臺灣博碩士論文加值系統

摘要
本論文探討離散時間非線性系統的反覆式學習控制器
的設計。本文第一個重要貢獻是提出一個改良式P型反覆
學習控制器，並以sup-norm的方式證明整個學習系統的收
斂性。除了完整的理論分析之外，論文中並由電腦模擬驗
證其收斂速度與平均學習誤差皆較傳統P型反覆學習控制
器為佳。
另外，反覆式學習控制器在有初始誤差的強健性問題，
也一直是本領域的重要課題。傳統的研究發現當反覆學習
系統有初始誤差時，輸出學習誤差是不能趨近於零。雖然
在連續時間的反覆學習系統，已有文獻研究初始誤差對最
後的學習性能產生何種影響；但是在離散時間的反覆學習
系統，卻無任何的研究。本論文第二個重要貢獻是提出一
個觀點，驗證離散時間反覆學習系統在有初始誤差的情況
下，其實可以追蹤到第二個點以後的理想軌跡。
最後，本論文除了使用Matlab模擬其結果外，並使用
一個數位訊號處理器控制板來驗證改良式P型反覆學習控
制器的控制效果。
關鍵詞：反覆學習控制、sup-norm、P型反覆學習控制器、
改良式P型反覆學習控制器、數位訊號處理器

ABSTRACT
This thesis discusses the design of iterative learning
controller for discrete time nonlinear system. The first
contribution of this thesis is to propose a modified of P-type
iterative learning controller. A sup-norm approach is presented
to prove the convergence of the iterative learning system. In
addition to a complete theoretical analysis, some computer
simulations are given to demonstrate that the convergent rate
and average learning error are better than the traditional P-
type iterative learning controller.
The robustness problem of initial output error is an
important issue in the field of iterative learning system. In
the previous work, it is found that the output learning error
can''t converge to zero when there exists an initial output
error. In the study of continuous-time iterative learning
system, there are some works investigate the effect of initial
output error on the performance of final iteration. But no
researches deal with the discrete-time iterative learning
system. The second contribution of this thesis is to propose a
new point on the problem of initial output error. It is shown
that despite of the initial error, the system output can
actually track the desire output after the initial instant.
Finally, in addition to the Matlab simulation result, a
digital signal processor based control card is used to
demonstrate all the theoretical analysis given in the thesis.
Keywords：iterative learning control, sup-norm, P-type
iterative learning controller, modified P-type
iterative learning controller, digital signal
processor.

目錄
致謝..........................................................I
中文摘要.....................................................II
ABSTRACT.....................................................III
目錄.........................................................IV
表錄..........................................................V
圖錄..........................................................VI
第一章 緒論...................................................1
1.1由來....................................................1
1.2基本假設................................................1
1.3反覆學習控制的基本型式..................................2
1.4離散型反覆學習控制器....................................3
1.5本論文的研究動機........................................4
第二章 改良式P型離散反覆學習控制器之理論分析..................6
2.1沒有初始誤差的情況......................................6
2.2有初始誤差的情況.......................................17
第三章 電腦模擬..............................................24
第四章 數位信號處理器TMS320C50...............................41
4.1 DSP TMS320C5X簡介.....................................41
4.2定點式DSP與浮點式DSP的差異.............................42
4.3 DSP控制板的應用與通訊架構.............................44
4.4捨入誤差之探討.........................................49
4.5以DSP控制板驗證前章之範例..............................51
第五章 結論與建議............................................60
參考文獻......................................................62

