臺灣博碩士論文加值系統

本論文主要的研究主題，敘述如下：首先，應用現有的一些技術，將線性奇異系統分解轉換可得到一具有直接傳輸項之線性等效正則模型。其次，針對此連續時間具有直接傳輸項之線性等效正則模型，開發出具有高增益特性及最佳化之線性二次型類比追蹤器與觀測器。然後，基於此線性二次型類比追蹤器與觀測器，分別使用具有預估特性與另一種方式之數位重新設計方法，各自發展出在相同的輸入與初值條件下，可使數位化控制模型與理論上設計良好的連續模型之狀態變數可緊密貼近的相對應數位追蹤器，以及當模型之狀態變數不可測時之數位觀測器。最後，針對包含有直接傳輸項的連續時間線性非時變之正則模型，提出結合適用於此類模型之線性類比追蹤器之反覆學習控制的策略；此策略中，乃經由此線性類比追蹤器以得到學習控制律之適當控制輸入初值，如此，可有效地改善軌跡追蹤之性能；並藉由狀態初值學習法則，亦可解除典型反覆學習控制設計中初始條件設定之限制。在本論文中，以多個例題來說明所提方法之有效性。

The research objectives of this dissertation are stated as follows. First, via some existing techniques, the linear singular system can be decomposed into an equivalent regular system with a feedthrough term, from input to output. Second, the high-gain optimal linear quadratic analog tracker and observer for this equivalent model are developed. Third, based on this linear quadratic analog tracker (LQAT) and observer, the prediction-based digital redesign and alternative digital redesign methodologies are carried out, respectively, to derive the digital tracker for the state of the digitally controlled model closely matches the state of theoretically well-design continuous-time model with the same input and initial condition; and the digital observer while, as the states of both digitally controlled model and continuous-time model are unmeasured in turn. Finally, an iterative learning control (ILC) strategy, by combined with the LQAT, for the continuous-time linear time-variant (LTI) regular model with a singular feedthrough term is presented. The tracking performance improvement is achieved through the initial control input obtained by the LQAT, and the initial condition constraint, in typical ILC design, is removed by together with initial state learning law. Some illustrative examples are given to demonstrate the effectiveness of the proposed methodologies.

中文摘要 i
Abstract ii
Acknowledgement iii
Contents iv
List of Figures vi
List of Symbols and Abbreviations ix
1 Introduction 1
1.1 Literature Survey 2
1.1.1 Singular system tracking problems 2
1.1.2 Digital redesign 5
1.1.3 Iterative learning control 13
1.2 Dissertation Overview 15
2 The Equivalent Model of the Linear Singular System 17
2.1 Introduction to the Matrix Sign Function 18
2.2 The Regular Pencil and Standard Pencil 19
2.3 The Decomposition of Singular Systems 20
2.4 Summary 28
3 Optimal Tracker and Observer for the Equivalent Model of the Sampled-Data Linear Singular System: Digital Redesign 29
3.1 Introduction 30
3.2 Optimal Linear Quadratic Analog Tracker and Observer 30
3.3 Prediction-Based Quadratic Digital Tracker 34
3.4 Prediction-Based Quadratic Digital Observer 37
3.5 Illustrative Examples 42
3.6 Summary 54
4 An Alternative Digital Redesign for the Equivalent Model of the Sampled-Data Linear Singular System 55
4.1 Introduction 56
4.2 An Optimal Tracker for the Regular Model with a Feedthrough Term 56
4.3 Illustrative Examples 63
4.4 Summary 75
5 Iterative Learning Control for the LTI Regular Model with a Feedthrough Term Via LQAT 76
5.1 Introduction 77
5.2 ILC Scheme for LTI Regular Model with a Feedthrough Term 78
5.2.1 ILC scheme for a singular feedthrough term 78
5.2.2 ILC scheme for a nonsingular feedthrough term 83
5.3 New ILC Strategy for LTI Regular Model with a Feedthrough Term 84
5.4 Illustrative Examples 85
5.5 Summary 94
6 Conclusions 95
6.1 Conclusions 95
6.2 Future Research Directions 97
References 98
Appendix A The Principal th Root of a Matrix and the Associated Matrix Sector Function 107
Biography 111
Publication List 112

1.Ahn, H. S., Choi, C. H., and Kim, K. B., “Iterative learning control for a class of nonlinear systems, Automatica, vol. 29(6), pp. 1575-1578, 1993.
