小波变换在系统阶次辨识和控制器设计中的应用研究
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摘要
本文对小波变换在线性系统阶次辨识、控制系统综合性能指标及自适应控制中的应用进行了研究。主要包括以下几个方面的内容：
（1）比较系统地介绍了小波分析理论的发展简史，综述了小波分析理论在自动控制中应用的研究现状，并探讨了小波变换在自动控制中的应用前景。
（2）研究了小波变换在信号奇异性检测中的应用，分析了线性系统脉冲响应的奇异性和线性系统阶次的之间的关系，提出了利用连续小波变换进行线性系统脉冲响应信号奇异性检测的阶次辨识的新方法。通过理论分析和仿真实验，证明了该方法可以准确地判定出线性系统传递函数的分子分母的阶次差。
（3）通过大量的仿真实验研究了二阶系统阶跃响应的小波变换特性，由此提出了两个基于小波变换的控制系统的性能指标，见式（5-1）和式(5-2)。借助于遗传算法针对这两个性能指标进行PID控制器的参数寻优，仿真实验表明这两个基于小波变换的性能指标是可行的。
（4）将基于小波变换进行阶次辨识的新方法应用于检测系统阶跃扰动出现的位置，据此本文提出了一种基于小波变换阶次辨识的扰动自适应PID控制器设计的新方法。仿真结果表明，此控制器不仅可以准确地跟踪设定值，而且可以及时地抑制出现在不同位置的阶跃扰动，具有良好的控制效果和实用价值。
This thesis puts the particular emphasis on the study and application of wavelet transform to the order identification of linear system, the integrated performance index of control system and the adaptive Control. The main contributions of the thesis are as follow.
The developing history of wavelet analysis theory is systematically summarized, the current situation of its application to the field of automatic control is thoroughly investigated. The prospects of combining wavelet analysis theory with automatic control theory are also explored.
The application of wavelet transform in the singularity detection of signal is studied. The relationship between the singularity of impulse response of system and the order of linear system is analyzed in this paper. A new method based on CWT to detect the singularity of the impulse response of linear TI system is proposed here to identify the order of the system. The effective of this method is proved by theory and the simulation results.
With a lot of simulations, the wavelet transform's character of second-order system is studied. Furthermore, two performance indexes based on wavelet transform are proposed, details as (5-1) and (5-2). Optimizing the parameter of the PID controller with the aid of genetic algorithm, the simulation result shows that these two integrated performance indexes based on wavelet transform are feasible.
Applying the new order identification method based on wavelet transform to detect the positions of step disturbances, a new adaptive PID controller of perturbation based on the new order identification method is designed. The simulation shows that the controller can not only track the set point accurately, but also suppress the step disturbance appeared in different position in time. This controller is effective and useful.
（1）比较系统地介绍了小波分析理论的发展简史，综述了小波分析理论在自动控制中应用的研究现状，并探讨了小波变换在自动控制中的应用前景。
（2）研究了小波变换在信号奇异性检测中的应用，分析了线性系统脉冲响应的奇异性和线性系统阶次的之间的关系，提出了利用连续小波变换进行线性系统脉冲响应信号奇异性检测的阶次辨识的新方法。通过理论分析和仿真实验，证明了该方法可以准确地判定出线性系统传递函数的分子分母的阶次差。
（3）通过大量的仿真实验研究了二阶系统阶跃响应的小波变换特性，由此提出了两个基于小波变换的控制系统的性能指标，见式（5-1）和式(5-2)。借助于遗传算法针对这两个性能指标进行PID控制器的参数寻优，仿真实验表明这两个基于小波变换的性能指标是可行的。
（4）将基于小波变换进行阶次辨识的新方法应用于检测系统阶跃扰动出现的位置，据此本文提出了一种基于小波变换阶次辨识的扰动自适应PID控制器设计的新方法。仿真结果表明，此控制器不仅可以准确地跟踪设定值，而且可以及时地抑制出现在不同位置的阶跃扰动，具有良好的控制效果和实用价值。
This thesis puts the particular emphasis on the study and application of wavelet transform to the order identification of linear system, the integrated performance index of control system and the adaptive Control. The main contributions of the thesis are as follow.
The developing history of wavelet analysis theory is systematically summarized, the current situation of its application to the field of automatic control is thoroughly investigated. The prospects of combining wavelet analysis theory with automatic control theory are also explored.
The application of wavelet transform in the singularity detection of signal is studied. The relationship between the singularity of impulse response of system and the order of linear system is analyzed in this paper. A new method based on CWT to detect the singularity of the impulse response of linear TI system is proposed here to identify the order of the system. The effective of this method is proved by theory and the simulation results.
