高阶开关功率变换器中的非线性动力学行为及其控制研究
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摘要
非线性科学作为一门研究非线性现象共性的交叉学科、综合学科,不断地揭示着世界的非线性本质,不断地推动着人们用之改造世界的进程。各个学科领域都存在非线性问题,电力电子技术领域也不例外。开关功率变换器是电力电子电路与系统的重要组成部分,属于一类分段切换系统,具有强非线性和时变特性,能表现出丰富的非线性动力学行为。因此,运用非线性科学的理论与方法对开关功率变换器进行研究,有利于揭示其非线性本质；有利于指导电力电子技术领域的工程实践,优化变换器的稳定性、可靠性设计：有利于奠定电力电子学的理论基础,丰富非线性科学的内容与方法。
自上世纪八九十年代开关功率变换器中的非线性现象被首次报道以来,国内外研究者从仿真、理论、实验等多维度,对开关功率变换器中的非线性动力学行为及其控制与应用展开了较为广泛的研究,形成了电力电子学非线性研究的重要分支。但已有研究多集中于低阶开关功率变换器,而鲜有对高阶开关功率变换器的非线性研究。基于此,本文以高阶开关功率变换器为研究对象,基于非线性动力学的分岔与混沌理论,对其非线性建模、非线性动力学行为的描述与分析、非线性动力学行为的控制与应用等展开研究,旨在揭示高阶开关功率变换器的非线性本质,指导高阶开关功率变换器的设计与应用。具体工作包括：
(1)开关功率变换器非线性研究述评与非线性动力学基础。第1章分析了开关功率变换器非线性研究的意义,从变换器的非线性建模、动力学行为及其分析、动力学行为的控制与应用等三个方面,综述了相关研究概况。并基于此,提出了本文的研究价值与内容。第2章介绍了非线性动力学基础,主要包括分岔与混沌理论,总结了非线性动力学的研究方法,并给出了常用数值研究方法及其在开关功率变换器非线性研究中的应用与实现。
(2)高阶开关功率变换器的非线性建模。建模是进行变换器非线性研究的前提,广泛使用的建模方法有状态空间平均法和离散时间映射法。本文第3章针对高阶开关功率变换器的复杂性,提出了一种综合运用这两种方法的建模方法,并将之应用于电流模式控制Cuk变换器的建模与稳定性分析,建立了变换器闭式迭代映射模型,得到了变换器稳定性判据的解析表达式,分析了电路参数对变换器稳定性的影响。仿真结果验证了此建模方法的有效性。
(3)高阶开关功率变换器中的非线性动力学行为及其分析。混沌现象可以发生在二阶及其以上非自治开关功率变换器(一阶断续电流模式非自治变换器亦可)、三阶及其以上自治开关功率变换器中。因此,四阶开关功率变换器在一定的参数范围内定会发生分岔、混沌等非线性动力学行为。本文第4章对耦合有干扰信号的峰值电流模式SEPIC变换器中的间歇分谐波与间歇混沌现象进行了研究,通过数值仿真和电路仿真展示了间歇现象,并采用时间分岔到参数分岔的策略,基于离散时间映射模型、雅克比矩阵特征值分析法进行了相应的理论分析。仿真结果与理论分析一致表明干扰信号的强度和频率决定着间歇的类型与周期。此外,提出了基于变换器间歇现象的微弱周期信号检测方法。第5章对自治高阶开关功率变换器(滑模控制SEPIC变换器)的稳定性与复杂动力学行为进行了研究,基于滑模变结构理论,为SEPIC变换器进行了滑模控制设计,得到了变换器的等效平均模型,分析了平衡点的稳定性。通过对雅克比矩阵及其特征值的分析,判定变换器随着参考电流的增大发生了超临界Hopf分岔,并得到不同电路参数下变换器的稳定边界曲面。数值仿真结果验证了理论分析的正确性,并展示了滑模SEPIC变换器经由Hopf分岔、单极限环、双极限环、准周期而进入混沌状态的演化过程。
(4)高阶开关功率变换器中非线性动力学行为的控制研究。对开关功率变换器中非线性动力学行为进行控制研究,是变换器非线性研究应用于工程实践的必然要求。传统的控制方法和一些特定的混沌控制方法,一般都可以应用于变换器的分岔与混沌控制,但目前关于高阶变换器的混沌控制研究很少。因此,本文第6章对高阶变换器的分岔与混沌控制进行了探讨。以峰值电流模式SEPIC变换器为例,采用时间延迟反馈控制法,对非自治高阶变换器系统中的混沌进行了有效的控制,给出了延迟反馈增益的取值范围；以滑模控制SEPIC变换器为例,采用外加周期信号的非反馈控制方法,对自治高阶开关功率变换器系统中的混沌进行了有效控制。此外,采用变量线性反馈控制方法,对滑模控制SEPIC变换器中的Hopf分岔行为进行了控制,并基于滑模变结构原理进行了理论分析。
Nonlinear science, as a comprehensive and interdisciplinary subject for studying the generality of nonlinear phenomena, reveals the nonlinear nature of the world and promotes the process of changing the world constantly. Power electronics field has its own nonlinear problems as in the other disciplinary fields. Switching power converter is an important component in power electronics circuit and system, which belongs to a class of piecewise switching system with strong nonlinearity and time-varying characteristics. Therefore, studying on the power converters based on nonlinear theories and methods are beneficial to reveal the nonlinear nature of the power converters, to guide the engineering practice by optimizing the stability and reliability design of the converters, to establish the theoretical foundations of the power electronics, and to enrich the contents and methods of nonlinear science.
