电气专业毕业论文外文翻译

本科毕业设计

外文文献及译文

文献、资料题目：Designing Stable Control Loops 文献、资料来源：期刊

文献、资料发表（出版）日期：2010.3.25

院（部）：信息与电气工程学院

专业：电子信息工程

班级：电信B124

姓名：尚营军

学号：201203014414

指导教师：黄成玉

翻译日期：2016.5.10

外文文献：

Designing Stable Control Loops

The objective of this topic is to provide the designer with a practical review of loop compensation techniques applied to switching power supply feedback control. A top-down system approach is taken starting with basic feedback control concepts and leading to step-by-step design procedures, initially applied to a simple buck regulator and then expanded to other topologies and control algorithms. Sample designs are demonstrated with Math cad simulations to illustrate gain and phase margins and their impact on performance analysis.

I. I NTRODUCTION

Insuring stability of a proposed power supply solution is often one of the more challenging aspects of the design process. Nothing is more disconcerting than to have your lovingly crafted breadboard break into wild oscillations just as its being demonstrated to the boss or customer, but insuring against this unfortunate event takes some analysis which many designers view as formidable. Paths taken by design engineers often emphasize either cut-and-try empirical testing in the laboratory or computer simulations looking for numerical solutions based on complex mathematical models. While both of these approach a basic understanding of feedback theory will usually allow the definition of an acceptable compensation network with a minimum of computational effort.

II. S TABILITY D EFINED

Fig. 1. Definition of stability

Fig. 1 gives a quick illustration of at least one definition of stability. In its simplest terms, a system is stable if, when subjected to a perturbation from some source, its response to that

perturbation eventually dies out. Note that in any practical system, instability cannot result in a completely unbounded response as the system will either reach a saturation level –or fail. Oscillation in a switching regulator can, at most, vary the duty cycle between zero and 100% and while that may not prevent failure, it wills ultimate limit the response of an unstable system. Another way of visualizing stability is shown in Fig. 2. While this graphically illustrates the concept of system stability, it also points out that we must make a further distinction between large-signal and small-signal stability. While small-signal stability is an important and necessary criterion, a system could satisfy thisrt quirement and yet still become unstable with a large-signal perturbation. It is important that designers remember that all the gain and phase calculations we might perform are only to insure small-signal stability. These calculations are based upon – and only applicable to –linear systems, and a switching regulator is – by definition –a non-linear system. We solve this conundrum by performing our analysis using small-signal perturbations around a large-signal operating point, a distinction which will be further clarified in our design procedure discussion。

Fig. 2. Large-signal vs. small-signal stability

III. F EEDBACK C ONTROL P RINCIPLES

Where an uncontrolled source of voltage (or current, or power) is applied to the input of our system with the expectation that the voltage (or current, or power) at the output will be very well controlled. The basis of our control is some form of reference, and any deviation between the output and the reference becomes an error. In a feedback-controlled system, negative feedback is used to reduce this error to an acceptable value –as close to zero as we want to spend the effort to achieve. Typically, however, we also want to reduce the error quickly, but inherent with feedback control is the tradeoff between system response and system stability. The more responsive the feedback network is, the greater becomes the risk of instability. At this point we should also

mention that there is another method of control –feedforward.With feed forward control, a control signal is developed directly in response to an input variation or perturbation. Feed forward is less accurate than feedback since output sensing is not involved, however, there is no delay waiting for an output error signal to be developed, andfeedforward control cannot cause instability. It should be clear that feed forward control will typically not be adequate as the only control method for a voltage regulator, but it is often used together with feedback to improve a regulator’s response to dynamic input variations.

The basis for feedback control is illustrated with the flow diagram of Fig. 3 where the goal is for the output to follow the reference predictably and for the effects of external perturbations, such as input voltage variations, to be reduced to tolerable levels at the output Without feedback, the reference-to-output transfer function y/u is equal to G, and we can express the output asy Gu With the addition of feedback (actually the subtraction of the feedback signal)

y Gu yHG

and the reference-to-output transfer function becomes

y/u=G/1+GH

If we assume that GH __ 1, then the overall transfer function simplifies to

y/u=1/H

Fig. 3. Flow graph of feedback control

Not only is this result now independent of G,it is also independent of all the parameters of the system which might impact G (supply voltage, temperature, component tolerances, etc.) and is determined instead solely by the feedback network H (and, of course, by the reference).Note that the accuracy of H (usually resistor tolerances) and in the summing circuit (error amplifier offset voltage) will still contribute to an output error. In practice, the feedback control system, as modeled in Fig. 4, is designed so thatG __ H and GH __ 1 over as wide a frequency range as possible without incurring instability. We can make a further refinement to our generalized power

regulator with the block diagram shown in Fig. 5. Here we have separated the power system into two blocks –the power section and the control circuitry. The power section handles the load current and is typically large, heavy, and subject to wide temperature fluctuations. Its switching functions are by definition, large-signal phenomenon, normally simulated in most stability analyses as just a two states witch with a duty cycle. The output filter is also considered as a part of the power section but can be considered as a linear block.

