臺灣博碩士論文加值系統

本論文採用強健控制，將量化回授理論應用於ALMA計畫中的nutator系統。Nutator為多輸入多輸出的系統，系統目的在於消除天文反射望遠鏡觀察太空物體時所接收到的背景雜訊。運作的環境位於5000公尺高海拔處的Atacama沙漠，溫差超過攝氏40度，且環境陣風速度高達每秒20公尺，工作環境十分嚴苛。nutator的規格要求極高且追求精確，穩定時間需小於0.01秒、上升時間小於0.005秒、最大上升超越量小於10%。雖然傳統的PID控制器也可以達到所要求的表現規格，但在系統因環境變數而產生參數變化時，便無法維持系統的強健性。相反的，在經過模擬與實驗，量化回授理論不但能夠達到規格要求，更表現出傳統PID控制器所不具備的強健特性，明顯提升nutator於真實運作環境中所必須擁有的強健控制性能。

This thesis presents a robust control method, Quantitative Feedback Theory (QFT) to the Atacama Large Millimeter Array (ALMA) nutator. Nutator, a Multi-Input Multi-Output (MIMO) system and is used on an astronomical telescope to remove the background noise while observing objects in the space. The nutator works in a harsh environment: large temperature variation within -20℃ to 20℃, the 5000 meters high altitude and the wind speed of 20 meters per second. The requirements of the specification are expected to maintain in a high level: the 0.01 second of the settling time, 0.005 second of the rise time and the maximum overshoot should be less than 10%. Though the traditional PID control may achieve the specification requirements, but it may not be able to maintain the system performance when the parameter variation happens. However, the QFT control method does reach a stronger robustness than the PID control method. The QFT control can not only achieve the performance requirements but also fulfill the robustness characteristic that the nutator needs in the real working environment.

Robust Control of the Nutator i
論文口試委員審定書 ii
授權書 iii
摘要 iv
Abstract v
誌謝 vii
Contents viii
List of Tables x
List of Figures xi
Chapter 1 Introduction 1
1.1 Background 1
1.2 Literature review 2
Chapter 2 ALMA Nutator System 4
2.1 Mechanical description of ALMA nutator 4
2.2 Mathematical model 5
2.3 Control system 10
Chapter 3 MIMO PID Design 13
3.1 Overview of PID 13
3.2 MIMO PID design steps 14
Chapter 4 MIMO QFT Design 19
4.1 Overview of QFT 19
4.2 MIMO QFT design steps 27
Chapter 5 Simulations and Results 33
5.1 Control performance 33
5.2 Robustness achievement 45
Chapter 6 Conclusions 51
References 53
 

References
[1]Gasho, V., Radford, S. and Kingsley, J.,“ALMA high performance nutating
subreflector,”SPIE 2002, Proceedings 4837, pp. 430-437, 2002.
[2]Jiang, H., Chen, M.-T., Han, J., “Control Characteristics of the ALMA Nutator,” Proceedings of the IEEE International Conference on Control Applications, art. no. 5611324, pp. 962-966, 2010.
[3]黃榮興, “天文台反射望遠鏡控制系統之設計 研究成果報告”, 行政院國家科學委員會專題研究計畫, 2008.
[4]Horowitz, I., “Quantitative Feedback Theory,” IEE Proceedings D: Control Theory and Applications 129 (6), pp. 215-226, 1982.
[5]Horowitz, I., “Survey of quantitative feedback theory (QFT),” International Journal of Control 53 (2), pp. 255-291, 2001.
[6]Garcia-Sanz, M. and Houpis, H., “Quantitative feedback theory. In memoriam of Isaac Horowitz,” International Journal of Robust and Nonlinear Control 17 (2-3), pp. 91-94, 2007.
[7]Horowitz I., “Some ideas for QFT research,” International Journal of Robust and Nonlinear Control 13 (7), pp. 599-605, 2003.
[8]Kerr, L., Lan, Y., and Jayasuriya, S., “Non-sequential MIMO QFT control of the X-29 aircraft using a generalized formulation,” International Journal of Robust and Nonlinear Control 17 (2-3), pp. 107-134, 2007.
[9]Shi, Z., Wang, F., and Wang, Z., “Design of missile lateral channel controller based on QFT,” Proceedings of International Conference on Computational and Information Sciences, art. no. 6086350 , pp. 917-920, 2011.

[10]Barreras, M., Villegas, C., Garcia-Sanz, M., Kalkkuhl, J., “Robust QFT tracking controller design for a car equipped with 4-wheel steer-by-wire,” Proceedings of IEEE International Conference on Control Applications, art. no. 4067369 , pp. 1312-1317, 2007.
[11]Rico, J., Gil-Martinez, M., “Multivariable QFT robust control of a heat exchanger,” Mediterranean Conference on Control and Automation, art. no. 5983125 , pp. 588-593, 2011.
[12]Ang, H., Chong, G., Li, Y., “PID control system analysis, design, and technology,” IEEE Transactions on Control Systems Technology 13 (4), pp. 559-576, 2005.
[13]Rivera, E., Morari, M., Skogestad, S. “Internal model control 4. PID controller design,” Industrial &; Engineering Chemistry Process Design and Development 25 (1), pp. 252-265, 1986.
[14]Zhuang, M., Atherton, P. “Automatic tuning of optimum PID controllers,” IEE Proceedings D: Control Theory and Applications 140 (3), pp. 216-224, 1993.
[15]Astrom, J., Hagglund, T. “The future of PID control,” Control Engineering Practice 9 (11), pp. 1163-1175, 2001.
[16]Houpis, C., Rasmussen, S., Garcia-Sanz, M., Quantitative Feedback Theory Fundamentals and Applications, NY: Taylor &; Francis Group. 2006.