Since the nonlinear phenomenon in power converter was reported in 1980s, the domestic and foreign researchers have widely carried out the study on the nonlinear dynamical behaviours and their control of power converters from the multi-dimensional viewpoints of computer simulation, theoretical analysis, and circuit experiments, resulting in a nonlinear study branch in power electronics. But the existing nonlinear studies are almost for lower order converters, while few work for higher converters. Based on this situation, higher order converters are selected as the research objects, and their modelling, descriptions, analysis and control of nonlinear dynamical behaviours are carried out in this dissertation with the aim to reveal the nonlinear nature of higher order converters, and to guide the design and application of higher order converters. The concrete work is as follows:
(1) Review on nonlinear study in switching power converters and the basis of nonlinear dynamics. Chapter one analyzes the research significance of nonlinear study in power converters, gives an overview on the related research backgrounds from three aspects including nonlinear modelling, nonlinear dynamical behaviours, and control of nonlinear phenomena, and based on which, puts forward the research value and contents of this dissertation. Chapter two introduces the basis of nonlinear dynamics including bifurcation and chaos theory, summarizes the research methods in nonlinear dynamics, and presents some commonly used numerical methods and their applications to nonlinear study of power converters.
(2) Nonlinear modelling of higher switching power converters. Modelling is the essential prerequisite of nonlinear study on power converters, which has two widely used methods including state-space average approach and discrete-time mapping approach. Aiming at strong nonlinearity and complexity of higher order power converters, an integrative modelling method by integrating these two approaches is proposed and is applied to the modelling and stability analysis of a peak-current-mode controlled Cuk converter in chapter three. The closed-form iterative mapping model is constructed, and analytical expression of the stability criterion is achieved. Furthermore, the relationship between the stability and the circuit parameters is studied. The results of simulation verify the validity of the proposed modelling method and stability analysis.
