本文關(guān)鍵詞： 低通濾波器 群時延 延遲混沌系統(tǒng) 延遲反饋控制 廣義同步　出處：《東北師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：濾波器作為一種使有用頻率信號通過,而抑制無用頻率信號的電路,它的幅頻特性和濾波作用,已經(jīng)被人們熟知和廣泛應(yīng)用。然而,從相頻群時延角度考慮,濾波器除了衰減掉無用頻段信號外,還有一個重要特性,就是對信號具有相移作用,可以實現(xiàn)延遲。本文主要研究了從模擬電子技術(shù)角度利用有源低通濾波器實現(xiàn)延遲混沌系統(tǒng)的問題,其電路結(jié)構(gòu)簡單,容易實現(xiàn),且能將無窮維微分方程轉(zhuǎn)化為有限維微分方程,為延遲混沌系統(tǒng)的分析打開了一條新的途徑。并且實現(xiàn)了混沌延遲反饋控制以及延遲混沌系統(tǒng)的廣義同步等應(yīng)用;最后結(jié)合數(shù)值計算,在電路上加以實現(xiàn),得到了與理論分析一致的實驗結(jié)果。本文的具體研究工作如下:1.低通濾波器理論分析。首先分析了巴特沃思、貝塞爾、切比雪夫三種二階濾波器的幅頻特性與群時延特性。然后分別對巴特沃思濾波器與貝塞爾濾波器的二階級聯(lián)方式和高階形式進行了理論分析,為利用濾波器實現(xiàn)混沌信號的不失真延遲奠定理論基礎(chǔ)。2.延遲混沌電路的實現(xiàn)。以一個三階和二階延遲混沌系統(tǒng)為例,對它們分別進行了動力學(xué)特性分析;提出了將延時微分方程轉(zhuǎn)換為常微分方程的方法,結(jié)合理論分析結(jié)果,選擇合適的濾波器連接方式,實現(xiàn)了對混沌信號的不失真延遲;通過數(shù)值計算與電路實驗,從實際應(yīng)用角度證實濾波器延遲作用的理論分析結(jié)果。3.混沌延遲反饋控制。延遲反饋控制的基本思想是將系統(tǒng)中的某一信號經(jīng)一定的延時得到的信號再反饋到系統(tǒng)中,將系統(tǒng)穩(wěn)定到一定的周期態(tài)。以一個三階連續(xù)混沌系統(tǒng)為例,利用濾波器得到了延遲混沌信號,實現(xiàn)延遲反饋控制,得到了多個周期軌道,從而達到控制的目的。4.延遲混沌系統(tǒng)的廣義同步。以Rossler延遲混沌系統(tǒng)為例,利用主動被動的同步方法,實現(xiàn)了驅(qū)動系統(tǒng)和響應(yīng)系統(tǒng)之間的廣義同步及狀態(tài)切換,利用低通濾波器在電路上加以實現(xiàn),得到了與理論分析和數(shù)值計算相一致的結(jié)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.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN713;TM132

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