Fig. 4. The general power regulator

IV. T HE B UCK C ONVERTER

The simplest form of the above general power regulator is the buck –or step down –topology whose power stage is shown in Fig. 6. In this configuration, a DC input voltage is switched at some repetitive rate as it is applied to an output filter. The filter averages the duty cycle modulation of the input voltage to establish an output DC voltage lower than the input value.The transfer function for this stage is defined by

tON=switch on -time

T = repetitive period (1/fs)

d = duty cycle

Fig. 5. The buck converter.

Since we assume that the switch and the filter components are lossless, the ideal efficiency of

T his conversion process is 100%, and regulation of the output voltage level is achieved by controlling the duty cycle. The waveforms of Fig.6 assume a continuous conduction mode (CCM)

M eaning that current is always flowing through the inductor – from the switch when it is closed,

A nd from the diode when the switch is open. The analysis presented in this topic will emphasize CCM operation because it is in this mode that small-signal stability is generally more difficult

to achieve. In the discontinuous conduction mode (DCM), there is a third switch condition in which the inductor, switch, and diode currents are all 5-4 zero. Each switching period starts from the same state (with zero inductor current), thus effectively reducing the system order by one and making small-signal stable performance much easier to achieve. Although beyond the scope of this topic,there may be specialized instances where the large-signal stability of a DCM system is of greater concern than small-signal stability.

There are several forms of PWM control for the buck regulator including,

? Fixed frequency (fS) with variable tON and variable tOFF

? Fixed tON with variable tOFF and variable fS

? Fixed tOFF with variable tON and variable fS

? Hysteretic (or “bang-bang”) with tON, tOFF,and fS all variable

Each of these forms have their own set of advantages and limitations and all have been successfully used, but since all switch mode regulators generate a switching frequency component and its associated harmonics as well as the intended DC output, electromagnetic interference and noise considerations have made fixed frequency operation by far the most popular.

With the exception of hysteretic, all other forms of PWM control have essentially the same small-signal behavior. Thus, without much loss in generality, fixed fS will be the basis for our discussion of classical, small-signal stability.

Hysteretic control is fundamentally different in that the duty factor is not controlled, per se. Switch turn-off occurs when the output ripple voltage reaches an upper trip point and turn-on occurs at a lower threshold. By definition, this is

a large-signal controller to which small-signal stability considerations do not apply. In a small signal sense, it is already unstable and, in a mathematical sense, its fast response is due more to feed forward than feedback.

R EFERENCES

[1] D. M. Mitchell, “DC-DC Switching Regulator Analysis”, McGraw-Hill, 1988,

DMMitchell Consultants, Cedar Rapids, IA, 1992(reprint version).

[2] D. M. Mitchell, “Small-Signal Mathcad Design Aids”, (Windows 95 / 98 version), e/j BLOOM Associates, Inc., 1999.

[3] George Chryssis, “High-Frequency Switching Power Supplies”, McGraw-Hill Book Company, 1984.

[4] Ray Ridley, “A More Accurate Current- Mode Control Model”, Unitrode Seminar Handbook, SEM-1300, Appendix A2.

[5] Lloyd Dixon, “Control Loop Design”, Unitrode Seminar Handbook, SEM-800.

[6] Lloyd Dixon, “Control Loop Design –SEPIC Preregulator Design”, Unitrode Seminar Handbook, SEM-900, Topic 7.

[7] Lloyd Dixon, “Closin g the Feedback Loop”, Unitrode Seminar Handbook, SEM-300.

中文翻译：

控制电路设计

摘要：

本篇论文的写作目的，是为给设计师们提供一个实际性的说明，那就是线性补偿技术在电源转换与电流反馈操作中是如何应用的。一个组织管理严密的系统电路需要一开始就有一个基础的电流反馈操作理论的支持，并且通过一步步的设计步骤，从初步阶段应用到一个简单升压调节器，然后再扩展到其他的拓扑学与算数控制学中去。matchad模拟器也验证了设计样本中幅相裕度整定在分布设计中是存在的，并且还影响着实验的分析报告。一、简介：