(3) Nonlinear dynamical behaviours and their analysis in higher power converters. Chaotic phenomena can frequently appear in no less than two-order non-autonomous converters (one-order discontinuous current mode non-autonomous converter as well) or in no less than three-order autonomous converters. So four-order converters can present rich nonlinear dynamical behaviours such as bifurcation and chaos. Intermittent subharmonics and chaos in a peak-current-mode controlled SEPIC converter coupled with intruding interference is studied in chapter four. The intermittent phenomena are observed by means of numerical simulation and circuit simulation. Furthermore the relation between the circuit parameters and the threshold amplitude of interference is discussed. By mapping time-bifurcation into parameter-bifurcation, discrete-time mapping model and the analysis method of characteristic multiplier of Jacobian matrix are applied to theoretical analysis. The theoretical results are consistent with the simulation results and indicate that the intermittent type and period are decided by the strength and frequency of the intruding interference. Furthermore, a weak periodic signal detection method is proposed based on intermittency of switching converters. Stability analysis and complex dynamical behaviors of a sliding-mode controlled SEPIC converter, which is an autonomous higher order converter, are studied in chapter five. Based on sliding-mode variable structure theory, sliding-mode control of the SEPIC converter is achieved, the equivalent average model is obtained, and stability of the equilibrium point is analyzed. Analysis of the Jacobian matrix and its characteristic eigenvalues proves that the converter loses stability via a super critical Hopf bifurcation with the reference current increased, and that the circuit parameters can make important influence on the stability. Simulation results demonstrate the theoretical analysis, and show the route to chaos via Hopf bifurcation, single limit cycle, double limit cycle, and quasi-periodicity.
(4) Control of nonlinear dynamical behaviours in higher order switching power converters. Applications of nonlinear study results to engineering practice must require the researchers to study on the control of nonlinear phenomena. Generally speaking, traditional control techniques and some special chaos control techniques can be used to control of bifurcation and chaos in power converters. But up to present, control of nonlinear dynamical behaviours is seldom investigated, so some explorations on this topic are implemented in chapter six. Firstly, time-delayed feedback control method is effectively applied to control chaos in non-autonomous higher order converter, with a peak-current-mode controlled SEPIC converter as a case study, and the value range of the feedback gain is obtained by bifurcation diagram. Secondly, external periodic signal method is successfully used to control chaos in autonomous power converter, with a sliding-mode controlled SEPIC converter as an example. Lastly, variable linear feedback control method is used to realize the Hopf bifurcation control in a sliding-mode controlled SEPIC converter, and the theoretical analysis is carried out based on sliding-mode theory, which is in agreement with the simulation results.
