DC-DC变换器高阶系统动力学量化分析及其控制
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摘要
DC-DC变换器是构建各种类型电力电子变换器的基本电路单元，其运行稳定性和可靠性对分析电力电子变换器工作性能具有重要借鉴意义。DC-DC变换器倍周期分岔、边界碰撞分岔、共存吸引子和混沌等非线性动力学现象已被实验分析所证实。然而，目前研究主要集中在Buck、Boost和Flyback变换器等低阶系统中，而对于状态变量高于4阶的高阶系统，如uk、SEPIC和DC-DC全桥变换器等的研究甚少，尤其是分岔和混沌现象的量化分析及控制研究，尚属于开始阶段。为此，量化分析与控制DC-DC开关变换器高阶系统的非线性动力学行为，将进一步深化对电力电子变换器稳定性及非线性特性的认识。
本文完成的研究工作有如下几点：
(1)对电流单环控制电感性负载高阶uk变换器分析了其在余二维分岔点处系统复杂的不稳定性及不同分岔现象的共存特性；对具有恒流源负载的uk变换器的快慢标分岔共存现象进行理论分析，揭示其非线性动力学特性。
(2)提出开关时间映射与模态符号序列的方法，揭示了uk变换器高阶系统复杂动力学行为，并利用联合熵概念对其复杂非线性状态进行量化分析；根据SPEIC变换器拓扑结构特点，基于Lemper-Ziv复杂度理论提出其Weight复杂度和稳定指数概念，量化了其高阶系统稳定性和非线性动力学特性。
(3)建立松散耦合变压器结构、电压外环控制的DC-DC全桥谐振变换器非线性模型，分析了其谐振工作时的Hopf分岔等非线性行为，这对于构建稳定、可靠的基于DC-DC全桥谐振变换器的谐振无线电能传输系统具有理论和工程意义。
(4)提出了LLC谐振全桥DC-DC变换器非线性镇定控制方法，该方法可以通过对变换器状态变量进行采样反馈，有效地镇定其不良非线性动力学行为，由此进一步探讨了混沌多卷波扩频技术降低了变换器EMI的控制技术。
综上所述，本论文以uk、SPEIC、松散耦合变压器DC-DC全桥谐振变换器、LLC谐振全桥DC-DC变换器4种高阶DC-DC变换器为研究对象，采用非线性动力学方法，系统量化分析了它们的复杂非线性动力学行为，提出了新的非线性行为镇定方法和EMI抑制技术，促进了高阶DC-DC变换器系统动力学特性的研究。
DC-DC converter is the basic circuit unit of many other types of power electronicconverters, the stability and the reliability of its operational status has important referentialsignificance to analyze the working performance of the power electronic converters. Thenonlinear dynamics phenomena of DC-DC converter, such as period-doubling bifurcations,border collision bifurcation, coexisting attractors and chaos, have been verified byexperimental analysisis. However, the current researches have focused on low order systems,such as Buck, Boost, and Flyback converters. And there is little studies for high order systems,including uk, SEPIC and full-bridge DC-DC converters, which have more than four statevariables. Especially, quantitative analysis and control of bifurcation and chaos phenomenafor DC-DC coverters of high order systems are in the beginning state. Therefore, quantitativeanalysis and control of nonlinear dynamical behavior in high order systems of DC-DCswitching converters will help ones to further broaden the understanding of power electronicstechnology and its applications.
The study in this dissertation can be summarized as follows:
(1) The complex instabilities and coexistion of different bifurcation phenomena nearcodimension-2bifurcation point are analyzed in a single inner current loop controlled ukconverter with an inductive impedance load. the coexistion phenomena of fast-and slow-scalebifurcation behavior is analyzed theoretically in a uk converter with a constant currentsource load, and its characteristics of nonlinear dynamics is revealed.
(2) The switching time map and modal symbolic sequence method is utilized to reveal thecomplex dynamic behavior in high order system of DC-DC converter, and the quantitativeanalysis of its complex nonlinear states is actualized in terms of joint entropy. According tothe characteristics of changing topologies of SPEIC converter, moreover, the stability indexconcept is put forward to quantify the stabilities and nonlinear dynamic character of its highorder systems based on Lemper-Ziv complexity.
(3) The nonlinear model of DC-DC full-bridge resonace converter is estabilished withloosely coupled transformer and voltage mode control, and the onlinear behavior of thesystem, e.g. Hopf bifurcation, is analyzed when it work in resonace state. There has theoryand engineering significance to design the more stable and reliable resonance wireless powertransmission system based on DC-DC full-bridge resonance converter.
(4) The nonlinear stabilizing method of LLC resonance full-bridge DC-DC converter isput forward. The state variables of the converter is sampled and fed back in this method,which effectively stabilizes the bad behavior of nonlinear dynamics. Moreover, the EMI ofthis converter is reduced by the spread spectrum technology with chaotic n-croll wave.
