乾式非織物(Dry Non-woven Fabric)製程技術中，影響產品品質與機械性質(Mechanical Properties)的關鍵，在於棉網密度均勻性(Web Density Uniformity)之控制。因此，本研究針對乾式非織物羅拉式梳棉機(Roller Carding)之動態建模與棉網密度均勻性之控制。首先建立乾式非織物羅拉式梳棉機之動態系統進行模型分析，其次考慮比例-積分-微分(Proportional-Integral-Derivative , PID)控制器的設計來改善系統的動態響應性能，並結合專家(Expert PID)控制器的應用。本研究依照上述提出的控制方法使乾式非織物羅拉式梳棉機系統輸出之棉網密度均勻性達到預期之目標。
本研究針對乾式非織物羅拉式梳棉機系統進行分析，其推導過程中先將系統其中一組梳棉單元，其中包含錫林(Cylinder)、分梳羅拉(Worker Roller)、剝取羅拉(Stripper Roller)進行理論探討與研究。並假定移行率(Collecting Power)為常數的條件下進行分析。接著探討乾式非織物羅拉式梳棉機系統內梳棉單元的轉動角度及角速度的關係，並且分析出梳棉單元之延遲時間。其延遲時間採用Pade近似法(Pade Approximation)作為系統模型的簡化。最後利用上述的條件進行探討，並推導梳棉單元系統之轉移函數，再將其推展至四組梳棉單元。接著再推廣至乾式非織物羅拉式梳棉機系統，包含梳棉單元(Carding Unit)、喂入羅拉(Feed Roller)、刺輥(Take-In)及道夫(Doffer)等進行串聯一起，並求出乾式非織物羅拉式梳棉機系統之轉移函數。此外，由於乾式非織物羅拉式梳棉機系統之轉移函數為高階系統，一般在PID控制器的設計上較為困難。因此本研究利用Routh近似法(Routh Approximation)，將原始高階系統模型，在不影響其物理特性之下，降為低階系統。並且利用低階系統之轉移函數作根軌跡圖及穩定性分析，選擇適當的控制器，並將所設計控制器之參數代回原始高階系統，進行電腦模擬分析以使乾式非織物羅拉式梳棉機系統輸出之棉網密度均勻性達到響應目標。
由電腦模擬分析得知本系統為穩定系統，但系統響應速度緩慢且存在穩態誤差，其所設計之比例-積分(Proportional-Integral , PI)控制器驗證原始高階系統之後，明顯改善系統之響應速度且消除穩態誤差。同時，加入控制器後，系統暫態響應會有最大超越量之發生。於是本研究設計一輸入修正(Input Shaping)訊號波形作為線性疊加原理(linear Superposition)，可有效抑制系統之最大超越量的發生，並消除輸出振盪現象。以使系統成功地達到快速的響應速度且無最大超越量之目標，並藉其設計之專家PID控制器作為系統性能之比較分析。

When it comes to the technology of dry non-woven fabric process, the factor which influences products and machinery properties most is the control for web density uniformity. As a result, this study focuses on dynamic modeling of card roller of dry non-woven fabric and the control for web density uniformity. At first, a dynamic system of card roller of dry non-woven fabric is established and the model analysis is conducted. Next, the PID type controller is designed to improve dynamic response performance of the system, and then the expert PID controller is under consideration.
In the mathematical modeling, one card unit includes cylinder, worker roller, and stripper roller of the system is first discussed. The migration is assumed as a constant. Then, the relationship between rotational speed and the angle of card unit of the card roller system is studied. The web arrival time is regarded as time delay and based on Pade Approximation for model simplification. Further, the transfer function of the card unit system is derived, and it is applied to four card units and finally to the whole card roller system including card units, feed roller, take-in and doffer. The transfer function of card roller system is a high order system, the Routh Approximation is applied to convert it into a low order one without changing its physical properties. Moreover, the transfer function of the low order system is used for root locus plot and stability analysis in which to choose a suitable controller. Then, the designed controller is brought into the original high order system for simulation to make sure if the web density uniformity achieves the control objective.
From simulation, the system is recognized as a stable system. However, the system transient response is slow, and steady-state error is observed. After the proportion integral (PI) controller is applied to the high order system, the response speed is improved greatly, and the steady-state error is eliminated but overshoot still exists. Therefore, the input shaping is used so as to effectively avoid maximum overshoot and eliminate output oscillation. Finally, the designed expert PID controller is employed for system performance comparision.