自上世纪八九十年代开关功率变换器中的非线性现象被首次报道以来,国内外研究者从仿真、理论、实验等多维度,对开关功率变换器中的非线性动力学行为及其控制与应用展开了较为广泛的研究,形成了电力电子学非线性研究的重要分支。但已有研究多集中于低阶开关功率变换器,而鲜有对高阶开关功率变换器的非线性研究。基于此,本文以高阶开关功率变换器为研究对象,基于非线性动力学的分岔与混沌理论,对其非线性建模、非线性动力学行为的描述与分析、非线性动力学行为的控制与应用等展开研究,旨在揭示高阶开关功率变换器的非线性本质,指导高阶开关功率变换器的设计与应用。具体工作包括：
(1)开关功率变换器非线性研究述评与非线性动力学基础。第1章分析了开关功率变换器非线性研究的意义,从变换器的非线性建模、动力学行为及其分析、动力学行为的控制与应用等三个方面,综述了相关研究概况。并基于此,提出了本文的研究价值与内容。第2章介绍了非线性动力学基础,主要包括分岔与混沌理论,总结了非线性动力学的研究方法,并给出了常用数值研究方法及其在开关功率变换器非线性研究中的应用与实现。
(2)高阶开关功率变换器的非线性建模。建模是进行变换器非线性研究的前提,广泛使用的建模方法有状态空间平均法和离散时间映射法。本文第3章针对高阶开关功率变换器的复杂性,提出了一种综合运用这两种方法的建模方法,并将之应用于电流模式控制Cuk变换器的建模与稳定性分析,建立了变换器闭式迭代映射模型,得到了变换器稳定性判据的解析表达式,分析了电路参数对变换器稳定性的影响。仿真结果验证了此建模方法的有效性。
(3)高阶开关功率变换器中的非线性动力学行为及其分析。混沌现象可以发生在二阶及其以上非自治开关功率变换器(一阶断续电流模式非自治变换器亦可)、三阶及其以上自治开关功率变换器中。因此,四阶开关功率变换器在一定的参数范围内定会发生分岔、混沌等非线性动力学行为。本文第4章对耦合有干扰信号的峰值电流模式SEPIC变换器中的间歇分谐波与间歇混沌现象进行了研究,通过数值仿真和电路仿真展示了间歇现象,并采用时间分岔到参数分岔的策略,基于离散时间映射模型、雅克比矩阵特征值分析法进行了相应的理论分析。仿真结果与理论分析一致表明干扰信号的强度和频率决定着间歇的类型与周期。此外,提出了基于变换器间歇现象的微弱周期信号检测方法。第5章对自治高阶开关功率变换器(滑模控制SEPIC变换器)的稳定性与复杂动力学行为进行了研究,基于滑模变结构理论,为SEPIC变换器进行了滑模控制设计,得到了变换器的等效平均模型,分析了平衡点的稳定性。通过对雅克比矩阵及其特征值的分析,判定变换器随着参考电流的增大发生了超临界Hopf分岔,并得到不同电路参数下变换器的稳定边界曲面。数值仿真结果验证了理论分析的正确性,并展示了滑模SEPIC变换器经由Hopf分岔、单极限环、双极限环、准周期而进入混沌状态的演化过程。
(4)高阶开关功率变换器中非线性动力学行为的控制研究。对开关功率变换器中非线性动力学行为进行控制研究,是变换器非线性研究应用于工程实践的必然要求。传统的控制方法和一些特定的混沌控制方法,一般都可以应用于变换器的分岔与混沌控制,但目前关于高阶变换器的混沌控制研究很少。因此,本文第6章对高阶变换器的分岔与混沌控制进行了探讨。以峰值电流模式SEPIC变换器为例,采用时间延迟反馈控制法,对非自治高阶变换器系统中的混沌进行了有效的控制,给出了延迟反馈增益的取值范围；以滑模控制SEPIC变换器为例,采用外加周期信号的非反馈控制方法,对自治高阶开关功率变换器系统中的混沌进行了有效控制。此外,采用变量线性反馈控制方法,对滑模控制SEPIC变换器中的Hopf分岔行为进行了控制,并基于滑模变结构原理进行了理论分析。
Nonlinear science, as a comprehensive and interdisciplinary subject for studying the generality of nonlinear phenomena, reveals the nonlinear nature of the world and promotes the process of changing the world constantly. Power electronics field has its own nonlinear problems as in the other disciplinary fields. Switching power converter is an important component in power electronics circuit and system, which belongs to a class of piecewise switching system with strong nonlinearity and time-varying characteristics. Therefore, studying on the power converters based on nonlinear theories and methods are beneficial to reveal the nonlinear nature of the power converters, to guide the engineering practice by optimizing the stability and reliability design of the converters, to establish the theoretical foundations of the power electronics, and to enrich the contents and methods of nonlinear science.