In summary, four high order DC-DC converters, including uk converter, SPEICconverter, DC-DC full-bridge resonance converter with loosed coupled transformer and LLCresonance full-bridge DC-DC converter, is took as the studing object in this dissertation. Thenonlinear dynamic method is utilized to quantify and analyze their complex nonlineardynamics behavior. Additionally, the novel stabilizing method of nonlinear behavior and thetechnology of suppressing EMI are put forward. This dissertation promotes the study ofdynamic characteristic in high order DC-DC converter.
本文完成的研究工作有如下几点：
(1)对电流单环控制电感性负载高阶uk变换器分析了其在余二维分岔点处系统复杂的不稳定性及不同分岔现象的共存特性；对具有恒流源负载的uk变换器的快慢标分岔共存现象进行理论分析，揭示其非线性动力学特性。
(2)提出开关时间映射与模态符号序列的方法，揭示了uk变换器高阶系统复杂动力学行为，并利用联合熵概念对其复杂非线性状态进行量化分析；根据SPEIC变换器拓扑结构特点，基于Lemper-Ziv复杂度理论提出其Weight复杂度和稳定指数概念，量化了其高阶系统稳定性和非线性动力学特性。
(3)建立松散耦合变压器结构、电压外环控制的DC-DC全桥谐振变换器非线性模型，分析了其谐振工作时的Hopf分岔等非线性行为，这对于构建稳定、可靠的基于DC-DC全桥谐振变换器的谐振无线电能传输系统具有理论和工程意义。
(4)提出了LLC谐振全桥DC-DC变换器非线性镇定控制方法，该方法可以通过对变换器状态变量进行采样反馈，有效地镇定其不良非线性动力学行为，由此进一步探讨了混沌多卷波扩频技术降低了变换器EMI的控制技术。
综上所述，本论文以uk、SPEIC、松散耦合变压器DC-DC全桥谐振变换器、LLC谐振全桥DC-DC变换器4种高阶DC-DC变换器为研究对象，采用非线性动力学方法，系统量化分析了它们的复杂非线性动力学行为，提出了新的非线性行为镇定方法和EMI抑制技术，促进了高阶DC-DC变换器系统动力学特性的研究。
DC-DC converter is the basic circuit unit of many other types of power electronicconverters, the stability and the reliability of its operational status has important referentialsignificance to analyze the working performance of the power electronic converters. Thenonlinear dynamics phenomena of DC-DC converter, such as period-doubling bifurcations,border collision bifurcation, coexisting attractors and chaos, have been verified byexperimental analysisis. However, the current researches have focused on low order systems,such as Buck, Boost, and Flyback converters. And there is little studies for high order systems,including uk, SEPIC and full-bridge DC-DC converters, which have more than four statevariables. Especially, quantitative analysis and control of bifurcation and chaos phenomenafor DC-DC coverters of high order systems are in the beginning state. Therefore, quantitativeanalysis and control of nonlinear dynamical behavior in high order systems of DC-DCswitching converters will help ones to further broaden the understanding of power electronicstechnology and its applications.
The study in this dissertation can be summarized as follows:
(1) The complex instabilities and coexistion of different bifurcation phenomena nearcodimension-2bifurcation point are analyzed in a single inner current loop controlled ukconverter with an inductive impedance load. the coexistion phenomena of fast-and slow-scalebifurcation behavior is analyzed theoretically in a uk converter with a constant currentsource load, and its characteristics of nonlinear dynamics is revealed.
(2) The switching time map and modal symbolic sequence method is utilized to reveal thecomplex dynamic behavior in high order system of DC-DC converter, and the quantitativeanalysis of its complex nonlinear states is actualized in terms of joint entropy. According tothe characteristics of changing topologies of SPEIC converter, moreover, the stability indexconcept is put forward to quantify the stabilities and nonlinear dynamic character of its highorder systems based on Lemper-Ziv complexity.
(3) The nonlinear model of DC-DC full-bridge resonace converter is estabilished withloosely coupled transformer and voltage mode control, and the onlinear behavior of thesystem, e.g. Hopf bifurcation, is analyzed when it work in resonace state. There has theoryand engineering significance to design the more stable and reliable resonance wireless powertransmission system based on DC-DC full-bridge resonance converter.
(4) The nonlinear stabilizing method of LLC resonance full-bridge DC-DC converter isput forward. The state variables of the converter is sampled and fed back in this method,which effectively stabilizes the bad behavior of nonlinear dynamics. Moreover, the EMI ofthis converter is reduced by the spread spectrum technology with chaotic n-croll wave.
In summary, four high order DC-DC converters, including uk converter, SPEICconverter, DC-DC full-bridge resonance converter with loosed coupled transformer and LLCresonance full-bridge DC-DC converter, is took as the studing object in this dissertation. Thenonlinear dynamic method is utilized to quantify and analyze their complex nonlineardynamics behavior. Additionally, the novel stabilizing method of nonlinear behavior and thetechnology of suppressing EMI are put forward. This dissertation promotes the study ofdynamic characteristic in high order DC-DC converter.
引文
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