2.Ahn, H. S., Chen, Y. Q., and Moore, K. L., “Iterative learning control: brief survey and categorization, IEEE Transactions on System, Man, and Cybernetics, Part C: Applications and Reviews, vol. 37(6), pp. 1099-1121, 2007.
3.Arimoto, S., “Learning control theory for robotic motion, International Journal of Adaptive Control and Signal Processing, vol. 4(6), pp. 543-564, 1990.
4.Arimoto, S., Kawamura, S., and Miyazaki, F., “Bettering operation of robots by learning, Journal of Robotic Systems, vol. 1(2), pp. 123-140, 1984.
5.Arimoto, S., Naniwa, T., and Suzuki, H., “Selective learning with a forgetting factor for robotic motion control, The 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA, USA, Jan., vol. 9, pp. 728-733, 1991.
6.Burl, J.B., “Singular system-a tutorial, Circuits, Systems and Computers, 1985. Nineteenth Asilomar Conference on Digital Object Identifier, pp.529-533, 1985.
7.Barton, K. L. and Alleyne, A. G., “A cross-coupled iterative learning control design for precision motion control, IEEE Transactions on Control Systems Technology, vol. 16(6), pp. 1218-1231, 2008.
8.Bien, Z. and Huh, K. M., “High-order iterative learning control algorithm, Proceedings Institution Electrical Engineering Control Theory and Applications, Part D , vol. 136(3), pp. 105-112, 1989.
9.Bristow, D. A., Tharayil, M., and Alleyne, A. G., “A survey of iterative learning control, IEEE Control Systems Magazine, vol. 26(3), pp. 96-114, 2006.
10.Campbell, S. L., Singular Systems of Differential Equations II. Pitman, New York, 1982.
11.Chen, Y., Wen, C., Gong, Z., and Sun, M., “An iterative learning controller with initial state learning, IEEE Transactions on Automatic Control, vol. 44(2), pp. 371-376, 1999.
12.Chi, R., Hou, Z., Sui, S., Yu, L., and Yao, W., “A new adaptive iterative learning control motivated by discrete-time adaptive control, International Journal of Innovative Computing, Information and Control, vol. 4(6), pp. 1267-1274, 2008.
13.Chien, C. J. and Liu, J. S., “A P-type iterative learning controller for robust output tracking of nonlinear time-varying systems, International Journal of Control, vol. 64(2), pp. 319-334, 1996.
14.Chen, Y., Wen, C., Gong, Z., and Sun, M., “An iterative learning controller with initial state learning, IEEE Transactions on Automatic Control, vol. 44(2), pp. 371-376, 1999.
15.Doh, T. Y., Moon, J. H., Jin, K. B., and Chung, M. J., “Robust iterative learning control with current feedback for uncertain linear systems, International Journal of System Science, vol. 30(1), pp. 39-47, 1999.
16.Dedieu, H. and Ogorzalek, M. J., “Controlling chaos in Chua’s circuit via sampled inputs, International Journal of Bifurcation Chaos, vol. 4(2), pp. 447-455, 1994.
17.Du, Y. Y., Tsai, J. S. H., Guo, S. M., Su, T. J., and Chen, C. W., “Observer-based iterative learning control with evolutionary programming algorithm for MIMO nonlinear systems, International Journal of Innovative Computing, Information and Control, vol. 7(3), pp. 1357-1374, 2011.
18.Freeman, C. T., Alsubaie, M. A., Cai, Z., Rogers, E., and Lewin, P. L., “Model and experience-based initial input construction for iterative learning control, International Journal of Adaptive Control and Signal Processing, vol. 25(5), pp. 430-447, 2011.
19.Fujimoto, H., Hori, J., and Kawamura, A., “Perfect tracking control based on multi-rate feedback control with generalized sampling periods, IEEE Transactions on Industrial Electronics, vol. 48(3), pp. 636-644, 2001.
20.Fujimoto, H., Kawamura, A., and Tomizuka, M., “Generalized digital redesign method for linear feedback system based on n-delay control, IEEE/ASME Transactions on Mechaton, vol. 4, pp. 101-109, June 1999.
21.Gilbert, E. G., “Controllability and observability in multivariable control systems, SIAM Journal on Control, vol. 2(1), pp. 128-151, 1963.
22.Gantmacher, F. R., The Theory of Matrices II. Chelsea, New York, 1974.
