单周期控制Boost变换器Hopf分岔控制及电路实现

用平均模型分析了单周期控制Boost变换器的运行,分析表明在参考电压变化的情况下,单周期控制Boost变换器会出现Hopf分岔.Hopf分岔使得变换效率下降,器件应力增加.为了消除Hopf分岔,提出了采用washout滤波器的方法.建立了采用washout滤波器的单周期控制Boost变换器平均模型,对于washout滤波器中的两个新参数,可以用Routh-Hurwitz准则来确定.仿真和电路实验验证了所提方法的效果. 关键词： washout滤波器 单周期控制 Boost变换器 Hopf分岔     

不同开关频率下电压控制升压变换器中的Hopf分岔分析

由于电压控制升压变换器的传统平均模型中没有包含开关频率,从而无法分析开关频率的大小对电压控制升压变换器中Hopf分岔的影响. 通过建立电压控制升压变换器的含有开关频率的改进平均模型,分析了开关频率对电压控制升压变换器中Hopf分岔的影响,并设计硬件电路,给出电路试验结果. 研究表明:采用电压控制升压变换器的改进平均模型,可以有效地分析不同开关频率对电压控制升压变换器中Hopf分岔的影响; 随着开关频率的减小,电压控制升压变换器更易于发生Hopf分岔. 关键词： 改进平均模型 电压控制升压变换器 开关频率     

单周期控制三电平Boost功率因数校正变换器的慢尺度分岔分析

对单周期控制三电平Boost功率因数校正(PFC)变换器中存在的慢尺度分岔现象进行了研究, 基于Floquet乘子法分析了主要电路参数对系统稳定性的影响. 首先, 分析了该电路的工作原理, 并由输入输出功率平衡推导出电路的简化模型. 然后, 采用谐波平衡法求解出电路的周期解, 根据Floquet理论分析周期解的稳定性. 通过计算Floquet乘子, 分析了电路中电压反馈电阻R_vf 对系统慢尺度分岔行为的影响. 搭建电路仿真模型, 验证了简化模型及Floquet理论分析的正确性. 最后, 计算了电路中其他参数组成的稳定边界. 研究结果表明, 正确选择三电平Boost PFC变换器的电路参数对于其稳定运行, 提高输入侧功率因数具有重要意义.     

电流源负载峰值电流控制buck变换器的复杂次谐波振荡现象

电流源负载峰值电流控制buck变换器具有次谐波振荡快慢复杂现象.本文建立了它的分段光滑开关模型及离散迭代映射模型.根据离散迭代映射模型,通过数值仿真研究了电路参数对buck变换器的非线性动力学行为的影响,发现了具有快慢效应次谐波振荡吸引域的分岔图和呈现双环带状的庞加莱映射.根据分段光滑开关模型,采用龙格-库塔算法,仿真研究了buck变换器的时域波形和相轨图,研究结果表明:电感电流存在由次谐波振荡与降频次谐波振荡组成的n型次谐波振荡现象;输出电压存在快标与慢标结合的正弦次谐波振荡现象.实验结果验证了文中的分 关键词： 开关DC-DC变换器 迭代映射 电流源负载 次谐波振荡     

H桥正弦逆变器的快变和慢变稳定性及混沌行为研究

正弦逆变器是一个时变非线性系统,存在快变和慢变两种尺度的稳定性.以比例控制一阶H桥正弦逆变器为例,引入了快变和慢变两种尺度,建立了H桥正弦逆变器的快变和慢变离散模型.针对快变稳定性,提出了折叠图和功率谱分析方法;针对慢变稳定性,提出周期时变非线性离散系统慢变平衡点定义和慢变稳定性定理,指出了慢变不稳定是周期时变系统混沌行为的有效判据.研究表明,所提出的方法能够很好地分析正弦逆变器出现的快变和慢变不稳定现象及混沌行为. 关键词： 周期时变离散系统 H桥正弦逆变器 快变不稳定 慢变不稳定     

Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode

In this paper, the dynamic behavior analysis of the electromechanical coupling characteristics of a flywheel energy storage system （FESS） with a permanent magnet （PM） brushless direct-current （DC） motor （BLDCM） is studied. The Hopf bifurcation theory and nonlinear methods are used to investigate the generation process and mechanism of the coupled dynamic behavior for the average current controlled FESS in the charging mode. First, the universal nonlinear dynamic model of the FESS based on the BLDCM is derived. Then, for a 0.01 kWh/1.6 kW FESS platform in the Key Laboratory of the Smart Grid at Tianjin University, the phase trajectory of the FESS from a stable state towards chaos is presented using numerical and stroboscopic methods, and all dynamic behaviors of the system in this process are captured. The characteristics of the low-frequency oscillation and the mechanism of the Hopf bifurcation are investigated based on the Routh stability criterion and nonlinear dynamic theory. It is shown that the Hopf bifurcation is directly due to the loss of control over the inductor current, which is caused by the system control parameters exceeding certain ranges. This coupling nonlinear process of the FESS affects the stability of the motor running and the efficiency of energy transfer. In this paper, we investigate into the effects of control parameter change on the stability and the stability regions of these parameters based on the averaged-model approach. Furthermore, the effect of the quantization error in the digital control system is considered to modify the stability regions of the control parameters. Finally, these theoretical results are verified through platform experiments.     

平均电流控制型Boost功率因数校正变换器中的中频振荡现象分析

基于输入电压可用其有效值代替以及电感电流与输出电压的波动频率远低于变换器开关频率的假设,建立了用于描述平均电流控制型Boost PFC变换器动力学行为的小信号模型,研究了该变换器中的中频振荡现象问题,揭示了系统发生中频振荡现象的内在物理机理,并给出了系统发生中频振荡现象的参数边界.研究结果表明,该非线性现象不同于已发现的快尺度不稳定性现象和慢尺度不稳定性现象,其主要特征是其振荡频率介于交流输入电压线频率和开关频率之间.最后,电路实验结果证实了理论分析的正确性. 关键词： 中频振荡 平均电流控制 Boost功率因数校正变换器 小信号模型     

Stability and bifurcation in a voltage controlled negative-output KY Boost converter

The stability and bifurcation in a voltage controlled negative-output KY Boost converter is studied in this Letter. A glimpse at the stability and bifurcation from the power electronics simulator (PSIM) software are given. And then, its mathematical model and corresponding discrete model are derived. The stability and bifurcation of the converter are determined with the help of the loci of eigenvalues of the Jacobian matrix. It is found that the Hopf bifurcation is easy to come in this converter when the value of its energy-transferring capacitor increases. Finally, the analytical results are confirmed by the circuit experiment.     

电压控制正极性输出罗变换器的改进平均模型建模及稳定性分析

基于平均建模法并考虑到正极性输出罗(positive output super-lift Luo, POSL Luo)变换器中能量传输电容电压存在突变的事实, 建立了POSL Luo变换器的改进平均模型, 推导并分析了POSL Luo变换器输出电压对占空比的传递函数. 建立了电压控制POSL Luo变换器的输出电压对基准电压的传递函数, 分析了系统的稳定性. 采用PSIM软件进行电路仿真以及设计硬件电路进行电路实验, 以PSIM仿真结果和电路实验结果验证了模型的有效性和理论分析的正确性. 研究结果表明: 相比于POSL Luo变换器已有的平均模型, 采用本文的改进平均模型可有效的分析POSL Luo变换器的特性及电压控制POSL Luo变换器的稳定性.     

Chaotic breathers in delayed electro-optical systems

We show that in integro-differential delayed dynamical systems, a hybrid state of simultaneous fast-scale chaos and slow-scale periodicity can emerge subsequently to a sequence of Hopf bifurcations. The resulting time trace thereby consists in chaotic oscillations "breathing" periodically at a significantly lower frequency. Experimental evidence of this type of dynamics in delayed dynamical systems is achieved with a Mach-Zehnder modulator optically fed by a semiconductor laser and is subjected to a delayed nonlinear electro-optical feedback. We also propose a theoretical understanding of the phenomenon.     

Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation

The coexistence of a resting condition and period-1 firing near a subcritical Hopf bifurcation point, lying between the monostable resting condition and period-1 firing, is often observed in neurons of the central nervous systems. Near such a bifurcation point in the Morris-Lecar （ML） model, the attraction domain of the resting condition decreases while that of the coexisting period-1 firing increases as the bifurcation parameter value increases. With the increase of the coupling strength, and parameter and initial value dependent synchronization transition processes from non-synchronization to compete synchronization are simulated in two coupled ML neurons with coexisting behaviors： one neuron chosen as the resting condition and the other the coexisting period-1 firing. The complete synchronization is either a resting condition or period-1 firing dependent on the initial values of period-1 firing when the bifurcation parameter value is small or middle and is period- 1 firing when the parameter value is large. As the bifurcation parameter value increases, the probability of the initial values of a period- 1 firing neuron that lead to complete synchronization of period- 1 firing increases, while that leading to complete synchronization of the resting condition decreases. It shows that the attraction domain of a coexisting behavior is larger, the probability of initial values leading to complete synchronization of this behavior is higher. The bifurcations of the coupled system are investigated and discussed. The results reveal the complex dynamics of synchronization behaviors of the coupled system composed of neurons with the coexisting resting condition and period-1 firing, and are helpful to further identify the dynamics of the spatiotemporal behaviors of the central nervous system.     

Control of Codimension-2 Bautin Bifurcation in Chaotic Lu System

In this paper, we design a feedback controller, and analytically determine a control criterion so as to control the codimension-2 Bautin bifurcation in the chaotic Lfi system. According to the control criterion, we determine a potential Bautin bifurcation region （denoted by P） of the controlled system. This region contains the Bautin bifurcation region （denoted by Q） of the uncontrolled system as its proper subregion. The controlled system can exhibit Bautin bifurcation in P or its proper subregion provided the control gains are properly chosen. Particularly, we can control the appearance of Bautin bifurcation at any appointed point in the region P. Due to the relationship between Bantin bifurcation and Hopf bifurcation, the control scheme thereby is also viable for controlling the creation and stability of the Hopf bifurcation. In the controller, there are two terms： a linear term and a nonlinear cubic term. We show that the former determines the location of the Hopf bifurcation while the latter regulates its criticality. We also carry out numerical studies, and the simulation results confirm our analyticai predictions.     

Branch Processes of Vortex Filaments and Hopf Invariant Constraint on Scroll Wave

In this paper, by making use of Duan＇s topological current theory, the evolution of the vortex filaments in excitable media is discussed in detail. The vortex filaments are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of a complex function Z（x, t）. [t is also shown that the Hopf invariant of knotted scroll wave filaments is preserved in the branch processes （splitting, merging, or encountering） during the evolution of these knotted scroll wave filaments. Furthermore, it also revealed that the ＂exclusion principle＂ in some chemical media is just the special case of the Hopf invariant constraint, and during the branch processes the ＂exclusion principle＂ is also protected by topology.     

Hopf bifurcation analysis and circuit implementation for a novelfour-wing hyper-chaotic system

In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare′ maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.     

Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation

The nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film(GMF)-shaped memory alloy(SMA) composite plate subjected to in-plane stochastic excitation are studied. GMF is prepared based on an SMA plate, and combined into a GMF–SMA composite plate. The Van der Pol item is improved to explain the hysteretic phenomena of GMF and SMA, and the nonlinear dynamics model of a GMF–SMA composite cantilever plate subjected to in-plane stochastic excitation is developed. The stochastic stability of the system is analyzed, and the steady-state probability density function of the dynamic response of the system is obtained. The condition of stochastic Hopf bifurcation is discussed, the reliability function of the system is provided, and then the probability density of the first-passage time is given. Finally, the stochastic optimal control strategy is proposed by the stochastic dynamic programming method.Numerical simulation shows that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the system’s reliability is improved through stochastic optimal control, and the firstpassage time is delayed. A GMF–SMA composite plate combines the advantages of GMF and SMA, and can reduce vibration through passive control and active control effectively. The results are helpful for the engineering applications of GMF–SMA composite plates.     

