本文選題：混沌系統(tǒng) + 符號動力學��； 參考：《吉林大學》2014年博士論文

【摘要】：混沌系統(tǒng)是混沌理論研究和混沌應用的重要組成部分，充分了解混沌系統(tǒng)的混沌行為和混沌形成機理，能夠?qū)崿F(xiàn)混沌的控制和反控制。傳統(tǒng)的非線性行為分析方法是從線性或確定性的角度分析和研究，往往不能滿足控制性能日益提高的要求，本論文在前人工作的基礎(chǔ)上，對混沌系統(tǒng)的非線性特性進行了深入研究。以典型的離散動力系統(tǒng)Logistic映射和開關(guān)變換器為例，將拓撲共軛理論、符號動力學、相對熵和信息熵等理論有機結(jié)合起來，并將這些理論應用到這兩種典型離散動力系統(tǒng)的研究中，得到了一些新的混沌動力學行為指標，從而證明了本文所提出的方法的正確性和有效性，進一步豐富了混沌理論，為混沌理論的工程應用打下基礎(chǔ)，并在文章的最后設(shè)計了基于電壓和電流雙環(huán)控制的串聯(lián)型開關(guān)變換器。 本文將相對熵理論應用于具有混沌特征的典型Logistic映射的混沌狀態(tài)分析中，提出了基于符號動力學和時間不可逆性量化Logistic映射混沌特性的新指標。首先將Logistic混沌系統(tǒng)的數(shù)值序列轉(zhuǎn)化為符號序列，選擇合適的符號序列長度和編碼長度，通過一系列推導得出Logistic混沌系統(tǒng)存在時間不可逆性，相對熵可以量化處于混沌狀態(tài)的Logistic系統(tǒng)離開平衡狀態(tài)的距離，并且相對熵的數(shù)值與混沌系統(tǒng)的初始值x0無關(guān)，只取決于系統(tǒng)的參數(shù)μ，進而證明了并非混沌系統(tǒng)的所有特征參數(shù)都具有初值依賴性。 本文對基于相對熵理論的開關(guān)變換器的時間不可逆性進行研究，提出了一種量化開關(guān)變換器處于混沌狀態(tài)時的離開平衡狀態(tài)的新的動力學行為指標。由于開關(guān)變換器處于電感電流不連續(xù)狀態(tài)時可以等效為一階的離散動力系統(tǒng)，文中以典型的DCM Boost變換器為例，基于拓撲共軛理論將數(shù)值序列以粗�；男问睫D(zhuǎn)化為符號序列，運用滑動窗口的方法，計算得出轉(zhuǎn)化后的符號字頻率，進而通過計算前向和后向序列的概率比值，得出了DCM Boost開關(guān)變換器的相對熵數(shù)值。由于相對熵值可以量化開關(guān)變換器的混沌狀態(tài)離開平衡狀態(tài)的距離，從而可以對開關(guān)變換器混沌系統(tǒng)的變化趨勢做出合理的預判，為揭示開關(guān)變換器的非線性特性提供新的思路和方法。也進一步證明了相對熵理論對于處于混沌狀態(tài)的開關(guān)變換器分析的適用性。 在基于信息熵理論分析開關(guān)變換器的混沌特性的研究中，本文針對開關(guān)變換數(shù)值序列的分布特點，結(jié)合信息熵理論提出了直接計算開關(guān)變換器數(shù)值序列分布特征。文中基于一階不連續(xù)導電模式Buck和Boost變換器，討論參數(shù)變化時對應的信息熵。研究結(jié)果表明，熵增加原理的前提下，信息熵能夠區(qū)分周期態(tài)和混沌行為，隨著反饋參數(shù)k的增加，信息熵趨近理論極大值，當初始值x0變化時，對應的數(shù)值序列信息熵的沒有改變，證明了混沌系統(tǒng)的信息熵不具有初始值依賴關(guān)系。由于開關(guān)轉(zhuǎn)換器的數(shù)字序列滿足一定的分布特征,從宏觀數(shù)值分布的開關(guān)變換器混沌系統(tǒng)做出合理的預期,為進一步理解混沌和混沌控制開關(guān)變換器的特點提供了理論依據(jù)。 本文的最后設(shè)計了基于電壓和電流雙環(huán)控制的串聯(lián)型Buck開關(guān)變換器。實驗結(jié)果表明控制電路采用電壓、電流雙環(huán)控制，因此電路響應快，限制了開關(guān)管的最大電流，，極大地改善了工作特性，在輸入電壓在20～90V范圍改變時頻率較穩(wěn)定，接入容性負載時工作狀態(tài)影響較少，且具有短路和過流保護功能。這種電源成本低、工作穩(wěn)定，可使用在寬電壓工作的工業(yè)用各種報警器產(chǎn)品和爆閃式信號燈中。
[Abstract]:Chaotic system is an important part of chaos theory research and chaos application. The chaotic behavior and chaos formation mechanism are fully understood, and chaos control and anti control can be realized. The traditional nonlinear behavior analysis method is analyzed and studied from the angle of linearity or certainty, which often can not satisfy the increasing control performance. On the basis of previous work, this paper studies the nonlinear characteristics of the chaotic system, and combines the theory of topological conjugation, symbolic dynamics, relative entropy and information entropy, and applies these theories to the two types of two codes, taking the typical discrete power system and switching converters as an example. In the study of the discrete dynamic system, some new chaotic dynamic behavior indexes are obtained, which proves the correctness and effectiveness of the proposed method. It further enriches the chaos theory and lays the foundation for the engineering application of chaos theory. At the end of the article, we set up the series opening based on the double loop control of voltage and current. Turn off converter.
In this paper, the relative entropy theory is applied to the chaotic state analysis of a typical Logistic mapping with chaotic characteristics. A new index based on symbolic dynamics and time irreversibility is proposed to quantify the chaotic characteristics of the Logistic mapping. First, the numerical sequence of the Logistic chaotic system is transformed into a symbol sequence, and the proper sequence length of the symbol sequence is selected. The encoding length is derived from a series of derivation that the Logistic chaotic system has time irreversibility. The relative entropy can quantify the distance from the equilibrium state of the chaotic Logistic system, and the relative entropy value is independent of the initial value x0 of the chaotic system. It only depends on the parameters of the system, and then proves that the chaotic system is not a chaotic system. The characteristic parameters are all dependent on the initial value.