23.Gunnarsson, S., Norrlof, M., Rahic, E., and Ozbek, M., “On the use of accelerometers in iterative learning control of a flexible robot arm, International Journal Control, vol. 80(3), pp. 363-373, 2007.
24.Goodwin, G. C. and Sin, K. S., Adaptive Filtering Prediction and Control. Prentice Hall, Englewood, 1984.
25.Guo, S. M., Shieh, L. S., Chen, G., and Lin, C. F., “Effective chaotic orbit tracker: a prediction-based digital redesign approach, IEEE Transactions on Circuits and Systems-I, Fundamental Theory and Applications, vol. 47(11), pp. 1557-1570, 2000.
26.Guo, S. M. , Shieh, L. S., Lin, C. F., and Chandra, J., “State-space self-tuning control for nonlinear stochastic and chaotic hybrid systems, International Journal of Bifurcation Chaos, vol. 11(4) , pp. 1079-1113, 2001.
27.Horowitz, R., “Learning control of robot manipulators, ASME: Journal of Dynamic Systems, Measurement, and Control, vol. 115, pp. 402-411, 1993.
28.Hillenbrand, S. and Pandit, M., “An iterative learning controller with reduced sampling rate for plants with variations of initial states, International Journal of Control, vol. 73(10), pp. 882-889, 2000.
29.Ieko, T., Ochi Y., and K. Kanai, “Digital redesign of linear state-feedback law via principle of equivalent areas, Journal of Guidance, Control, and Dynamics, vol. 24, pp. 857-859, 2001.
30.Jamshidi, M., Large Scale System: Modeling and Control. Elsevier Science Publishing, New York, 1983.
31.Jiang, P., Bamforth, L. C. A., Feng, Z., Baruch, J. E. F., and Chen, Y. Q., “Indirect iterative learning control for a discrete visual servo without a camera-robot model, IEEE Transactions on System, Man, and Cybernetics Part B: Cybernetics, vol. 37(4), pp. 863-876, 2007.
32.Kuo, B. C., Digital Control Systems. Holt, Rinehart and Winston, New York, 1980.
33.Kim, D. I. and Kim, S., “An iterative learning control method with application for CNC machine tools, IEEE Transactions on Industry Applications. vol. 32(1), pp. 66-72, 1996.
34.Liu, X. P., “Asymptotic output tracking of nonlinear differential-algebraic control systems, Automatica, vol. 34(3), pp. 393-397, 1998.
35.Longman, R. W., “Iterative learning control and repetitive control for engineering practice, International Journal of Control, vol. 73(10), pp. 930-954, 2000.
36.Lee, K. H. and Bien, Z., “Initial condition problem of learning control, IEE Proceedings, Part-D, Control Theory and Applications, vol. 138(6), pp.525-528, 1991.
37.Lee, H. S. and Bien, Z., “Study on robustness of iterative learning control with nonzero initial error, International Journal of Control, vol. 64(3), pp. 345-359, 1996.
38.Lee, H. J., Park, J. B., and Joo, Y. H., “An efficient observer-based sampled-data control: digital redesign approach, IEEE Transaction Circuits and Systems-I, Fundamental Theory and Applications, vol. 50(12), pp. 1595-1601, 2003.
39.Lewis, F. L. and Syrmos, V. L., Optimal Control. John Wiley and Sons, New York, 1995.
40.Moore, K. L., “Iterative learning control-An expository overview, Applied Computational Control, Signal Processing, and Circuits, vol. 1, pp. 151-241, 1999.
41.Maeder, U., Cagienard, R., and Morari, M., Explicit Model Predictive Control. Springer-Berlin, Heidelberg, 2007.
42.Mertzios, B. G., Christodoulou, M. A., Syrmos, B. L., and Lewis, F. L., “Direct controllability and observability time domain conditions of singular systems, IEEE Transactions Automatic Control, vol. 33(8), pp. 788-791, 1988.
43.Moore, K. L., Dahleh, M., and Bhattacharyya, S. P., “Iterative learning control: A survey and new results, Journal of Robotic System, vol. 9(5), pp. 563-594, 1992.
44.Meng, D., Jia, Y., Du, J., and Yu, F., “Robust design of a class of time-delay iterative learning control systems with initial shifts, IEEE Transactions Circuits and Systems I: Regular Papers, vol. 56(8), pp. 1744-1757, 2009.
