本論文乃是根據李亞普諾夫穩定性理論 (Lyapunov Theorem)，提出n階適應積分可變結構微分估測器(AIVSDE)之設計方法。文中所設計之微分估測器不僅改善現有之AIVSDE，而且可用來估測具有n+1階有界微分且連續之平滑訊號的n次微分。分析結果顯示出調整一些參數可以幫助輸入含有高頻雜訊的微分估測器。在估測結構中，使用適應性演算法追蹤未知輸入訊號上界之要求。本論文可以保證微分估測器的穩定性，並與近年來提出高階順滑模態控制法之微分估測器比較模擬之準確性。

Based on the Lyapunov stability theorem, a methodology of designing an nth order adaptive integral variable structure derivative estimator (AIVSDE) is proposed in this thesis. The proposed derivative estimator not only is an improved version of the existing AIVSDE, but also can be used to estimate the nth derivative of a smooth signal which has continuous and bounded derivatives up to n+1. Analysis results show that adjusting some of the parameters can facilitate the derivative estimation of signals with higher frequency noise. The adaptive algorithm is incorporated in the estimation scheme for tracking the unknown upper bounded of the input signal as well as their's derivatives. The stability of the proposed derivative estimator is guaranteed, and the comparison between recently proposed derivative estimator of high-order sliding mode control and AIVSDE is also demonstrated.

List of Figures iv
List of Table viii
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Thesis . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 Design of the First Order AIVSDE 4
2.1 Design of the First Order AIVSDE . . . . . . . . . . . . . . . . 4
2.2 Analysis of System’s Performance in the Presence of Noise . . 7
Chapter 3 Design of the Second Order AIVSDE 14
3.1 Design of the Second Order AIVSDE . . . . . . . . . . . . . . 14
3.2 Analysis of System’s Performance in the Presence of Noise . . 24
Chapter 4 Design of the nth Order AIVSDE 30
Chapter 5 Simulations 41
Chapter 6 Conclusions 61
Bibliography 61

[1] T. Floquet, J. P. Barbot, and W. Perruquetti, Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems,” Automatic, pp. 1077 - 1083; 2003.
[2] B. C. Kuo, Automatic Control Systems, eighth edition, USA: John Wiley & Sons, Inc., 2003.
[3] Y. Chang and C. C. Cheng, “Design of adaptive sliding surfaces for systems with mismatched perturbations to achieve asymptotical stability,” IET Control Theory & Applications., Vol. 1 No. 1, pp. 417 -421; 5p; 2007.
[4] C. H. Chou, and C. C. Cheng, “A decentralized model reference adaptive variable structure controller for arge-scale time-varying delay systems,” IEEE Trans. Automat. Contr., Vol. 48, No. 7, pp. 1213 -1217; 2003.
[5] C. C. Cheng, and C. Y. Juan, “Design of derivative estimator using adaptive integral variable structure technique,” Proc. of 2000 American Contr. Conf., pp. 3187 -3191; 2000.
[6] C. C. Cheng, and M. W. Chang, “Design of Derivative Estimator Using Adaptive Sliding Mode Technique,” merican Contr. Conf., pp. 2611-2615; 2006.
[7] C. C. Cheng, and S. H. Chien, “Adaptive sliding mode controller design based on T-S fuzzy system models,” Automatica, Vol. 42, No. 6, pp. 1005- 1010; 6p; 2006.
[8] V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Automat. Contr., Vol. AC-22 , No. 2, pp. 212 - 222; 1977.
[9] M. S. Chen, Y. R. Hwang and M. Tomizuka, “A state-dependent boundary layer design for sliding mode control,” IEEE Trans. Automat. Contr., Vol. 47, No. 10, pp. 1677 - 1681; 2002.
[10] L. Jiang, and Q. H. Wu, “Nonlinear adaptive control via sliding-mode state and perturbation observer ,” Proc. of IEE Control Theory and Applications , Vol. 149, No. 4, pp. 269 - 277; 2002.
[11] A. Levant, “Robust exact differentiation via sliding mode technique,” Automatica, Vol. 3, No. 34 pp. 379- 384; 1998
[12] J. X. Xu, T. H. Lee, and W. Mao, “On the design of daptive derivative estimator using variable structure,” Proc. of 1995 American Contr. Conf., pp. 529- 533; 1995.
[13] J. X. Xu, Q. W. Jia, and T. H. Lee, “On the design of a nonlinear adaptive variable structure derivative estimator,” IEEE Trans. Automat. Contr., Vol. 45, No. 5, pp. 1028- 1033; 2000.
[14] B. Z. Golembo, S. V. Emelyanov, V. I. Utkin, and A. M. Shubladze, “Application of piecewise-continuous dynamic systems to filtering problem,” Automat. Remote Contr., No. 3, pp. 62 - 72; 1976.
[15] A. Levant, “Higher-order sliding modes, differentiation and outputfeedback control,” Int. J. Control, Vol.76, pp. 924 - 941; 2003.
[16] A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, fourth edition, McGraw-Hill Higher Education, Inc., International Edition 2002.
[17] 交通部,無線電頻率分配表,交通部,2007.06.