Symmetrical dynamics of peak current-mode and valley current-mode controlled switching dc-dc converters with ramp compensation

The discrete iterative map models of peak current-mode (PCM) and valley current-mode (VCM) controlled buck converters, boost converters, and buck--boost converters with ramp compensation are established and their dynamical behaviours are investigated by using the operation region, parameter space map, bifurcation diagram, and Lyapunov exponent spectrum. The research results indicate that ramp compensation extends the stable operation range of the PCM controlled switching dc--dc converter to D>0.5 and that of the VCM controlled switching dc--dc converter to D<0.5. Compared with PCM controlled switching dc--dc converters with ramp compensation, VCM controlled switching dc--dc converters with ramp compensation exhibit interesting symmetrical dynamics. Experimental results are given to verify the analysis results in this paper.     

开关变换器斜坡补偿动力学机理研究

在反馈控制电路中引入适当的斜坡补偿电流,既可以有效拓宽电流控制开关DC-DC变换器稳定工作范围,实现混沌镇定控制,又可以使其工作模式从断续导电模式转移至连续导电模式,实现工作模式转移.以电流控制Buck-Boost变换器为例,通过建立含斜坡补偿的具有两个电感电流边界的二维离散时间模型和相应的Jacobi矩阵,深入研究了开关DC-DC变换器斜坡补偿的动力学机理.通过分析稳定性失稳和边界碰撞分岔的条件,讨论了斜坡补偿对开关DC-DC变换器稳定周期振荡和工作模式转移的影响,分别给出了相应的稳定性分界线和模式转移分界线.制作了实验电路,由实验结果说明了斜坡补偿对开关DC-DC变换器混沌镇定控制和工作模式转移的物理意义,并验证了理论分析的正确性.     

V2控制Buck变换器等效建模与分岔分析

通过对V²控制Buck变换器电路进行降阶处理, 利用不同工作模式, 推导了两个边界电压, 建立了V²控制Buck变换器的等效一阶同步映射迭代模型, 研究了它的非线性分岔行为. 通过稳定性和工作模式分析, 推导了V²控制Buck变换器从稳定的周期1工作状态到次谐波振 荡状态转移以及从电感电流不连续导电模式 (DCM) 到连续导电模式 (CCM) 转移的条件. 研究结果表明, 当电路参数变化时, V²控制Buck 变换器发生了倍周期分岔和边界碰撞分岔, 不同的参数变化有着不同的分岔路由. 搭建了仿真和实验电路, 仿真和实验结果验证了等效迭代模型的有效性和理论分析的正确性. 关键词： 2控制')" href="#">V²控制 迭代模型 分岔 工作模式     

基于双缘调制的数字电压型控制Buck变换器离散迭代映射建模与动力学分析

建立了双缘调制数字电压型控制Buck变换器的离散迭代映射模型. 在该模型的基础上, 详细研究了双缘调制数字电压型控制Buck变换器的非线性动力学行为. 以输入电压、负载电阻等电路参数作为分岔参数, 绘制了输出电压和电感电流的分岔图, 并通过分岔图的分析发现了两种相似却又不同的Hopf分岔现象. 采用庞加莱截面、时域仿真波形和相轨图, 对比分析了两种不同的Hopf分岔和低频振荡现象, 并引入离散迭代映射模型的雅克比矩阵的特征值分析方法, 从理论上证明了两种Hopf分岔的存在性和差异性. 首次观察到基于双缘调制的数字电压型控制Buck变换器出现了奇数倍周期分岔现象, 并通过时域仿真波形和相轨图验证了该现象的真实性. 为更加接近实际电路, 考虑电容和电感的等效串联电阻, 使用Psim进行仿真, 其结果与理论仿真结果基本一致, 验证了理论仿真的正确性.     