1. 余盛機， "非織物製造技術"，大學圖書供應社，1977。
2. 郭秉臣，"非織造布學"，中國紡織出版社，2002。
3. 朱大鈞編著， "梳棉工程"，中原打字印刷行，1976。
4. Jacek, S., "Model for the Optimal Control of the Cross-Lapper Drive", Journal Textile Machinery Society Japan, Vol. 44, No. 4, pp 69-73 (1998).
5. Belozerov, B. P., Gaida, L.T., and Sokhatski, V. S., "State and Prospects of Development of Domestic Equipment for Manufacture of Needle-punched, Non-woven Materials from Polymer Melts", Fibre Chemistry, Vol. 21, No. 4, pp 276-279 (1990).
6. Belykth, V. P., Poikhalo, M. P., and Belozerov, B. P., "System for Automated Design of Equipment for the Manufacture of Non-woven Materials from Polymer Melts", Fibre Chemistry, Vol. 21, No.4, pp 279-283 (1990).
7. Schaff, A. J., and Ogale, A. A., "Tensile Viscoelastic Properties of Spunbonded Non-woven Polypropylene Backing", Textile Research Journal, Vol. 61, No. 7, pp 386-392 (1991).
8. Catling, H., and Davies, I., "Conservation of Mean Level in Autolevelling", Journal of Institute Textile, Vol. 57, No. 3, pp 395-415 (1966).
9. Davies, I., "Some Theoretical Limitations of Sliver Autolevelling System", Journal of Industrial Textile, Vol.59, No. 5, pp 10-38 (1968).
10. Bowels, A. H., and Davies, I., "The Influence of Drawing and Doubling Processes on the Evenness of Spun Yarns", Part V : Automatic Control of Regularity, Textile Institute and Industry, Vol. 17, pp 72-76 (1979).
11. Grosber, P. G., and Iype, C., "Automatic Control of Card-web Linear Density-Part I: The Theoretical Possibility of Short-term Control", Journal of Industrial Textile Vol. 83, No.3, pp 375-379 (1992).
12. Grosberg, P., and Iype, C., "Automatic Control of Card-web Linear Density-Part II: Experimental Verification of Short-term Control", Journal of Industrial Textile, Vol. 83, No.3, pp 380-385 (1992).
13. Yueyang, G., and Ruiqi, C., "Applying a Generalized Predictive Control Theory to a Carding Autoleveller", Textile Research Journal, Vol. 73, No. 9, pp 755-761 (2003).
14. Grosberg, I., and Iype, C., "The Effect of Dynamic Changes in Doffer Speed on Cylinder Loading", Journal of Industrial Textile, Vol. 82, No. 4, pp 457-464 (1991).
15. Rust, J. P., and Gutierrez, H. Z., "Mathematical Modeling and Simulation for Carding", Textile Research Journal, Vol. 64, No.10, pp 573-578 (1994).
16. Rust, J. P., and Gutierrez, H. Z., "Modeling and Simulation for Control in Carding", Textile Research Journal, Vol. 65, No.11, pp 638-643 (1995).
17. Kuo, C. F. J., and Wang, C. C., "Stochastic Control of Card Output Density", Textile Research Journal, Vol. 73, No.3, pp 195-200 (2001).
18. Kuo, C. F. J., and Hsieh, T. C., "Model Reduction and Controller Design of a Whole Roller Carding System", Textile Research Journal, Vol. 72, No.2, pp 98-102 (2002).
19. Kuo, C. F. J., and Hsieh, T. C., "Dynamic Analysis and Control of a Whole Roller Carding System", Textile Research Journal, Vol. 71, No.11, pp 943-947 (2001).
20. Kenison, Michael., and Singhose, W., "Concurrent Design Input Shaping and Proportional Plus Derivative Feedback Control", Transactions of the ASEM, Journal Dynamic System Measurement and Control, Vol. 124, September, pp 398-405 (2002).
21. Singhose, W., Biediger, O. E., and Chen H. Y., "Reference Command Shaping Using Specified Negative Amplitude Iuput Shapers for Vibration Reduction", Transactions of the ASEM, Journal Dynamic System Measurement and Control, Vol. 126, September, pp 210-214 (2004).
