物製造技術中影響產品優劣原因中，以棉網均勻度(uniformity)控制為主要關鍵。成型機系統在往復動作時需要以穩定的等速度前進後退，且在進行折返運動時能精確停在折返點位置。
本文主要是在研究水平式棉網成型機(flat-bed cross lapper machine)的系統建模與控制。首先以拉格蘭吉方程式(Lagrange’s Equation)推導出成型機動態方程式，並分別以步階函數(step input function)及正弦函數(sinusoid function)為馬達扭矩輸入訊號，藉由輸入訊號的響應特性得知系統狀態響應圖，了解其動態特性。並分別設計線性控制器與非線性控制器以求得系統之輸出目標。
線性控制器的設計，首先以Runge-Kutta解非線性動態系統平衡點，對非線性系統以平衡點作泰勒級數(Taylor series expansion)展開式得到線性化(linearization)系統，分別以古典控制理論(classical control theory)與現代控制理論(modern control theory)設計控制器。古典控制理論控制器之設計，首先求得高階線性化系統轉移函數(transfer function)，利用近似法(approximation criterion)求得低階系統轉移函數，並再以設計PI控制器，將低階系統控制器套回高階系統獲得系統輸出響應而驗證水平式棉網成型機系統移動架速度響應。
現代控制理論控制器之設計，利用狀態回授控制(state feedback control)以極點配置法(pole-placement method )，設計線性化系統之閉迴路(close loop)極點(pole)位置，以符合系統輸出目標。
非線性控制器之設計，直接設計系統輸出目標和給定追蹤函數(target function)，期望系統輸出可以達到追蹤函數，其控制器之設計分別以滑動模式控制(sliding control)及狀態回授線性化(state feedback linearization)結合滑動模式控制。滑動模式控制是藉由系統控制律(control law)的切換，由控制法則迫使系統進入系統軌跡(trajectory)進入滑動平面，而達到控制目的。狀態回授線性化控制(state feedback linearization control)，主要是選擇不同狀態簡化系統原本狀態的非線性行為的方法，將原系統模式等效為簡單型式的模式，並且由誤差函數(error function)的微分方程式決定系統穩定，並且加上滑動模式控制來消除系統中的不確定項(uncertainty)以達到更好的輸出響應。

The non-woven cross lapper machine is mainly reciprocating motioned via a pulley-roller system with a carriage. This system can fold non-woven production in desired thickness and width. In non-woven manufacture, technology influences products of good and bad reasons, with uniform control of the web as the main key. In non-woven factory production, the reciprocating motion required in stabilizing speed and motion has to be precisely maintained in between return points.
This study’s purpose is to build a model and control for flat-bed cross lapper machine. We first used Lagrange’s Equation to provide the system’s dynamic equation, followed by step input function and sinusoid function as torque signals provided by the motor. The input signal response and the system dynamic can then be determined. We also designed a linear control system and a non-linear control system to achieve design requirement.
For designing a linear control system, we first used the Runge-Kutta method to determine the equilibrium points of this non-linear system. Then, we used the Taylor series expansion to linearize this system and use both the classical and modern control theory to design the controller. To design the system by using the classical control theorem, we determined the higher order transfer function first and then used the approximant method to determine lower order transfer function to design PID controller. Using this low order control system into higher order control system allowed us to obtain system responses that could be compared to those of the flat-bed cross-lapper machine.
For designing the modern control system, we could design by two ways: state feedback control and pole-placement design control. Then, we designed this linear system’s characteristic roots to achieve the goal.
We designed the non-linear system by directly designing the system output and target function and expecting this system’s output to reach target function; this controller was designed by sliding control and state feedback linearization. The idea of sliding control is forcing the system’s trajectory into sliding surface by switching the control law. State feedback linearization control is basically using different kind of states to simplify the original non-linear state, meaning that the new system will still keep equivalent to original system with error function but simpler. The error function can decide the stability of the system and if sliding control mode is added to reduce the uncertainty of system, we could obtain better results.

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