V2控制Buck变换器分岔与混沌行为的机理及镇定

V²控制的Buck变换器在反馈放大系数变化的情况下表现出丰富的非线性行为. 本文建立了V²控制Buck变换器的离散迭代模型, 利用单值矩阵方法研究了系统不稳定行为. 随着反馈放大系数的增大, 变换器从稳定的周期一状态发生一系列的倍周期分岔现象进入周期二、周期四, 不断倍化直至混沌态. 同时其单值矩阵的最大特征值也沿着实负轴穿越单位圆, 从而从稳定性的角度揭示了系统发生一系列倍周期分岔的机理. 基于单值矩阵理论, 利用正弦电压补偿方法镇定了系统的分岔和混沌行为, 得到了镇定后系统的稳定边界. 仿真和实验结果证明了本文分析方法和结论的正确性. 关键词： V²控制')" href="#">V²控制 Buck变换器 分岔 镇定控制     

Dynamical analysis and experimental verification of valley current controlled buck converter

The dynamical behaviours of valley current controlled buck converter are studied by establishing its corresponding discrete iterative map model in this paper. Time-domain waveforms and phase portraits of valley current controlled buck converter are obtained by Runge--Kutta algorithm through a piecewise smooth switching model. The research results indicate that the valley current controlled buck converter exhibits rich nonlinear phenomena, and it has routes to chaos through period-doubling bifurcation and border-collision bifurcation in a wide parameter range. Interesting inverse nonlinear behaviours compared with peak current controlled buck converter are observed in the valley current controlled buck converter. Analysis and simulation results are verified by experimental results.     

基于自适应斜坡补偿的双环电流模DC/DC混沌控制

提出了一种自适应斜坡补偿方法,将该方法引入到双环电流模buckDC/DC的混沌控制中,并给出实现该方法的电路结构.建立了双环电流模DC/DC系统稳定性分析的离散模型,理论分析了自适应斜坡补偿在双环控制下系统的稳定性条件,推导出了自适应因子k与系统工作的最大占空比的关系式.仿真结果表明该方法可有效控制系统的分岔和混沌现象,提高系统的工作范围和动态响应速度.     

基于自适应斜坡补偿的双环电流模DC/DC混沌控制

提出了一种自适应斜坡补偿方法,将该方法引入到双环电流模buck DC/DC的混沌控制中,并给出实现该方法的电路结构.建立了双环电流模DC/DC系统稳定性分析的离散模型,理论分析了自适应斜坡补偿在双环控制下系统的稳定性条件,推导出了自适应因子k与系统工作的最大占空比的关系式.仿真结果表明该方法可有效控制系统的分岔和混沌现象,提高系统的工作范围和动态响应速度.     

谷值V~2控制Boost变换器的精确建模与动力学分析

建立了谷值V2控制Boost变换器的离散迭代映射模型,在此基础上得到了输入电压、输出电容及其等效串联电阻(equivalent series resistance,ESR)变化时的分岔图,推导了不动点处的雅可比矩阵,利用特征值和最大Lyapunov指数对系统进行了稳定性分析,并验证了分岔图的正确性.重点研究了输入电压和输出电容及其ESR对谷值V2控制Boost变换器的动力学特性的影响.研究结果表明,输入电压增大时,变换器从周期1态经历1次倍周期分岔和边界碰撞分岔进入混沌状态;输出电容及其ESR具有相同的分岔路由,随着输出电容及其ESR的逐渐减小,变换器具有从周期1态经历周期2态、周期4态、周期8态、逐渐演变到混沌态的动力学行为.最后,用仿真和实验结果验证了本文理论分析的正确性.     

多频率控制开关变换器的自相似和混频现象分析

在多频率控制开关变换器的工作原理及状态方程的基础上,建立了多频率控制断续导电模式开关变换器的离散迭代映射模型,并推导了相应的特征值方程和Lyapunov指数.根据离散迭代映射模型,对多频率控制开关变换器进行了分岔分析.结果表明:在电路参数变化时,变换器存在边界碰撞分岔行为和多周期行为;当误差界限电压较大时,变换器表现出自相似现象,而当误差界限电压较小时,变换器则表现出混频现象.采用Lyapunov指数研究了变换器的稳定性,验证了分岔分析的正确性.经过电路仿真,进一步分析了负载变化时变换器的时域波形和相轨图,并验证了离散迭代映射模型的有效性和理论分析的正确性.最后通过实验结果验证了文中的仿真结果.     