Noise-induced synchronous stochastic oscillations small scale cultured heart-cell networks

This paper reports that the synchronous integer multiple oscillations of heart-cell networks or clusters are observed in the biology experiment. The behaviour of the integer multiple rhythm is a transition between super- and sub- threshold oscillations, the stochastic mechanism of the transition is identified. The similar synchronized oscillations are theoretically reproduced in the stochastic network composed of heterogeneous cells whose behaviours are chosen as excitable or oscillatory states near a Hopf bifurcation point. The parameter regions of coupling strength and noise density that the complex oscillatory rhythms can be simulated are identified. The results show that the rhythm results from a simple stochastic alternating process between super- and sub-threshold oscillations. Studies on single heart cells forming these clusters reveal excitable or oscillatory state nearby a Hopf bifurcation point underpinning the stochastic alternation. In discussion, the results are related to some abnormal heartbeat rhythms such as the sinus arrest.     

A New Route to the Interpretation of Hopf Invariant

We discuss an object from algebraic topology, Hopf invariant, and reinterpret it in terms of the Ф-mapping topological current theory. The main purpose of this paper is to present a new theoretical framework, which can directly give the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclidean space R^2n-1. For the sake of this purpose we introduce a topological tensor current, which can naturally deduce the （n- 1）-dimensional topological defect in R^2n-1 space. If these （n- 1）-dimensional topological defects are closed oriented submanifolds of R^2n-1, they are just the （n - 1）-dimensional knots. The linking number of these knots is well defined. Using the inner structure of the topological tensor current, the relationship between Hopf invariant and the linking numbers of the higher-dimensional knots can be constructed.     

Hopf Bifurcation Control of a Hyperchaotic Circuit System

This paper is concerned with the Hopf bifurcation control of a new hyperchaotic circuit system. The stability of the hyperchaotie circuit system depends on a selected control parameter is studied, and the critical value of the system parameter at which Hopf bifurcation occurs is investigated. Theoretical analysis give the stability of the Hopf bifurcation. In particular, washout filter aided feedback controllers are designed for delaying the bifurcation point and ensuring the stability of the bifurcated limit cycles. An important feature of the control laws is that they do not result in any change in the set of equilibria. Computer simulation results are presented to confirm the analytical predictions.     

互联网时滞对偶拥塞控制模型动力学特征的分析与计算

以互联网拥塞控制的一种时滞对偶改进模型为研究对象,应用标准形理论、中心流形定理和霍普夫分岔理论,从动力学角度研究互联网拥塞控制的分岔与稳定性分析方法.研究表明,模型的分岔与稳定性主要由通信时延决定,当通信时延超过临界值时模型产生分岔现象,使互联网的链路代价函数发生振荡.并得到该模型的分岔方向及分岔周期解等动力学特征的定量计算公式,为时滞对偶模型的设计提供理论依据.研究结论概括为两个定理,其正确性得到计算机仿真验证.     

电感电流连续模式下Boost变换器的分数阶建模与仿真分析

基于分数阶微积分理论以及实际电容和实际电感在本质上是分数阶的事实,建立电感电流连续模式下Boost变换器的分数阶数学模型以及分数阶状态平均模型并进行理论分析,给出Boost变换器运行于电感电流连续模式下的参数条件.最后,基于Matlab/Simulink软件建立运行于电感电流连续模式下Boost变换器的分数阶仿真模型,并进行数值仿真分析以验证分数阶建模与理论分析的正确性. 关键词： Boost变换器 电感电流连续模式 分数阶微积分 数值仿真