开关变换器双缘调制数字电压型控制技术

发布时间：2018-02-27 17:17

本文关键词： 双缘调制数字控制离散迭代映射模型动力学行为 z域模型　出处：《西南交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：开关变换器的脉冲宽度调制(Pulse Width Modulation,PWM)可以分为单缘调制方式和双缘调制方式。现有文献中多数采用的PWM方式为单缘调制,较少使用双缘调制;双缘调制方式不仅具有单缘调制的优点,而且避开了单缘调制的缺点。因此,研究不同的PWM方式对开关变换器性能的影响具有重要意义。以Buck变换器为例,将双缘调制与数字电压型控制结合,本论文研究了双缘调制数字电压型控制开关变换器的稳定性,建立其相应的离散映射模型,使用数值仿真,研究了系统的非线性动力学行为。通过分岔图,观察到双缘调制数字电压型控制Buck变换器中存在两种相似而不相同的Hopf分岔现象,并通过时域波形和庞加莱截面对这两种现象进行了详细分析。推导了系统的雅克比矩阵,观察其特征值穿过单位圆的位置和方向均不同,从理论上分析了两种Hopf分岔的差异性。此外,还发现了双缘调制数字电压型控制Buck变换器存在从周期一跳变到周期三的奇数倍周期分岔现象;通过时域波形和相轨图的仿真和实验,验证了奇数倍周期分岔现象的存在性。将PWM技术进行归一化分析,研究了基于归一化PWM技术的数字电压型控制开关变换器的稳定性。建立系统的离散映射模型,通过数值仿真和时域仿真,观察到Hopf分岔和倍周期分岔现象,分析了调制方式对系统稳定性的影响。建立了系统的闭环z域传递函数,并通过求解特征方程,得到系统的特征值,从理论上证明了 Hopf分岔和倍周期分岔的存在性。推导了稳定性边界的数学解析式,根据数学解析式,绘制出变换器的状态域分布图。根据解析式和状态域分布图,从理论上分析了调制方式对变换器工作稳定性的影响,并且得到了关于调制波参数以及PI参数的稳定调节范围。推导的理论解析式和绘制的状态域分布图,对于指导电路参数的选择和设计具有重要指导意义。最后,将双缘调制方式与双环电压型控制结合,研究了开关变换器的双缘调制数字均值电压控制技术,分析其工作原理,推导了相应的占空比算法。建立了系统的闭环z域传递函数,通过求解传递函数的特征值,判断特征值与单位圆的位置关系,进而分析输出电容等效串联电阻对于系统稳定性的影响。通过电路仿真,对比数字均值电压、数字峰值电压、数字均值电流和数字电压型等四种控制方法,数字均值电压控制具有更好的负载瞬态特性,以及良好的输出电压稳态精度。在占空比D0.5时,数字均值电压控制不存在次谐波振荡现象,具有更好的稳定性。
[Abstract]:Pulse Width Modulation (PWM) of switching converter can be divided into single edge modulation and double edge modulation. Dual edge modulation not only has the advantages of single edge modulation, but also avoids the disadvantages of single edge modulation. Therefore, it is important to study the effect of different PWM modes on switching converter performance. Taking Buck converter as an example, Combining double edge modulation with digital voltage mode control, this paper studies the stability of double edge modulation digital voltage mode control switching converter, establishes its corresponding discrete mapping model, and uses numerical simulation. The nonlinear dynamic behavior of the system is studied. By means of bifurcation diagram, it is observed that there are two similar and different Hopf bifurcation phenomena in digital voltage-mode controlled Buck converters with double margin modulation. The two phenomena are analyzed in detail by time domain waveform and Poincare cross section. The Jacobian matrix of the system is derived, and the position and direction of the eigenvalues passing through the unit circle are observed to be different. The difference between the two Hopf bifurcations is analyzed theoretically. In addition, it is found that the double edge modulation digital voltage-mode controlled Buck converters have odd period doubling bifurcation from period one jump to period 3. The existence of odd periodic bifurcation is verified by the simulation and experiment of time domain waveform and phase rail diagram. The PWM technique is used to normalize the analysis. The stability of digital voltage-source controlled switching converter based on normalized PWM technology is studied. The discrete mapping model of the system is established. Through numerical simulation and time domain simulation, the phenomena of Hopf bifurcation and period doubling bifurcation are observed. The effect of modulation mode on the stability of the system is analyzed. The closed-loop Z domain transfer function of the system is established, and the eigenvalue of the system is obtained by solving the characteristic equation. The existence of Hopf bifurcation and period doubling bifurcation is proved theoretically, and the mathematical analytical formula of stability boundary is derived. According to the mathematical analytic formula, the state domain distribution diagram of the converter is drawn. The influence of modulation mode on the stability of the converter is analyzed theoretically, and the stable range of modulation wave parameters and Pi parameters are obtained. It is of great significance to guide the selection and design of circuit parameters. Finally, combining dual-edge modulation with double-loop voltage mode control, the digital mean voltage control technology of switching converter is studied, and its working principle is analyzed. The corresponding duty cycle algorithm is derived, and the closed loop z domain transfer function of the system is established. By solving the eigenvalue of the transfer function, the position relationship between the eigenvalue and the unit circle is determined. Then the effect of output capacitance equivalent series resistance on system stability is analyzed. Through circuit simulation, four control methods, digital mean voltage, digital peak voltage, digital mean current and digital voltage source, are compared. The digital mean voltage control has better load transient characteristics and better output voltage steady-state accuracy. When the duty cycle is D0.5, the digital mean voltage control has no sub-harmonic oscillation phenomenon and has better stability.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TM46

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