峰值/谷值电流型控制开关DC-DC变换器的对称动力学现象分析

峰值电流和谷值电流控制开关DC-DC变换器在较宽的电路参数范围内具有对称动力学现象.文中建立了峰值电流和谷值电流控制buck,boost,及buck-boost变换器的统一离散迭代映射模型,并导出了统一的分段光滑迭代映射方程及特征值方程,通过数值仿真得到了占空比变化时的正、逆分岔图和Lyapunov指数谱.研究结果表明,峰值/谷值电流型控制开关变换器的分岔图和Lyapunov指数具有关于点或轴对称的现象.时域仿真结果验证了数值仿真结果,并进一步表明,随着占空比的变化,峰值/谷值电流型控制开关变换器具有对称动力学现象、对称动力学现象和非对称动力学现象共存、非对称动力学现象.     

峰值/谷值电流型控制开关DC-DC变换器的对称动力学现象分析

峰值电流和谷值电流控制开关DC-DC变换器在较宽的电路参数范围内具有对称动力学现象.文中建立了峰值电流和谷值电流控制buck,boost,及buck-boost变换器的统一离散迭代映射模型,并导出了统一的分段光滑迭代映射方程及特征值方程,通过数值仿真得到了占空比变化时的正、逆分岔图和Lyapunov指数谱.研究结果表明,峰值/谷值电流型控制开关变换器的分岔图和Lyapunov指数具有关于点或轴对称的现象.时域仿真结果验证了数值仿真结果,并进一步表明,随着占空比的变化,峰值/谷值电流型控制开关变换器具有对称动力学现象、对称动力学现象和非对称动力学现象共存、非对称动力学现象.     

脉冲序列控制电流断续模式Buck变换器的动力学建模与边界碰撞分岔

通过建立一个开关周期内输出电容电荷变化量对应的输出电压变化量, 建立了工作于电感电流断续模式(discontinuous conduction mode, DCM)的脉冲序列(pulse train, PT)控制Buck变换器的近似离散时间模型, 研究了负载电阻及输入电压变化时PT控制DCM Buck变换器的边界碰撞分岔行为. 通过构造相应的迭代映射曲线, 分别分析了不同负载电阻时PT控制DCM Buck变换器的周期1、周期2和周期3运行轨迹的不动点稳定性, 揭示了PT控制DCM Buck变换器在不同周期态时的边界碰撞分岔的形成机理. 研究结果表明, 随参数变化, PT控制DCM Buck变换器始终运行在不同的周期态, 各周期态的切换由边界碰撞分岔引起, 李雅谱诺夫指数始终小于零. 利用PSIM电路仿真软件, 给出了不同负载电阻时的时域波形和相轨图. 实验结果验证了理论分析和仿真结果的正确性, 同时说明了本文动力学建模的可行性.     

Period-doubling bifurcation in two-stage power factor correction converters using the method of incremental harmonic balance and Floquet theory

In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance (IHB) and Floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC-DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated post-regulator DC-DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis.     

斜坡补偿电流模式控制开关变换器的动力学建模与分析

降压型、升压型和升压-降压型DC-DC变换器是应用广泛的基本开关DC-DC变换器.电流模式控制开关DC-DC变换器在较宽的电路参数范围内具有两个边界,基于开关切换前后电感电流的上升和下降斜率,建立了斜坡补偿电流模式控制开关DC-DC变换器的统一模型.该模型进行无量纲归一化处理后只有三个参数,可有效展示开关DC-DC变换器在电感电流连续传导模式(CCM)和电感电流不连续传导模式(DCM)时的动力学特性.利用此模型,导出了轨道状态发生转移时的两个分界线方程,由此确定了开关DC-DC变换器的稳定周期1域、CCM鲁棒混沌域和DCM弱混沌强阵发域三个工作状态区域.开关DC-DC变换器二维参数映射图和电流模式控制降压型DC-DC变换器的电路实验观察验证了由两条分界线划分工作状态域的正确性.     

