有源低通滤波器在混沌电路中的应用

发布时间：2018-01-26 09:08

本文关键词： 低通滤波器群时延延迟混沌系统延迟反馈控制广义同步　出处：《东北师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：滤波器作为一种使有用频率信号通过,而抑制无用频率信号的电路,它的幅频特性和滤波作用,已经被人们熟知和广泛应用。然而,从相频群时延角度考虑,滤波器除了衰减掉无用频段信号外,还有一个重要特性,就是对信号具有相移作用,可以实现延迟。本文主要研究了从模拟电子技术角度利用有源低通滤波器实现延迟混沌系统的问题,其电路结构简单,容易实现,且能将无穷维微分方程转化为有限维微分方程,为延迟混沌系统的分析打开了一条新的途径。并且实现了混沌延迟反馈控制以及延迟混沌系统的广义同步等应用;最后结合数值计算,在电路上加以实现,得到了与理论分析一致的实验结果。本文的具体研究工作如下:1.低通滤波器理论分析。首先分析了巴特沃思、贝塞尔、切比雪夫三种二阶滤波器的幅频特性与群时延特性。然后分别对巴特沃思滤波器与贝塞尔滤波器的二阶级联方式和高阶形式进行了理论分析,为利用滤波器实现混沌信号的不失真延迟奠定理论基础。2.延迟混沌电路的实现。以一个三阶和二阶延迟混沌系统为例,对它们分别进行了动力学特性分析;提出了将延时微分方程转换为常微分方程的方法,结合理论分析结果,选择合适的滤波器连接方式,实现了对混沌信号的不失真延迟;通过数值计算与电路实验,从实际应用角度证实滤波器延迟作用的理论分析结果。3.混沌延迟反馈控制。延迟反馈控制的基本思想是将系统中的某一信号经一定的延时得到的信号再反馈到系统中,将系统稳定到一定的周期态。以一个三阶连续混沌系统为例,利用滤波器得到了延迟混沌信号,实现延迟反馈控制,得到了多个周期轨道,从而达到控制的目的。4.延迟混沌系统的广义同步。以Rossler延迟混沌系统为例,利用主动被动的同步方法,实现了驱动系统和响应系统之间的广义同步及状态切换,利用低通滤波器在电路上加以实现,得到了与理论分析和数值计算相一致的结果。
[Abstract]:Filter is a kind of circuit which can make useful frequency signal pass through and suppress useless frequency signal. Its amplitude-frequency characteristic and filter function have been well known and widely used. However, from the angle of phase frequency group delay, the filter has been widely used. The filter not only attenuates the useless frequency band signal, but also has the function of phase shift. Delay can be realized. In this paper, the problem of using active low-pass filter to realize delayed chaotic system from the point of analogue electronic technology is studied. Its circuit structure is simple and easy to realize. And the infinite-dimensional differential equation can be transformed into a finite-dimensional differential equation. It opens a new way for the analysis of delayed chaotic system, and realizes the application of chaotic delay feedback control and generalized synchronization of delayed chaotic system. Finally, the numerical calculation is used to realize it in the circuit, and the experimental results are obtained in agreement with the theoretical analysis. The specific research work of this paper is as follows: 1. Theoretical analysis of low-pass filter. Firstly, Butterworth is analyzed. The amplitude-frequency characteristics and group delay characteristics of Bessel and Chebyshev second-order filters are analyzed respectively. Then the second-order cascading mode and high-order form of Butterworth filter and Bessel filter are analyzed theoretically. This paper lays a theoretical foundation for the realization of undistorted delay of chaotic signal by using filter. 2. The realization of delayed chaotic circuit. Taking a third and second order delayed chaotic system as an example, the dynamic characteristics of them are analyzed respectively. The method of transforming delay differential equation into ordinary differential equation is put forward. Combining with the theoretical analysis results, a suitable filter connection method is selected to realize the non-distortion delay of chaotic signal. Through numerical calculation and circuit experiment. From the point of view of practical application, the theoretical analysis result of filter delay action is proved. 3. Chaotic delay feedback control. The basic idea of delay feedback control is to refeedback the signal of a certain signal in the system after a certain delay. Into the system. Taking a three-order continuous chaotic system as an example, the delayed chaotic signal is obtained by using filter, and the delay feedback control is realized, and several periodic orbits are obtained. In order to achieve the purpose of control. 4. Generalized synchronization of delayed chaotic system. Taking Rossler delayed chaotic system as an example, the active and passive synchronization method is used. The generalized synchronization and state switching between the drive system and the response system are realized, and the low pass filter is used to realize it in the circuit. The results are in agreement with the theoretical analysis and numerical calculation.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN713;TM132

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