With a lot of simulations, the wavelet transform's character of second-order system is studied. Furthermore, two performance indexes based on wavelet transform are proposed, details as (5-1) and (5-2). Optimizing the parameter of the PID controller with the aid of genetic algorithm, the simulation result shows that these two integrated performance indexes based on wavelet transform are feasible.
Applying the new order identification method based on wavelet transform to detect the positions of step disturbances, a new adaptive PID controller of perturbation based on the new order identification method is designed. The simulation shows that the controller can not only track the set point accurately, but also suppress the step disturbance appeared in different position in time. This controller is effective and useful.
引文
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[3] S. Mallat, "Multiresolution Approximation and wavelet Orthornormal Bases of L2(R)",Trans. Amer. Math. Soc. VOL, 315:69-87,September 1989.
[4] Ingrid Daubechies, "Orthonormal Bases of Compactly Supported Wavelets", Communications on Pure and Applied Mathematics, VOL.XLI:909-996,1988.
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[6] Martin Vetterli, Senior Member, "Wavelet and Filter Banks: Theory and Design", IEEE TRANS ON SIGNAL PROCESSING, VOL. 40:2207-2232, NO.9,SEPTEMBER,1992.
[7] Cormac Herley, martin Vetterli, "Wavelet and Recursive Filter banks", IEEE TRANSACTIONS OF SIGNAL PROCESSING VOL. 41:2536-2556, NO. 8. AUGUST 1993.
[8] Hamid Drim, Stephane Mallat and David Donoho, "On Denoising and Best Signal Representation", IEEE Transactions On Information Theory, VOL.45, No.7 November 1999.
[9] H. A. Presig and D. W. Rippin, "Theory and Application of The Modulatin Function Method-Ⅰ. Review and Theory of The Method and Theory of The Spline-type Modelating Functions",Computers chem..endng,Vol. 17 No. 1 pp.1-16,1993
[10] John F. Carrier and George Stephanopoulos, "Wavelet-Based Modulation in Control-Relevant Precess Identification", AICHE journal, Vol. 44:341-360,No. 2,February 1998
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[12] Wei Sun, Ahmet Palazoglu, "Detecting Abnormal Precess Trends by Wavelet-Domain Hidden Markov Models", AICHE Journal, Vol.49:140-150, No.1, January 2003.
[13] Milos I. Doroslovacki, and Howard Fan, "Wave-Based Linear System Modeling and Adaptive Filtering", IEEE RANSACTIONA ON SIGNAL PROCESS. VOL. 44, NO. 5, MAY 1996.
[14] M.Doroslovacki, H. Fan, and P.Djuric, "Discrete-time wavelets: time-frequency localization, shift-invariance, modeling of linear time-invariant systems", presented at Conf.Inform. Sciences and Systems,Princeton,NJ, March 1992.
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[16] M. Doroslovacki and H.Fan, "Wavelet-Based Linear System Modeling and Adaptive Filtering," IEEE Trans. Signal Processing, Vol. 44, No. 5, pp. 1156-1167,1996.
[17] N. Surshbabu and J. Farrell, "Wavelet-Baed System Identification for Nonlinear Control Applications", Proceddings of IEEE Control and Decision Conference, pp.236-241,1995.
[18] Yi-Ming Wang, Sung-II Kwon, Amy Regan,and Tony Rohlev, "System Identification of the Linac RF System Using A Wavelet Method and Ites Applications in the SNS LLRF Control System", Proceeding of the 2001 Particle Accelerator Conference ,Chicago. pp. 1613-1165.
[19] Pavel Vaclavek &Petr Vavrin, "System Identification in Frequency Domain Using Orthonormal Bases",
[20] M. Shamma, M.doroslovacki, Comparison of Wavelet and Other Transform Bases LMS Adapt Algorithms for Colors Inputs, 2000 Conerence on Information Science and Systems, Princeton University, March 15-17,2000
[20] Benveniste A., R. Nikouhah and A.S. Willsky(1990), "Multiscale system theory", Proceedings of the 29th conference on Decision and Control, Honolulu, Hawaii, USA, pp. 140-145.
[22] 崔锦泰 著，程正兴 译，《小波分析导论》，西安交通大学出版社，1997
[23] Albert Boggess, Francis J. Narcowich, 《A First Course in Wavelets with Fourier Analysis》, 电子工业出版社，2002
[24] Stephane Mallat 著，杨力华，戴道清，黄文良，湛秋辉译，《信号处理的小波导引》，机械工业出版社，2002.9
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[26] 秦前清，杨宗凯 著，《实用小波分析》，西安电子科技大学出版社，1994
[27] 胡昌华，张军波，夏军，张伟著，《基于MATLAB 的系统分析与设计－小波分析》，西安电子科技大学出版社，1999
[28] 飞思科技产品研发中心编著，《MATLAB 6.5辅助小波分析与应用》，电子工业出版社，2003
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