在本論文中，我們針對可變結構系統控制和使用步階迴歸技術來處理不匹配的不確定性並應用我們的理論結果對直流馬達作速度控制。 此論文有提到不匹配摩擦力項,可利用未知輸入觀測器可將系統的狀態及外部干擾估測出來。搭配該估側器,使用可變結構控制系統和步階迴歸系統來達到DC 馬達的速度控制。針對速度可看出此系統的性能可將原先的轉移函數視為一階的轉移函數且直流的增益為1,且頻寬可任意的調整。

In this thesis, we consider the variable structure system (VSS) control using the backstepping technique to deal with the mismatched uncertainty and apply our theoretical results to DC motor velocity control. In the presence of mismatched friction force, the unknown input observer is then used to provide the estimates of the states of the system as well as the friction term. With these estimates, the VSS control method is used to fulfill the backstepping control method for DC motor velocity control. The overall system performance is determined by a first-order transfer function with unit DC gain and arbitrary bandwidth.

Contents
1 Introduction 5
1.1 Survey of Related Researches and Motivation . . . 5
2 Experimental System 11
2.1 Instruments . . . . . . . . . . . . . . . . . . . 11
2.1.1 DC servo motor and the encoder . . . . . . . . . . . . . . . . 12
2.1.2 linearamplifier. . . . . . . . . . . . . . . . . 13
2.1.3 The data acquisition card . . . . . . . . . . .. 14
2.2 Veriation of Motor Parameters . . . . . . . . .. 15
2.2.1 motor parameter measurements using a tachometer . . . . . . 16
2.2.2 motor parameter measurement method of current . 20
2.2.3 Estimation of parameters of the servo motor . . 22
3 Speed Control by Backstepping with VSS 24
3.1 The state-space model and the unknown input observer . 25
3.2 Backstepping VSS Control . . . . . . . . . . . . . 31
4 Conclusions and Discussions 45

