| 电力电子电路中的分岔、混沌及其应用研究 |
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| 引用本文： | 于东升.电力电子电路中的分岔、混沌及其应用研究[J].煤炭学报,2012,37(5):889-890. |
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| 作者姓名： | 于东升 |
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| 作者单位： | 中国矿业大学矿业工程学院,江苏徐州,221116 |
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| 摘 要： | 以Twin-T电路和基于忆阻器的混沌电路(Memristor based Chaotic Circuit-MCC)为辅助,主要分析了数字控制电力电子电路中的分岔和混沌现象,并将混沌应用到电力电子电路中,以达到性能优化的目的。通过在Twin-T电路中两个电容直接相连的连接点上接入发光二极管元件,设计了一个新Twin-T混沌电路。以控制信号强度为分岔参数绘制分岔图,结果显示系统随控制信号强度增加经周期递加分岔步入混沌振荡。利用忆阻器元件取代蔡氏电路非线性二极管,结合分岔图、功率谱、最大Lya-punov指数等数值分析工具研究了系统分岔路径和双涡卷奇异吸引子结构。考虑到Twin-T电路优良的选频特性,设计了一种基于Twin-T电路的陷波混沌控制器。此控制器包含了一个陷波滤波器和一个电压电流转换接口电路。理论分析和实验结果均表明此控制器可以快速有效地将系统混沌控制到周期轨道上。超混沌系统具有至少两个大于零的Lyapunov指数,系统动态规律也更为复杂。通过修改MCC,设计了一个新的四阶超混沌电路。采用奇异值分解方法计算系统的Lyapunv指数谱,结果显示系统在某些参数区间内具有两个Lyapunov指数的值大于零。目前对变换器电路中的分岔和混沌现象研究多集中在模拟控制方式下,对于数字控制方式产生的时间延迟和量化误差很少考虑。以一台数字控制同步Buck变换器(Synchronous Buck Converter-SBC)为研究对象,利用z域小信号模型分析了比例-积分补偿策略下系统的分岔行为。在此基础上,利用描述函数等效出量化误差在控制环路引入的动态增益,并估算出系统的极限环区间。开关磁阻调速系统(Switched Reluctance Drive-SRD)可以看作是包含运动部件的电力电子电路。由于其特殊的定转子双凸极结构,系统存在铁磁饱和、频繁换相等非线性特征。在假设相电感与相电流无关的基础上,对比了模拟和数字两种控制方式下SRD的分岔行为。考虑到线性模型精度不高的因素,设计了一个新的基于指数函数的磁链非线性模型,利用分岔图和功率谱分析工具研究了数字控制SRD非线性模型中的分岔和混沌行为。以MCC为测试对象,验证了相空间重构技术恢复系统原吸引子的有效性。采用互信息量和虚假邻点方法获取最佳重构时延和嵌入维数,同时结合G-P算法和小数据量方法计算了系统的分形维和最大Lyapunov指数。在此基础上,基于MATLAB的Simulink仿真环境构建了采用模糊控制策略的SRD系统,并计算其重构相空间的分形维和最大Lyapunov指数。计算结果表明模糊控制SRD系统存在较大范围的混沌区间。混沌信号的一些特殊性质可以采取措施加以利用。以MCC电压信号作信号源,实现了SBC的混沌扩频。基于模糊控制SRD存在较大范围混沌区间这一研究结论,提出一种基于反馈转差变换率序列的SRD系统混沌扩频策略,仿真和实验结果均证实此扩频策略可以有效降低系统在开关频率及次谐波点的功率谱尖峰幅值。同时,分析数字控制SRD变换器不同单相故障下滤波电容电压频率谱,结合细节电压信号的混沌特征不变量,实现了变换器单相故障的识别。
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| 关 键 词： | 忆阻器混沌电路 同步Buck变换器 开关磁阻 混沌 分岔 混沌扩频 故障诊断 |
Research on bifurcation,chaos and its applications in power electronic circuits |
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| YU Dong-sheng.Research on bifurcation,chaos and its applications in power electronic circuits[J].Journal of China Coal Society,2012,37(5):889-890. |
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| Authors: | YU Dong-sheng |
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| Affiliation: | YU Dong-sheng(School of Mines,China University of Mining and Technology,Xuzhou 221116,China) |
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| Abstract: | With the assistant study of Twin-T circuit and memristor based chaotic circuit(MCC),bifurcation and chaos in several typical digitally controlled power electronic circuits were discussed.Additionally,chaos was then applied to power electronic circuits for the sake of improving the system performance. Twin-T circuit is widely used in oscillators and notch filter design due to its outstanding frequency-selecting ability.A new chaotic Twin-T circuit was designed by connecting a light-emitting diode to the junction of two capacitors in the original circuit topology.The bifurcation diagrams were drawn,which shows clearly that the output voltage evolved to chaos through period-adding bifurcation as the control signal strength coefficient increases. Memristor is regarded as the forth basic element except for resistor,capacitor and inductor.By replacing the nonlinear element in Chua’s circuit with memristor,MCC system was obtained.Bifurcation behavior and double-scroll strange attractor were studied by means of numerical methods such as bifurcation diagram,the largest Lyapunov exponent,power spectrum,etc.A chaos controller which includes a Twin-T notch filter and a voltage-current interface circuit was designed to adjust MCC from chaos to period in this dissertation.By modifying MCC system with an inductor and a negative conductance,a new four order hyperchaotic circuit was achieved. It has been validated that bifurcation and chaos are common phenomena in power electronic converters.However,the bifurcation phenomena in digitally controlled converter involving with time delay and quantization error is rarely concerned.The bifurcation phenomenon of a digitally proportional-integral(PI) controlled synchronous buck converter(SBC) was investigated by making use of z-domain small signal model.In addition,the limit cycle was estimated by taking into account the dynamic gain caused by quantization effect on the basis of describing function. Switched reluctance drive(SRD) can also be regarded as a converter circuit including a particular moving component.Based on the assumption that phase inductance is independent of phase current,the comparison of bifurcation behaviors between analogly and digitally controlled SRD were presented.Additionally,a new nonlinear model on the basis of exponential function was designed and brought to analyze the bifurcate and chaotic behaviors in SRD system by the aid of bifurcation diagram and power spectrum.In many cases,the topology as well as mathematic describing equations of a circuit is of impossibility to characterize by reason of the complex.A time series sampled from MCC was used to testify the validation of phase space reconstruction technique.Additionally,a fuzzy controlled SRD simulation model was built based on MATLAB SIMULINK environment.The calculation results of fractal dimension and the largest Lyapunov exponent demonstrate that in a wide parameter region,digitally controlled SRD behaves in chaotic oscillation. MCC was introduced as signal source to carry out the chaotic frequency spreading strategy for digitally controlled SBC.In accordance with the conclusion that fuzzy controlled SRD system can operate in a wide region chaotically,a chaotic frequency spreading strategy was designed by taking feedback acceleration as chaotic signal.In addition,the frequency spectrum of filter capacitor in SRD operated under the condition that different single phase faults come forth in the converter was analyzed.Single fault diagnosis of converter in SRD system is implemented on the strength of chaotic invariant extracted from detailed filter capacitor voltage. |
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| Keywords: | memristor based chaotic circuit synchronous Buck converter switched reluctance chaos bifurcation chaotic frequency spread fault diagnosis |
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