【作者】 周牡丹；

【导师】 颜玉崇；

【作者基本信息】 福州大学 ， 控制理论与控制工程， 2004， 硕士

【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。更多还原

【Abstract】 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.更多还原