Bore-Kuen Lee and Li-Wei Mau, ``An Output Tracking VSS Control in the Presence of Unmatched Uncertainty'', Proceeding of the 3rd Asian contol conforence, Shanghai, July 4-7,pp.705$\symbol{126}$710(2000).
A. Akoachere, C. Edwards, and S. K. Spurgeon,$"$ An LMI approach to the sliding mode static output feedback problem,$"$\QTR{it}{Proceeding of the 5th European Control Conference}(1999).
S. K. Bag, S. K. Spurgeon, and C. Edwards, ''Output feedback sliding mode design for linear uncertain systems,'' \QTR{it}{IEE Proc.-Control Theory Appl.}, vol. 144, no. 3, pp. 209-216(1997).
Han Ho Choi, $"$A new method for variable structure control system design: a linear matrix inequality approach$",$ \QTR{it}{Automatica}, vol. 33, no. 11, pp.2089-2097(1997).
H. H. Choi, ''An explicit formula of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties,'' \QTR{it}{Automatica}, vol. 34, no. 8, pp. 1015-1020(1998).
H. H. Choi, ''On the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties,'' \QTR{it}{Automatica}, vol. 35, pp. 1707-1715(1999).
E. J. Davison and S. H. Wang, ''On pole assignment in linear multivariable systems using output feedback,'' \QTR{it}{IEEE Trans. Automatic Control}, vol. 20, pp. 516-518(1975).
R. A. DeCarlo, S. H. Zak, and G. P. Matthews, $"$Variable structure control of nonlinear multivariable systems: A tutorial, $"$ \QTR{it}{Proceeding of the Institute of Electrical and Electronics Engineering}, vol. 76, pp.212-232(1988).
C. Edwards and S. K. Spurgeon, $"$Sliding mode stabilization of uncertain systems using only output information,$"$ \QTR{it}{Int. J. Control}, Vol. 62, No. 5, pp.1129-1144(1995).
C. Edwards, S. K. Spurgeon, and R. J. Patton, ''Sliding mode observers for fault detection and isolation,'' \QTR{it}{Automatica}, vol. 36, pp.541-553(2000).
El-Khazali and R. DeCarlo, $"$Output feedback variable structure control design,$"$ \QTR{it}{Automatica}, vol. 31, no. 6, pp.805-816(1995).
S. V. Emelyanov, S. K. Korovin, A. L. Nersisian, and YU. E. Nisenzon, $"$Output feedback stabilization of uncertain plants: A variable structure systems approach,$"$ \QTR{it}{Int. J. Control}, vol. 55, no. 1, pp.61-81(1992).
L.C. Fu and T. L. Liao, $"$Globally stable robust tracking of nonlinear system using variable structure control and with an application to robotic manipulator,$"$ \QTR{it}{IEEE Trans. Automatic Control, }AC-35\QTR{bf}{, }pp.1345-1350(1990).
B. S. Heck, S. V. Yallapragada, and M. K. H. Fan, ''Numerical methods to design the reaching phase of output feedback variable structure control,'' \QTR{it}{Automatica}, vol. 31, no. 2, pp. 275-279(1995).
Kou-Cheng Hsu, $"$Variable structure control design for uncertain dynamic systems with sector nonlinearities,$"$ \QTR{it}{Automatica}, vol. 34, no. 4, pp.505-508(1998).
Control Systems of Variable Structure}, John Wilay \& Sons, New York(1976).
H.-S. Jeong and V. I. Utkin, ''Sliding mode tracking control of systems with unstable zero dynamics,'' in Lecture Notes in Control and Information Sciences, vol. 247, \QTR{it}{Variable Structure Systems, Sliding Mode and Nonlinear Control}, edited by K. D. Young and \"{U}. \"{O}zg\"{u}ner, pp. 303-328(1999).
H. Kimura, ''Pole assignment by gain output feedback,'' \QTR{it}{IEEE Trans. Automatic Control}, vol. 20, pp. 509-516(1975).
H. Kimura, ''A further result on the problem of pole assignment by output feedback,'' \QTR{it}{IEEE Trans. Automatic Control}, vol. 22, pp. 458-463(1977).
P. Kudva, N. Viswanadham, and A. Ramakrishna, ''Observers for linear systems with unknown inputs,'' \QTR{it}{IEEE Trans. on Automatic Control}, vol. 25, no. 1, pp. 113-115 (1980).
Chi-Man Kwan, $"$Sliding mode control of linear systems with mismatched uncertainties, $"$ \QTR{it}{Automatica}, Vol. 31, NO. 2, pp.303-307(1995).
A. Levant, $"$Robust exact differentiation via sliding mode technique,$"$ \QTR{it}{Automatica}, vol. 34, no. 3, pp. 379-384(1998).
T.-K. Nam, T. Mita, X.\ Xin, and A. Shimada, ''Sliding mode control for invertible systems based on a direct design of interactors,'' \QTR{it}{Proceeding of the 37th IEEE Conf. on Decision and Control}, Tampa, Florida USA, pp.2425-2430(1998).
S. Oh and H. K. Khalil, $"$Output feedback stabilization using variable structure control,$"$ \QTR{it}{Int. J. Control}, vol. 62, no. 4, pp.831-848(1995).
D.-W. Park and S-.B. Choi, $"$Moving sliding surface for high-order variable structure systems,$"$ \QTR{it}{Int. J. Control}, vol. 72, no. 11, pp. 960-970(1999).
S. K. Park and H. K. Ahn, $"$Robust controller design with novel sliding surface,$"$ \QTR{it}{IEE Proc. Part D, Control Theory and Application}, vol. 146, no. 3, pp. 242-246(1999).
Y. B. Shtessel, ''Nonlinear output tracking in conventional and dynamic sliding manifolds,'' \QTR{it}{IEEE Trans. on Automatic Control}, vol. 42, no. 9, pp. 1282-1286(1997).
Vadim I. Utkin, $"$Discontinuous control systems: state of the art in theory and applications,$"$ \QTR{it}{Preprint of the 10th IFAC Congress, }Munich, Germany, pp.75-94(1987).
Sliding Modes in Control Optimization}, Springer-Verlag, New York(1992).
B. L. Walcott and S. H. Zak, 1988, $"$Combined observer-controller synthesis for uncertain dynamical systems with applications, $"$ \QTR{it}{IEEE Trans. System, Man, and Cybernetics}, Vol. 18, pp.88-104(1988).
S. V. Yallapragada, B. S. Heck, and J. D. Finney, ''Reaching conditions for variable structure control with output feedback,'' \QTR{it}{J. Guidance, Control, and Dynamics}, vol. 19, no. 4, pp. 848-853(1996).
K. Yasuda and Y. Nakatsuji, ''Robust sliding mode control of linear uncertain systems,'' \QTR{it}{Trans. SICE}, vol. 34, no. 6, pp. 516-522 (1998). (in Japanese)
K. D. Young, V. I. Utkin, and \"{U}mit \"{O}zg\"{u}ner, ''A control engineer's guide to sliding mode control,'' \QTR{it}{IEEE tr. Control Systems Technology}, vol. 7, no. 3, pp. 328-342(1999).
Taheshi Furuhashi, S. Sangwongwanich, and S.Okuma,''A position-and-velocity sensorless control for brushless DC motor using an adaptive sliding mode observer,'' \QTR{it}{IEEE Trans. on Industarial electronics, }vol.39, no. 2, pp. 89\symbol{126}95(1992).
Z. Chen, M. Tomita, S. Doki, and S. Okuma, '' New adaptive sliding observers for position and velocity-sensorless controls of brushless DC motors,'' \QTR{it}{IEEE Trans. on Industarial electronics, }vol.47, no. 3, pp. 582\symbol{126}591(2000).
A. Stotsky, J. K. Hedrick, and P.P. Yip, '' The use of sliding modes to simplify the backstepping control method,'' \QTR{it}{American Control Conference Albuquerque, }pp. 1703\symbol{126}1708 New Mexico June (1997).
T. Ahmed-Ali, F. L. Lagarrigue,'' Sliding observer-controller design for uncertain triangular nonlinear systems,'' \QTR{it}{Proceedings of the 36th Conference on Decision \& Control San Diego, California USA, }pp.3237\symbol{126}3242(1997).
A Generalized VSS Control Scheme with Internal Models}, master thesis, Chung-Hua University, 2001.
Brian Armstrong-Helouvry, ''Stick slip and control in low-speed motion,'' \QTR{it}{IEEE Trans. on Automatic Control, }vol.38, no. 10, pp. 1483\symbol{126}1495(1993).