45.Middleton, R. H. and Goodwin, G. C., Digital Control and Estimation — a Unified Approach. Prentice Hall, Englewood Cliffs, New Jersey, 1990.
46.Norrlof, M., “An adaptive iterative learning control algorithm with experiments on an industrial robot, IEEE Transactions on Robotics Automation, vol. 18(2), pp. 245-251, 2002.
47.Narendra, K. S. and Oleng, N. O., “Exact output tracking in decentralized adaptive control systems, IEEE Transactions on Automatic Control, vol. 47(2), pp. 390-395, 2002.
48.Nikoukhah, R., Willsky, A. S., and Levy, B. C., “Boundary-value descriptor systems:well posedness, reachability and observability, International Journal of Control, vol. 46(5), pp. 1715-1737, 1987.
49.Ouyang, P. R., Petz, B. A., and Xi, F. F., “Iterative learning control with switching gain feedback for nonlinear systems, Journal of Computational and Nonlinear Dynamics, vol. 6(1), art no. 011020, 2011.
50.Park, K. H., “An average operator-based PD-type iterative learning control for variable initial state error, IEEE Transactions on Automatic Control, vol. 50(6), pp. 865-869, 2005.
51.Park, K. H. and Bien, Z., “A generalized iterative learning controller against initial state error, International Journal of Control, vol. 73(10), pp. 871-881, 2000.
52.Park, K. H., Bien, Z., and Hwang, D. H., “A study on the robustness of a PID-type iterative learning controller against initial state error, International Journal of System Science, vol. 30(1), pp. 49-59, 1999.
53.Porter, B. and Mohamed, S. S., “Iterative learning control of partially irregular multivariable plants with initial state shifting, International Journal of Systems Science, vol. 22(2), pp. 229-235, 1991.
54.Porter, B. and Mohamed, S. S., “Iterative learning control of partially irregular multivariable plants with initial impulse action, International Journal of Systems Science, vol. 22(3), pp. 447-454, 1991.
55.Roberts, J. D., “Linear model reduction and solution of the algebraic Riccati equation by use of the sign function, International Journal Control, vol. 32(4), pp. 677-687, 1980.
56.Rafee, N., Chen, T., and Malik, O. P., “A technique for optimal digital redesign of analog controllers, IEEE Trans. Control Systems Technology, vol. 5(1), pp. 89-99, 1997.
57.Rezaei, M., Gharaveisi, A., and Rezaei, A. A., “PID parameter selection based on iterative learning control, Contemporary Engineering Sciences, vol. 4(5), pp. 201-220, 2011.
58.Saab, S. S., “On the P-type learning control, IEEE Transactions on Automatic Control, vol. 39(11), pp. 2298-2302, 1994.
59.Saab, S. S., “Stochastic P-type/D-type iterative learning control algorithms, International Journal of Control, vol. 76(2), pp. 139-148, 2003.
60.Shieh, L. S., Chen, G., and Tsai, J. S. H., “Hybrid suboptimal control of multi-rate multi-loop sampled-data systems, International Journal of Systems Science, vol. 23(6), pp. 839-854, 1992.
61.Sadegh, N., Horowitz, R., Kao, W. W., and Tomizuka, M., “A unified approach to the design of adaptive and repetitive controllers for robotic manipulators, ASME: Journal of Dynamic Systems, Measurement, and Control, vol. 112, pp. 618-629, 1990.
62.Sugie, T. and Ono, T., “An iterative learning law for dynamical systems, Automatica, vol. 27(4), pp. 729-732, 1991.
63.Shieh, L. S., Tsay, Y. T., and Wang, C. T., “Matrix sector functions and their applications to system theory, IEE Proceeding D-Control Theory and Application, vol. 131, pp. 171-181, 1984.
64.Shieh, L. S., Tsay, Y. T., and Yates, R. E., “Some properties of matrix-sign functions derived from continued fractions, IEE Proceedings Part D, vol. 130(3), pp. 111-118, 1983.
65.Sun, L. Y. and Wang, Y. Z., “Stabilisation and control of aclass of non-linear Hamiltonian descriptor systems with application to non-linear descriptor systems, IET Control Theory Application, vol. 4(1), pp. 16-26, 2010.
66.Shieh, L. S., Wang, W. M., and Appu Panicker, M. K., “Design of PAM and PWM digital controller for cascaded analog system, ISA Transactions, vol. 37(3), pp. 201-213, 1998.