Since the nonlinear phenomenon in power converter was reported in 1980s, the domestic and foreign researchers have widely carried out the study on the nonlinear dynamical behaviours and their control of power converters from the multi-dimensional viewpoints of computer simulation, theoretical analysis, and circuit experiments, resulting in a nonlinear study branch in power electronics. But the existing nonlinear studies are almost for lower order converters, while few work for higher converters. Based on this situation, higher order converters are selected as the research objects, and their modelling, descriptions, analysis and control of nonlinear dynamical behaviours are carried out in this dissertation with the aim to reveal the nonlinear nature of higher order converters, and to guide the design and application of higher order converters. The concrete work is as follows:
(1) Review on nonlinear study in switching power converters and the basis of nonlinear dynamics. Chapter one analyzes the research significance of nonlinear study in power converters, gives an overview on the related research backgrounds from three aspects including nonlinear modelling, nonlinear dynamical behaviours, and control of nonlinear phenomena, and based on which, puts forward the research value and contents of this dissertation. Chapter two introduces the basis of nonlinear dynamics including bifurcation and chaos theory, summarizes the research methods in nonlinear dynamics, and presents some commonly used numerical methods and their applications to nonlinear study of power converters.
(2) Nonlinear modelling of higher switching power converters. Modelling is the essential prerequisite of nonlinear study on power converters, which has two widely used methods including state-space average approach and discrete-time mapping approach. Aiming at strong nonlinearity and complexity of higher order power converters, an integrative modelling method by integrating these two approaches is proposed and is applied to the modelling and stability analysis of a peak-current-mode controlled Cuk converter in chapter three. The closed-form iterative mapping model is constructed, and analytical expression of the stability criterion is achieved. Furthermore, the relationship between the stability and the circuit parameters is studied. The results of simulation verify the validity of the proposed modelling method and stability analysis.
(3) Nonlinear dynamical behaviours and their analysis in higher power converters. Chaotic phenomena can frequently appear in no less than two-order non-autonomous converters (one-order discontinuous current mode non-autonomous converter as well) or in no less than three-order autonomous converters. So four-order converters can present rich nonlinear dynamical behaviours such as bifurcation and chaos. Intermittent subharmonics and chaos in a peak-current-mode controlled SEPIC converter coupled with intruding interference is studied in chapter four. The intermittent phenomena are observed by means of numerical simulation and circuit simulation. Furthermore the relation between the circuit parameters and the threshold amplitude of interference is discussed. By mapping time-bifurcation into parameter-bifurcation, discrete-time mapping model and the analysis method of characteristic multiplier of Jacobian matrix are applied to theoretical analysis. The theoretical results are consistent with the simulation results and indicate that the intermittent type and period are decided by the strength and frequency of the intruding interference. Furthermore, a weak periodic signal detection method is proposed based on intermittency of switching converters. Stability analysis and complex dynamical behaviors of a sliding-mode controlled SEPIC converter, which is an autonomous higher order converter, are studied in chapter five. Based on sliding-mode variable structure theory, sliding-mode control of the SEPIC converter is achieved, the equivalent average model is obtained, and stability of the equilibrium point is analyzed. Analysis of the Jacobian matrix and its characteristic eigenvalues proves that the converter loses stability via a super critical Hopf bifurcation with the reference current increased, and that the circuit parameters can make important influence on the stability. Simulation results demonstrate the theoretical analysis, and show the route to chaos via Hopf bifurcation, single limit cycle, double limit cycle, and quasi-periodicity.
(4) Control of nonlinear dynamical behaviours in higher order switching power converters. Applications of nonlinear study results to engineering practice must require the researchers to study on the control of nonlinear phenomena. Generally speaking, traditional control techniques and some special chaos control techniques can be used to control of bifurcation and chaos in power converters. But up to present, control of nonlinear dynamical behaviours is seldom investigated, so some explorations on this topic are implemented in chapter six. Firstly, time-delayed feedback control method is effectively applied to control chaos in non-autonomous higher order converter, with a peak-current-mode controlled SEPIC converter as a case study, and the value range of the feedback gain is obtained by bifurcation diagram. Secondly, external periodic signal method is successfully used to control chaos in autonomous power converter, with a sliding-mode controlled SEPIC converter as an example. Lastly, variable linear feedback control method is used to realize the Hopf bifurcation control in a sliding-mode controlled SEPIC converter, and the theoretical analysis is carried out based on sliding-mode theory, which is in agreement with the simulation results.
引文
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