基於李亞普諾夫理論(Lyapunov Theorem) ,本論文為解決強韌追蹤問題,提出一個具有擾動估測器之參考模式調適可變結構控制器(MRAVSC)。 此控制器設計方法乃是針對任意相對級數並且在輸入端及輸出端含有相加性與相乘性的未模式化不確定量之多輸入多輸出線性非時變系統。 藉著上述控制器中所隱含的擾動估測器,擾動與追蹤誤差的微分皆可被估測。 再者,此控制器同時具有調適控制機制,此乃是用來調適擾動估測誤差的未知上界。 本控制器可保證閉迴路系統的uniformly ultimate boundedness特性。 最後,針對本論文所提出的控制器設計法則,以二個數值範例來展示其可行性。

Based on the Lyapunov stability theorem, a model reference adaptive variable structure control (MRAVSC) scheme with perturbation estimation is presented in this thesis for solving robust tracking problems. The plant considered belongs to a class of MIMO linear time invariant systems with arbitrary relative degree possessing additive and multiplicative unstructured uncertainties in the input and output channels. By introducing a perturbation estimation process embedded in the proposed control scheme, both the perturbations and differentials of tracking errors can be estimated. In addition, the proposed control scheme also contains an adaptive mechanism in order to automatically adapt the unknown upper bound of perturbation estimation error, and guarantee the property of uniformly ultimate boundedness for the closed-loop controlled system. Finally, two numerical examples are presented to demonstrate the feasibility of the proposed control scheme.

Abstract i
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . .1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . 4
Chapter 2 MRAVSC with Perturbation Estimation 5
2.1 System Descriptions and Assumptions . . . . . . . . . . . . 5
2.2 ProblemFormulation . . . . . . . . . . . . . . . . . . . . .8
2.3 Design of the Control Scheme . . . . . . . . . . . . . . . .19
2.4 Stability Analysis of the Proposed Control Scheme . . . . . 29
2.5 Summary of Design Procedure . . . . . . . . . . . . . . . . 38
Chapter 3 Simulations 39
Chapter 4 Conclusions 81
References 82
Appendix A 88
Appendix B 94