67.Sun, M. and Wang, D., “Iterative learning control with initial rectifying action, Automatica, vol. 38(7), pp. 1177-1182, 2002.
68.Shieh, L. S., Zho, X. M., and Zhang, J. L., “Locally optimal-digital redesign of continuous-time systems, IEEE Transactions on Automatic Control, vol. AC-36(4), pp. 511-515, 1989.
69.Tayebi, A. and Chien, C. J., “A unified adaptive iterative learning control framework for uncertain nonlinear systems, IEEE Transactions on Automatic Control, vol. 52(10), pp. 1907-1913, 2007.
70.Tsai, J. S. H., Chen, C. H., Lin, M. J., Guo, S. M., and Shieh, L. S., “Novel quadratic tracker for the equivalent model of the sampled-data linear singular system, Applied Mathematical Sciences, vol. 6(68), pp. 3381-3409, 2012.
71.Tsai, J. S. H., Du, Y. Y., Guo, S. M., Shieh, L. S., and Chen, C. W., “Improved observer-based digital redesign tracker for nonlinear sampled-data systems, The 2008 CACS International Automatic Control Conference (CACS/IACC'08), Tainan, Taiwan, Nov. 21-23, 2008.
72.Tsai, J. S. H., Du, Y. Y., Zhuang, W. Z., Guo, S. M., Chen, C. W., and Shieh, L. S., “Optimal anti-windup digital redesign of multi-input multi-output control systems under input constraints, IET Control Theory Applications, vol. 5(3), pp. 447-464, 2011.
73.Tsai, J. S. H., Shieh, L. S., and Yates, R. E., “Fast and stable algorithms for computing the principal nth root of a complex matrix and the matrix-sector function, International Journal of Computers and Mathematics with Applications, vol. 15(11), pp. 903-913, 1988.
74.Tsai, J. S. H., Shieh, L. S., Zhang, J. L., and Coleman, N. P., “Digital redesign of pseudo continuous-time suboptimal regulators for large-scale discrete systems, Control Theory Advance Technology, vol. 5(1), pp. 37-65, 1989.
75.Tsai, J. S. H., Wang, C. T., and Shieh, L. S., “Model conversion and digital redesign of singular systems, Journal of Franklin Institute, vol. 330, pp. 1063-1086, 1993.
76.Taybei, A. and Xu, J. X., “Observer-based iterative learning control for a class of time-varying nonlinear systems, IEEE Transactions on Circuits and Systems-I, Fundamental Theory and Application, vol. 50(3), pp. 452-455, 2003.
77.Wang, C. J. and Liao, H. E., “Impulse observability and impulse controllability of linear time-varying singular systems, Automatica, vol. 37(11), pp. 1867-1872, 2001.
78.Wang, H. J., Xue, A. K., Guo, Y. F., and Lu, R. Q., “Input-output approach to robust stability and stabilization for uncertain singular systems with time-varying discrete and distributed delays, Journal of Zhejiang University-Science A, vol. 9, pp. 546-551, 2008.
79.Wang, H., Xue, A., Lu, R., and Wang, J., “Reliable robust tracking control for Lure´s singular systems with parameter uncertainties, The 2008 American Control Conference, Seattle, WA, USA, June 11-13, pp. 4312-4317, 2008.
80.Xu, J. X., Panda, S. K., and Lee, T. H., Real-time Iterative Learning Control Design and Applications. Springer-Verlag, London, 2009.
81.Xu, J. X. and Tan, Y., “Robust optimal design and convergence properties analysis of iterative learning control approaches, Automatica, vol. 38(11), pp. 1867-1880, 2002.
82.Xu, J. X. and Tan, Y., Linear and Nonlinear Iterative Learning Control. Springer-Berlin, Heidelberg, 2003.
83.Xu, J. X. and Yan, R., “On initial conditions in iterative learning control, IEEE Transactions on Automatic Control, vol. 50(9), pp. 1349-1354, 2005.
84.Xu, J. X., Yan, R., and Chen, Y., “On initial condition in Iterative learning control, The 2006 American Control Conference, Minneapolis, Minnesota, USA, pp. 220-225, 2006.
85.Ye, Y., Tayebi, A., and Liu, X., “All-pass filtering in iterative learning control, Automatica, vol. 45(1), pp. 257-264, 2009.