Non-Smooth Bifurcation and Chaos in a DC-DC Buck Converter

A direct-current-direct-current （DC-DC） buck converter with integrated load current feedback is studied with three kinds of Poincaré maps. The external corner-collision bifurcation occurs when the crossing number per period varies, and the internal corner-collision bifurcations occur along with period-doubling and period-tripling bifurcations in this model. The multi-band chaos roots in external corner-collision bifurcation and often grows into 1-band chaos. A new kind of chaotic sliding orbits, which is more complex for non-smooth systems, is also found in this model.     

具有两个边界的Boost变换器分岔行为和斜坡补偿的镇定控制

电流控制型Boost变换器在较宽的电路参数下具有两个边界,建立了采用斜坡补偿电流的分段光滑迭代映射方程,并导出了轨道状态发生转移时的分界线方程,通过数值仿真得到了输入电压和斜坡补偿斜率变化时的逆分岔图和它们的动力学行为分布图.研究结果表明,随着输入电压逐步减小,Boost变换器从稳定的周期1态,经在边界1上发生边界碰撞分岔后进入连续传导模式（CCM）下的鲁棒混沌态,并经在边界2上发生边界碰撞分岔后进入不连续传导模式（DCM）下的强阵发性的弱混沌态.通过引入合适的斜坡补偿电流,Boost变换器的工作模式可以 关键词： Boost变换器 斜坡补偿 迭代映射方程 镇定控制     

峰值电流控制型功率因数校正Boost变换器的分岔行为

分析了电流控制型功率因数校正Boost变换器的分岔行为，包括了高频不稳定现象和低频分岔。电流连续导通模式下进行的功率因数校正变换器分析阻碍了对这种变换器全部动力学特性的认识。功率因数校正变换器可能会工作于电流断续导通模式，特别是在轻载的情况下这种现象更明显。因此，本文使用电流断续导通模型来分析可能工作在电流断续导通状态下功率因数校正变换器，得到了变换器的低频分岔图，使得变换器经历倍周期分岔通向混沌途径更加清楚。对于负载电阻和输出电容的分岔图也说明了变换器的稳定工作边界，这些对变换器的设计是十分有用的。     

Sampled-data modeling and dynamical effect of output-capacitor time-constant for valley voltage-mode controlled ewline buck-boost converter

By analyzing the output voltage ripple of a buck-boost converter with large equivalent series resistance (ESR) of output capacitor, one valley voltage-mode controller for buck-boost converter is proposed. Considering the fact that the increasing and decreasing slopes of the inductor current are assumed to be constant during each switching cycle, an especial sampled-data model of valley voltage-mode controlled buck-boost converter is established. Based on this model, the dynamical effect of an output-capacitor time-constant on the valley voltage-mode controlled buck-boost converter is revealed and analyzed via the bifurcation diagrams, the movements of eigenvalues, the Lyapunov exponent spectra, the boundary equations, and the operating-state regions. It is found that with gradual reduction of output-capacitor time-constant, the buck-boost converter in continuous conduction mode (CCM) shows the evolutive dynamic behavior from period-1 to period-2, period-4, period-8, chaos, and invalid state. The stability boundary and the invalidated boundary are derived theoretically by stability analysis, where the stable state of valley voltage-mode controlled buck-boost converter can enter into an unstable state, and the converter can shift from the operation region to a forbidden region. These results verified by time-domain waveforms and phase portraits of both simulation and experiment indicate that the sampled-data model is correct and the time constant of the output capacitor is a critical factor for valley voltage-mode controlled buck-boost converter, which has a significant effect on the dynamics as well as control stability.     

Mode shift and stability control of a current mode controlled buck-boost converter operating in discontinuous conduction mode with ramp compensation

By establishing the discrete iterative mapping model of a current mode controlled buck-boost converter, this paper studies the mechanism of mode shift and stability control of the buck-boost converter operating in discontinuous conduction mode with a ramp compensation current. With the bifurcation diagram, Lyapunov exponent spectrum, time-domain waveform and parameter space map, the performance of the buck-boost converter circuit utilizing a compensating ramp current has been analysed. The obtained results indicate that the system trajectory is weakly chaotic and strongly intermittent under discontinuous conduction mode. By using ramp compensation, the buck-boost converter can shift from discontinuous conduction mode to continuous conduction mode, and effectively operates in the stable period-one region.