In this paper, the time irreversibility of a switching converter based on the theory of relative entropy is studied. A new dynamic behavior index is proposed to quantify the off balance state of the switch converter in a chaotic state. As the switch converter is in the discontinuous state of the inductor current, it can be a discrete power system equivalent to a first order. Taking the typical DCM Boost converter as an example, based on the topological conjugation theory, the numerical sequence is transformed into a symbol sequence in coarse grained form. By using the sliding window method, the frequency of the converted symbol word is calculated, and then the relative entropy value of the DCM Boost switch converter is obtained by calculating the ratio of the probability of the forward and backward sequence. The relative entropy can quantify the distance of the chaotic state of the switching converter to leave the equilibrium state, so that the change trend of the chaotic system of the switch converter can be reasonably predicted. It provides a new idea and method to reveal the nonlinear characteristics of the switch converter. The applicability of the switch converter analysis.
In the study of the chaotic characteristics of switching converters based on information entropy theory, this paper presents a direct calculation of the distribution characteristics of the numerical sequence of switching converters based on the distribution characteristics of the switching transformation numerical sequences and the information entropy theory. In this paper, the corresponding parameter changes are discussed based on the first order discontinuous conduction mode Buck and Boost converter. The results show that, on the premise of entropy increasing principle, information entropy can distinguish between periodic state and chaotic behavior. With the increase of the feedback parameter K, the information entropy approaches the maximum value of the theory. When the initial value x0 changes, the information entropy of the corresponding numerical sequence does not change, which proves that the information entropy of the chaotic system does not have the initial value dependence. Because the digital sequence of the switching converter satisfies certain distribution characteristics, the chaotic system of the switch converter from the macroscopic numerical distribution makes a reasonable expectation, which provides a theoretical basis for further understanding the characteristics of the chaotic and chaotic control switch converters.
At the end of this paper, a series Buck switch converter based on voltage and current double loop control is designed. The experimental results show that the control circuit uses voltage and current double loop control, so the circuit response is fast, the maximum current of the switch tube is limited, the working characteristic is greatly improved, and the frequency is more stable when the input voltage is changed from 20 to 90V. When the load is loaded, the working state is less affected and has the function of short circuit and overcurrent protection. This power supply is low cost and stable. It can be used in various alarm products and flicker lamps for industrial use with wide voltage.

【學位授予單位】：吉林大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：TM46;O415.5

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