【作者】 王发强；

【导师】 马西奎；

【作者基本信息】 西安交通大学 ， 电气工程， 2009， 博士

【摘要】 非线性电路中的复杂动力学行为是现代电路理论及其应用中的一个重要研究课题,它包含着丰富的研究内容和广阔的应用前景。本文以分段光滑电路为对象,着重在以下几个方面开展了研究工作:1.能产生多混沌吸引子分段光滑自治电路的研究。提出了两类能够产生多涡卷混沌吸引子和一类能产生多折叠环面多涡卷混沌吸引子的分段光滑自治电路。建立了这三类分段光滑自治电路的数学模型,分析了电路参数对电路中出现的混沌动力学行为的影响,并指出了电路通向混沌的道路,同时,给出了混沌吸引子的个数与开关闭合个数的关系。2.单周控制DC-DC电路中多尺度分岔的研究。采用电路仿真、理论分析和电路实验分别研究了单周控制Buck电路中的快尺度分岔和单周控制Boost电路中的慢尺度分岔。研究结果表明:单周控制Buck电路中的快尺度分岔主要是由于电路工作频率小于时钟频率而引起的;单周控制Boost电路中的慢尺度分岔实质上是电路在远低于开关频率区域内发生了Hopf分岔。3.平均电流控制Boost PFC电路中多尺度分岔的研究。通过建立平均电流控制Boost PFC电路的简化模型,采用小信号模型方法分析了电路中的中尺度分岔,采用谐波平衡法和Floquet理论分析了电路中的慢尺度分岔以及采用非线性模型分析了电路中的次慢尺度分岔。给出了电路发生分岔行为的物理机理,并通过电路仿真和电路实验证实了各种简化模型的有效性和理论分析的正确性。4.含输入滤波器的平均电流控制Boost PFC电路中多尺度分岔的研究。通过建立含输入滤波器的平均电流控制Boost PFC电路的数学模型,采用谐波平衡法和Floquet理论分析了电路中的慢尺度分岔以及采用非线性模型分析了电路中的次慢尺度分岔。研究结果表明:滤波器参数(Rf,Cf,Lf)取值合适的情况下,输入滤波器的加入可能会使平均电流控制Boost PFC电路的稳定区域扩大,从而纠正了以往人们认为输入滤波器的加入只会导致平均电流控制Boost PFC电路失去原来稳定性的结论。5.多级PFC电路中多尺度分岔的研究。基于一定的假设条件,建立了级联PFC电路的简化模型,采用小信号模型方法分析了级联PFC电路中的中尺度分岔以及采用增量谐波平衡法和Floquet理论分析了级联PFC电路中的慢尺度分岔。电路仿真和电路实验证实了理论分析的正确性。此外,基于合适的假设,还建立了并联PFC电路的简化模型,采用谐波平衡法和Floquet理论分析了并联PFC电路中的慢尺度分岔,并指出了电路参数对并联PFC电路稳定性的影响与对单级PFC电路稳定性的影响存在着明显的差别。6.分段光滑电路中混沌与多尺度分岔控制方法的研究。首先提出采用线性反馈控制方法实现了蔡氏电路的同步控制。其次,提出了基于无源控制理论,设计无源控制器,实现了变型蔡氏电路的同步控制。而后,提出了采用电流反馈控制方法实现了单周控制Boost电路中慢尺度分岔的控制,确定了使电路运行于稳定状态时控制参数的取值范围,并通过电路仿真和电路实验验证了该控制方法的有效性和理论分析的正确性。最后,提出采用负载电流反馈控制方法实现了平均电流控制Boost PFC电路中慢尺度分岔的控制,采用谐波平衡法和Floquet理论确定了使电路运行于稳定状态时控制参数的取值范围,并通过电路仿真和电路实验验证了该控制方法的有效性和理论分析的正确性。更多还原