22. Fortgang, J., and Singhose, W., "Concurrent Design of Vibration Absorbers and Input Shapers", Transactions of the ASEM, Journal Dynamic System Measurement and Control, Vol. 127, September, pp 329-335 (2005).
23. Ziegler, G. J., and Nichols, B. N., "Optimum Setting for Automatic Controllers", Transactions of the ASME, Journal Dynamic System Measurement and Control, Vol. 65, No.5, pp 433-444 (1943).
24. Åström, K. J., and Årzén, E. K., "Expert Control", Automatica, Vol. 22, pp 277-286 (1986).
25. Årzén, E. K., "An Architecture for Expert Control Systems Based Feedback Control", Automatica, Vol. 25 pp 813-827 (1989).
26. Devanathan, R., Keong, C. C., and Kin, L. T., and Soon, C. Y., "An Expert PID Controller", IEEE International Workshop on Artificial Intelligence for Industrial Applications , pp 404-408 (1988).
27. Devanathan, R., Keong, C. C., and Pei, L. T., and Ting, C. Y., "Expert PID Controller for an Industrial Process", IEEE International Workshop on Artificial Intelligence for Industrial Applications , pp 525-530 (1989).
28. Wenli, D., Mandan, Lin., and Feng, Q., "The Application of Real-Time Expert Control System to Large Scale PTA Plant", IEEE Proceedings of the 4th World Congress on Intelligent Control and Automation, June 10-14, pp 450-453 (2001).
29. Jinbang, X., Jin, Z., and Ling, L., and Shuyun, W., " Expert PID Controller for AC/DC Converter", IEEE Proceedings of the 5th World Congress on Intelligent Control and Automation, June 15-19, pp 5586-5590 (2004).
30. 中國紡織工業研究中心，"梳棉機實務技術"，1991。
31. 楊滄洲，"棉系紡紗技術"，永大書局，新版，1980。
32. Vajta, M., "Some Remarks on Padé Approximations", Internal Report, 3rd Tempus Intcom Symposium, Department of Mathematical Sciences, University of Twente, September 9-14, pp 1-6 (2000).
33. Ahmed, M. M., and Khodier., "Perturbed Padé Approximation with High Accuracy", Applied Mathematics and Computation ,Vol. 148 ,pp 753-757 (2004).
34. Gutierrez, H. M., "Modeling, Instrumentation and Control for Carding", Masters Thesis, Integrated Manufacturing Systems Engineering Institute, North Carolina State University, July, (1993).
35. Choo, Y., "Improved Bilinear Routh Approximation Method for Discrete Time Systems," Transactions of the ASEM, Journal Dynamic System Measurement and Control, Vol. 123, March, pp 125-127 (2001).
36. Zhang, C., and Ding, G., "A Stable Series Expansion Method for Calculating Thermal Response Factors of Multi Layer Walls", Building and Environment, Vol. 38, pp 699-705 (2003).
37. Lin, P. G., and Daley, S., " Optimal-tuning PID Control for Industrial Systems", Control Engineering Practice, Vol. 9, pp 1185-1194 (2001).
38. Tan, K. K., Lee, H. T., and Jiang, X., "On-Line Relay Identification, Assessment and Tuning of PID Controller", Journal of Process Control, Vol. 11, pp 483-496 (2001).
39. Bohn, C., and Atherton, P. D., "An Analysis Package Comparing PID Anti-Windup Strategies", IEEE Control Systems, pp 34-40 (1995).
40. Bang, H., Tahk, J. M., and Choi, D. H., "Large Angle Attitude Control of Spacecraft With Actuator Saturation", Control Engineering Practice, Vol. 11, pp 989-997 (2003).
41. Lee, U. S., and Chang, H. P., "The Development of Anti-Windup Scheme for Time Delay Control With Switching Action Using Integral Sliding Surface", Transactions of the ASEM, Journal Dynamic System Measurement and Control, Vol. 125, December, pp 630-638 (2003).
42. Chee, F., Fernando, L. T., Savkin, V. A., and Heeden, V. V., "Expert PID Control System for Blood Glucose Control in Critically I11 Patients", IEEE Transactions on Information Technology in Biomedicine, Vol. 7,No. 4, December, pp 419-425 (2003).
43. 陶永華，"新型PID控制及其應用"，機械工業出版社，第二版，2002。
44. 劉金琨，"先進PID控制MATLAB仿真"，電子工業出版社，第二版，2004。