典型离散系统的混沌动力学研究

发布时间：2018-04-22 08:46

本文选题：混沌系统 + 符号动力学　；参考：《吉林大学》2014年博士论文

【摘要】：混沌系统是混沌理论研究和混沌应用的重要组成部分，充分了解混沌系统的混沌行为和混沌形成机理，能够实现混沌的控制和反控制。传统的非线性行为分析方法是从线性或确定性的角度分析和研究，往往不能满足控制性能日益提高的要求，本论文在前人工作的基础上，对混沌系统的非线性特性进行了深入研究。以典型的离散动力系统Logistic映射和开关变换器为例，将拓扑共轭理论、符号动力学、相对熵和信息熵等理论有机结合起来，并将这些理论应用到这两种典型离散动力系统的研究中，得到了一些新的混沌动力学行为指标，从而证明了本文所提出的方法的正确性和有效性，进一步丰富了混沌理论，为混沌理论的工程应用打下基础，并在文章的最后设计了基于电压和电流双环控制的串联型开关变换器。本文将相对熵理论应用于具有混沌特征的典型Logistic映射的混沌状态分析中，提出了基于符号动力学和时间不可逆性量化Logistic映射混沌特性的新指标。首先将Logistic混沌系统的数值序列转化为符号序列，选择合适的符号序列长度和编码长度，通过一系列推导得出Logistic混沌系统存在时间不可逆性，相对熵可以量化处于混沌状态的Logistic系统离开平衡状态的距离，并且相对熵的数值与混沌系统的初始值x0无关，只取决于系统的参数μ，进而证明了并非混沌系统的所有特征参数都具有初值依赖性。本文对基于相对熵理论的开关变换器的时间不可逆性进行研究，提出了一种量化开关变换器处于混沌状态时的离开平衡状态的新的动力学行为指标。由于开关变换器处于电感电流不连续状态时可以等效为一阶的离散动力系统，文中以典型的DCM Boost变换器为例，基于拓扑共轭理论将数值序列以粗粒化的形式转化为符号序列，运用滑动窗口的方法，计算得出转化后的符号字频率，进而通过计算前向和后向序列的概率比值，得出了DCM Boost开关变换器的相对熵数值。由于相对熵值可以量化开关变换器的混沌状态离开平衡状态的距离，从而可以对开关变换器混沌系统的变化趋势做出合理的预判，为揭示开关变换器的非线性特性提供新的思路和方法。也进一步证明了相对熵理论对于处于混沌状态的开关变换器分析的适用性。在基于信息熵理论分析开关变换器的混沌特性的研究中，本文针对开关变换数值序列的分布特点，结合信息熵理论提出了直接计算开关变换器数值序列分布特征。文中基于一阶不连续导电模式Buck和Boost变换器，讨论参数变化时对应的信息熵。研究结果表明，熵增加原理的前提下，信息熵能够区分周期态和混沌行为，随着反馈参数k的增加，信息熵趋近理论极大值，当初始值x0变化时，对应的数值序列信息熵的没有改变，证明了混沌系统的信息熵不具有初始值依赖关系。由于开关转换器的数字序列满足一定的分布特征,从宏观数值分布的开关变换器混沌系统做出合理的预期,为进一步理解混沌和混沌控制开关变换器的特点提供了理论依据。本文的最后设计了基于电压和电流双环控制的串联型Buck开关变换器。实验结果表明控制电路采用电压、电流双环控制，因此电路响应快，限制了开关管的最大电流，，极大地改善了工作特性，在输入电压在20～90V范围改变时频率较稳定，接入容性负载时工作状态影响较少，且具有短路和过流保护功能。这种电源成本低、工作稳定，可使用在宽电压工作的工业用各种报警器产品和爆闪式信号灯中。
[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.

【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM46;O415.5

【参考文献】