【Abstract】 The complex behavior in nonlinear circuit has become an important research subject in the modern circuit, which include extremely abundant contents and wide application prospects. In this dissertation, as an important part of nonlinear circuit research, the complex behavior in the piece-wise smooth circuit is investigated and the details are presented as follows:1. The multiple chaotic attractor in autonomous piece-wise smooth circuit is studied. Two kinds of multi-scroll chaotic attractor and another kind of multi-folded torus chaotic attractor in the autonomous piece-wise smooth circuits are constructed and analyzed. The mathmatical models are established, the effects of parameters on the chaos of the circuit and the route to chaos of the circuit are analyzed. Moreover, the relationship between the number of chaotic attractor and the number of closed switches are given.2. The multi-scale bifurcation in the one-cycle controlled DC-DC circuit is studied. The fast-scale bifurcation in the one-cycle controlled Buck circuit and the slow-scale bifurcation in one-cycle controlled Boost circuit are invesigated respectively with the circuit simulation, theoretical analysis and circuit experiment. The results shows: the main reason for the occurrence of fast-scale bifurcation in the one-cycle controlled Buck circuit is that the operation frequency of the circuit is lower than the clock frequency. But, for the slow-scale bifurcation in the one-cycle controlled Boost circuit, in fact, it is that the Hopf bifurcation happens in the area where the frequency is much lower than the switching frequency.3. The multi-scale bifurcation in average current controlled Boost PFC circuit is studied. By establishing the simplified models, the medium-scale bifurcation is investigated based on the small-sigal model, and the slow-scale bifurcation is investigated based on the harmonic balance method and Floquet theory, and also, the subslow-scale bifurcation is investigated based on the nonlinear model. The under mechanism of the above three kinds of bifurcaton are given. Finally, the effectiveness of the simplified models and the validity of the theoretical analyses are confirmed by the circuit simulations and circuit experiments. 4. The multi-scale bifurcation in the averge current controlled Boost PFC with an input filter is studied. The mathematical models of the circuit are constructed, the slow-scale bifurcaiton in the circuit is analyzed by means of the harmonic balance method and Floquet theory and the subslow-scale bifurcation is analyzed by means of the nonlinear model. The results show that the stable area may be enlarged when the extra input filter is added into the average current controlled Boost PFC circuit. These results change the conclusions that the extra input filter will only degrade the stability of the average current controlled Boost PFC circuit.5. The multi-scale bifurcation in the multi-stage PFC circuit is studied. Based on certain suitable assumptions, the simplified model of the cascade PFC circuit are established. And then, the medium-scale bifurcation is analyzed by using the small-signal model, and the slow-scale bifurcation is analyzed by using the method of incremental harmonic balance and Floquet theory. The effectiveness of the simplified model and the validity of the theoretical analysis are both confirmed by the circuit simulation and circuit experiment. Furthermore, the slow-scale bifurcation in parallel PFC circuit is analyzed by using the method of harmonic balance and Floquet theory. It is found that there are very important differences between the single-stage PFC circuit and the parallel PFC circuit.6. Control of multi-scale bifurction and chaos in the piece-wise smooth circuit is studied. Firstly, the linear feedback control is proposed to realize the synchronization of the Chua’s circuit. Secondly, based on the passive control theory, the passive controller is designed to realize the synchronization of the modified Chua’s circuit. Thirdly, the current feedback control is applied to realize the control of the slow-scale bifurcation in the one-cycle controlled Boost circuit. The span of the control parameters for maintaining the circuit in stable operation are fixed. Moreover, the effectiveness of the control method and the validity of the theoretical analysis are confirmed by the circuit simulation and circuit experiment. Finally, the load current feedback control is applied to control the slow-scale bifurcation in average current controlled Boost PFC circuit. Based on the simplified model, the span of control parameters for maintaining the circuit in stable operation is analzed by using the method of harmonic and Floquet theory, and then the effectiveness of the control method and the validity of the theoretical analysis are confirmed by the circuit simulation and circuit experiment.更多还原