◦
[1]Astr˙om, K. J. & Wittenmark, B. (1995). Adaptive Control (2nd edition).
Addison-Wesley Publishing Company, Inc..
[2]Chen, C. T. (1993). Analog and Digital Control System Design: Transfer-
Function, State-Space, and Algebraic Methods. Saunders College Publishing.
[3]Chen, Y. C., Lin, P. L. & Chang, S. (1992). Design of output tracking
via variable structure system: for plants with redundant inputs. IEE
Proceedings-D, Vol. 139, No. 4, pp. 421 − 428.
[4]Chien, C. J., Sun, K. C., Wu, A. C. & Fu, L. C. (1996). A robust MRAC
using variable structure design for multivariable plants. Automatica,
Vol. 32, No. 6, pp. 833 − 848.
[5]Chou, C. H. & Cheng, C. C. (2001). Design of adaptive variable structure
controllers for perturbed time-varying state delay systems. Journal of
Franklin Institute, Vol. 338, No. 1, pp. 35 − 46.
[6]Datta, A. & Ho, M. T. (1994). On modifying model reference adaptive
control schemes for performance improvement. IEEE Transactions on
Automatic Control, Vol. 39, No. 9, pp. 1977 − 1980.
[7]Datta, A. & Ioannou, P. A. (1994). Performance analysis and improvement
in model reference adaptive control. IEEE Transactions on Automatic
Control, Vol. 39, No. 12, pp. 2370 − 2387.
[8]DeCarlo, R. A., Zak, S. H. & Matthews, G. P. (1988). Variable structure
control of nonlinear multivariable systems: a tutorial. Proceedings of
the IEEE, Vol. 76, No. 3, pp. 212 − 232.
[9]Doyle, J. C., Francis, B. A. & Tannenbaum, A. R. (1992). Feedback Control
Theory. Macmillan Publishing Company.
[10]Edwards, C. & Spurgeon, S. K. (1998). Sliding Mode Control: Theory and
Applications. Taylor and Francis Ltd..
[11]Elmali, H. & Olgac, N. (1992). Sliding mode control with perturbation
estimation (SMCPE): a new approach. International Journal of Control,
Vol. 56, No. 4 pp. 923 − 941.
[12]Elmali, H. & Olgac, N. (1996). Satellite attitude control via sliding mode
with perturbation estimation. IEE Proceedings-Control Theory and Application,
Vol. 143, No. 3 pp. 276 − 282.
[13]Feng, C. B. & Wu, Y. Q. (1996). A design scheme of variable structure
adaptive control for uncertain dynamic systems. Automatica, Vol. 32,
No. 4, pp. 561 − 567.
[14]Fu, L. C. (1992). A new robust MRAC using variable structure design for
relative degree two plants. Automatica, Vol. 28, No. 5, pp. 911 − 925.
[15]Fu, L. C. & Liao, T. L. (1990). Globally stable robust tracking of nonlinear systems using variable structure control and with an application to a
robotic manipulator. IEEE Transactions on Automatic Control, Vol. 35,
No. 12, pp. 1345 − 1350.
[16]Hsiao, J. M. & Cheng, C. C. (1999). Design of robust tracking controllers
with perturbation estimation for mismatched systems. R.O.C. Automatic
Control Conference, pp. 199 − 201.
[17]Hsu, L. & Costa, R. R. (1989). Variable structure model reference adaptive
control using only input and output measurements: part 1. International
Journal of Control, Vol. 49, No. 2, pp. 399 − 416.
[18]Hung, J. Y., Gao, W. & Hung, J. C. (1993). Variable structure control:
a survey. IEEE Transactions on Industrial Electronics, Vol. 40, No. 1,
pp. 2 − 22.
[19]Ioannou, P. (1986). Robust adaptive controller with zero residual tracking
errors. IEEE Transactions on Automatic Control, Vol. 31, No. 8,
pp. 773 − 776.
[20]Ioannou, P. A. & Sun, J. (1996). Robust adaptive control. Prentice-Hall
International, NJ.
[21]Ioannou, P. A. & Tsakalis, K. S. (1986). A robust direct adaptive controller.IEEE Transactions on Automatic Control, Vol. 31, No. 11, pp. 1033 −
1043.
[22]Khalil, H. K. (1996). Nonlinear systems (2nd edition). Prentice-Hall, Upper
Saddle River, NJ.
[23]Kreisselmeier, G. (1986). A robust indirect adaptive - control approach.
International Journal of Control, Vol. 43, No. 1, pp. 161 − 175.
[24]Kreisselmeier, G. & Anderson, B. D. O. (1986). Robust model reference
adaptive control. IEEE Transactions on Automatic Control, Vol. 31,
No. 2, pp. 127 − 133.
[25]Kreisselmeier, G. & Narendra, K. S. (1982). Stable model reference adaptive
control in the presence of bounded disturbances. IEEE Transactions on
Automatic Control, Vol. 27, No. 6, pp. 1169 − 1175.
[26]Liao, T. L., Fu, L. C. & Hsu, C. F. (1992). Output tracking control of
nonlinear systems with mismatched uncertainties. Systems and Control
Letters, Vol. 18, pp. 38 − 47.
[27]Lin, Y. & Mao, J. (2001). A robust VS-MRAC using switching scheme for
the gain of control variables. International Journal of Control, Vol. 74,
No. 3 pp. 225 − 238.
[28]Lin, Y., Zhang, J. & Mao, J. (1997). Variable structure robust adaptive
control with unmodeled dynamics. Proceedings of the 36th Conference
on Decision and Control, pp. 3243 − 3248.
[29]Narendra, K. S. & Annaswamy, A. M. (1986). Robust adaptive control in
presence of bounded disturbances. IEEE Transactions on Automatic Control, Vol. 31, No. 4, pp. 306 − 315.
[30]Narendra, K. S., Lin, Y. H. & Valavani, L. S. (1980). Stable adaptive controller design, part II: proof of stability. IEEE Transactions on Automatic
Control, Vol. 25, No. 3, pp. 440 − 448.
[31]Narendra, K. S. & Valavani, L. S. (1978). Stable adaptive controller design -direct control. IEEE Transactions on Automatic Control, Vol. 23, No. 4,
pp. 570 − 583.
[32]Peterson, B. B. & Narendra, K. S. (1982). Bounded error adaptive control.
IEEE Transactions on Automatic Control, Vol. 27, No. 6, pp. 1161 −1168.
[33]Rohrs, C. E., Valavani, L., Athans, M. & Stein, G. (1985). Robustness
of continuous-time adaptive control algorithms in the presence of unmodeled
dynamics. IEEE Transactions on Automatic Control, Vol. 30,
No. 9, pp. 881 − 889.
[34]Sastry, S. & Bodson, M. (1989). Adaptive Control: Stability, Convergence
and Robustness. Prentice-Hall, Englewood Cliffs, NJ.
[35]Sun, J. (1993). A modified model reference adaptive control scheme for improved transient performance. IEEE Transactions on Automatic Control,
Vol. 38, No. 8, pp. 1255 − 1259.
[36]Tao, G. & Ioannou, P. A. (1991). Robust adaptive control - a modified
scheme. International Journal of Control, Vol. 54, No. 1 pp. 241− 256.
[37]Verghese, G. C., Fernandez R., B. & Hedrick, J. K. (1988). Stable, robust
tracking by sliding mode control. Systems and Control Letters, Vol. 10,
pp. 27 − 34.
[38]Wu, Y. & Yu, X. (1999). Variable structure control design for uncertain
dynamic systems with disturbances in input and output channels. Automatica,
Vol. 35, No. 2, pp. 311 − 319.
[39]Yeung, K. S., Cheng, C. C. & Kwan, C. M. (1993). A unifying design of
sliding mode and classical controllers. IEEE Transactions on Automatic
Control, Vol. 38, No. 9, pp. 1422 − 1427.
[40]Young, K. D., Utkin, V. I. & ¨Ozg¨uner, ¨U. (1999). A control engineer’s
guide to sliding mode control. IEEE Transactions on Control Systems
Technology, Vol. 7, No. 3, pp. 328 − 342.
[41]Zak, S. H. & Hui, S. (1993). Output feedback variable structure controllers
and state estimators for uncertain/nonlinear dynamic systems. IEE
Proceedings-D, Vol. 140, No. 1, pp. 41 − 50.