參考文獻
1.Uchiyama, M."Formation of high-speed motion pattern of a
mechanical arm by trial", Trans. SICE(Society for
Implementation and Control Engineers(in Japanese), vol.14,
pp.706-712,1978.
2.Arimoto, S., Kawamura, S., and Miyazaki, F.. "Bettering
operation of robots by learning ", J. of Robotic Systems,
vol.1, pp.123-140,1984.
3.Casalino, G. and Bartolini, G.. "A learning procedure for the
control of movements of robotic manipulators", IASTED Symp.
on Robotics and Automation, pp.108-111, 1984.
4.Craig,J.J. "Adaptive control of manipulators through repeated
trials", Proc. of ACC, San Diego, CA, June., 1984.
5.Hauser, J. E.,"Learning control for a class of nonlinear
systems". Proceedings of the IEEE 26th Conference on Decision
and Control ,Los Angeles, California, U.S.A., pp.859-
860.,1987.
6.Sugie, T., and Ono, T.,"An iterative learning control law for
dynamic systems". Automatica,27, pp.729-732,1991.
7.Heinzinger, G., Fenwick, D., Paden, B., and Miyazaki,F.
"Stability of learning control with disturbances and
uncertain initial conditions". IEEE Trans. of Automatic
Control, vol.37(1), pp.110-114,1992.
8.Kawamura, S., Miyazaki, F., and Arimoto, S., "Realization of
robot motion based on learning method", IEEE Trans. on
System, Man, and Cybernetics, vol.18, pp.126-134,1988.
9.Arimoto, S."Robustness of learning control for robot
manipulators". Proceedings of the IEEE International
Conference on Robotics and Automation, Cincinnati,
Ohio,U.S.A., pp.1528-1533, 1990.
10.Arimoto,S.,"Learning control theory for robotic motion",
Int.J. of Adaptive Control and Signal Processing, vol.4,
pp.543-564,1990.
11.Arimoto, S. Naniwa, T., Suzuki, H.,"Robustness of P-type
learning control with a forgetting factor for robotic
motions". Proceedings of the IEEE 29th Conference on
Decision and Control, Honolulu, Hawaii, U.S.A., pp.2640-
2645,1990.
12.Kuc, T. Y., Lee, J. S., and Nam, K.,"An iterative learning
control theory for a class of nonlinear dynamic systems".
Automatica, vol.28,pp.1215-1221,1992.
13.Geng, Z., Carroll, R. L., and Xie, J.,"Two-dimensional model
algorithm analysis for a class of iterative learning control
systems". International Journal of Control, vol.52, pp.833-
862, 1990.
14.Kurek, J. E. and Zaremba, M. B., "Iterative learning control
systhesis based on 2-D system theory". IEEE Trans. of
Automatic Control, vol.38(1),pp.121-125,1993.
15.Saab, S. S., "A discrete-time learning control algorithm for
a class of linear time-invariant systems". IEEE Trans. of
Automatic Control, vol.40(6), pp.1138-1141,1995.
16.Hwang, D. H., Bien, Z., and Oh, S. R., "Iterative learning
control method for discrete-time dynamic systems". IEE
Proceedings,Part-D,Control Theory and Applications, vol.138
(2), pp.139-144,1991.
17.Ishihara, T., Abe, K., and Takeda, T. "A discrete-time
design of robust iterative learning controller". IEEE Trans.
on Systems, Man and Cybernetics, vol.22(1), pp.74-84,1992.
18.Suzuki, T., Yasue, M., Okuma, S., and Uchikawa, Y.,
"Discrete-time learning control for robotic manipulators".
Advanced Robotics, vol.9(1), pp.1-14,1995.
19.Tso, S. K. and Ma, L. Y. X., "Discrete learning control for
robots: strategy, convergence and robustness". International
Journal of Control, vol.57(2), pp.273-291,1993.
20.Jang, T. J., Ahn, H. S., and Choi, C. H., "Iterative
learning control for discrete-time nonlinear systems".
International Journal of SystemsScience, vol.25(7), pp.1179-
1189, 1994.
21.Saab, S. S., "Discrete-time learning control algorithm for a
class of nonlinear systems". In Proc. of American Control
Conference,Seattle, Washington, USA., pp.2739-2743,1995.
22.Zeungnam Bien and Jian-Xin Xu, "Iterative learning control
analysis, design, integration and applications". Kluwer
Academic Publishers, pp.3-35, pp.83-103,1998.
23.Chiang-Ju Chien and Jing-Sin Liu, "A P-type iterative
learning controller for robust output tracking of nonlinear
time-varying systems". Int. J. Control, vol.64(2), pp.319-
334, 1996.
24.Hak-Sung Lee and Zeungnam Bien, "Study on robustness of
iterative learning control with non-zero initial error".
Int. J. Control,vol.64(3), pp.345-359, 1996.
25.Kwang-Hyun Park, Zeungnam Bien, and Dong-Hwan Hwang, "A
study on the robustness of a PID-type iterative learning
controller against initial state error". International
Journal of Systems Science, vol.30(1),pp.49-59,1999.
26.TMS320C5X User''s Guide. Texas Instruments Inc., 1993.
27.TMS320C1X/C2X/C2XX/C5X Assembly Language Tools. Texas
Instruments Inc., 1995.
28.TMS320C2X/C2XX/C5X Optimizing C Compiler User''s Guide.
Texas Instruments Inc.,1996.
29.Arun Chhabra and Ramesh lyer, "A block floating point
implemntation on the TMS320C54X DSP". TI Application Report
(spra610), pp.3-4, 1999.
30.鍾文政，柯鴻禧，"DSP TMS 320C50原理與實習應用"，長高電
腦圖書。
31.CSDK-50數位信號處理器控制板使用手冊。祥曦科技。
32.陳至剛，"數值分析與電腦工程應用"。雷諾資訊圖書，
pp.2-1~2-13。
33.胡竹生，陳榮偉，"定點數位訊號處理器應用程式設計與實驗"。
全華圖書，pp.2-2~2-7。