验证所提议的电源供给解决方案的稳定性，一直就是电路设计过程中一个极具挑战性的方面。最让你感到窘迫的，并不是你最为得意之作的电路板正在实验的重要阶段中，被突然闯入的无序振荡所打乱，而是你实验恰恰验证了许多电路设计者感到最为头疼的数据分析。电路设计师常常强调，在实验室里要注重切换实验的实用价值，或者是以复杂的数学模式为电脑集成系统所需要的数据处理。然而这两者的方向都是以电路设计的前提为基础。于是，对反馈原理最基本的理解将帮助我们去定义接受性补偿网系统的最小值计算范围。

二、稳定性的界定：

图1 稳定的定义

图1直接展示了至少一个关于稳定性的界定。用最简洁的术语来说，如果一个电路系统是稳定的，就算被从某些来源说产生的微扰所压制时，返回的微扰的也将会一并抵消。需要注意的是，在任何实用电路中，不稳定性不会导致一个完全无束缚的反应，这就如同电路既会达到饱和状态——也会处于缺损状态一样。正在调节器转化过程中的振荡极有可能在零和百分之一百间的负荷周期中波动，并且这种变化不可能阻止失败，它将最终制约

不稳定电路的回流电。

图2 展示的是另外一个设想的稳定性。尽管该图形象地展示了电路稳定性的观点，但与此同时，也指出了我们必须将大信号的稳定性与小信号的稳定性严格区分开来。然而小信号的稳定性是一个非常重要和非常需要的判断标准，一个电路也可以满足这个要求，并且会与一个大信号的微扰一起变得不稳定。重要的是，电路设计师们需要记得，所有我们可能执行的幅相裕度整定计算仅仅只是确保了小信号的稳定性。这些计算结果主要依靠——并且只适用于——线性电路，和一个转换调节器——被定义为——非线性的电路。我们通过用围绕小信号直流工作点周围小信号的微扰，来演算我们的分析结果，去解决这个迷团。这之中的具体差别将会在接下来的设计过程的有关探讨来说明。

图2 强信号和弱信号

三、反馈电流控制原理：

展示的是一个最基本的调节器，在这里，不受控制的电压来源（或者电流，或者功率）将会被应用到电路的输入，且在输出过程中被这个不受控制的电压（电流或者功率）的预期值完全的掌控。电流控制的基础是一些基准电压的结构，任何在输出电流和基准电压之间的偏差都是会导致电路的错误。在一个反馈操作电路中，负反馈回流电是用来减少在可接受的标准内这种错误——就如我们希望能从一开始付出努力，一直坚持到最后能成功一样。然而，按照典型的案例来说，我们也希望让错误不会那么快的发生，但是回流电控制电路本身就存在着频率响应与电路稳定性的互换。回流电路的频率响应越多，不稳定的危险性就越大。

在这一点上我们应该注意，另外一个控制方法——前反馈。通过前反馈的控制，一个控制信号将被直接地发展到去回应一个输出波动或者微扰中。前反馈没有回流电那么精准，因为检测输出电流不是那么复杂难懂，然而，无法否认的是，等待一个输出电流的错误信号会被发现，而且前反馈控制无法产生不稳定性。需要清楚表明的是，典型的前反馈控制将不像只有一个电压调节器的控制线路那么有效，但是前反馈的控制经常被用于和反

馈一起去加快调节器对动态输入变动的响应频率。

图3中的电流图阐述了反馈控制的基础，目标就是为了输出功率能跟着可以预测的基准电压，为了将外部微扰的影响，如同输出功率的变动一样，能会被减少到输出功率所能接受的等级上。

图3 反馈控制流图

如果没有反馈电，基准电压到输出功率的转换函数y/u就跟G是一样的，我们可以这样表达输出功率：

y=Gu

另外反馈电流（实际上是反馈信号的减法）：

y Gu yHG

之后r基准电压与输出功率的转换函数：

Y=G

u=1 GH

如果我们假设GH=1，那么整体的转换函数就是：

y/u=1/h

这个函数不仅使得G现在成为独立，它还使所有的电路参数都变得独立，这这可能会影响G（供给功率、温度、元件公差，等等）并且被只被回流电路H（并且，理所当然的，被基准电压作用）所代替来决定它。值得一提的是，H的准确性（通常称为电阻的公差）和电路的总和（错误放大补偿功率）将继续造成输出电流的错误。在实际中，反馈控制电路，如图4的模型所示，如此设计是为了使G ：H和GH=1的振动频率能越大范围越好并且不会产生任何不稳定性。

我们可以进一步的改良概括功率调节器就像图4所见到的一样。在这里我们有单独分开的功率系统进去到两个板块——功率段和控制电路。功率段处理电流的负荷，并且功率段通

常是大、重、经历广阔的温度范围波动。它的转换功能被定义为，大信号现象，通常在最稳定的分析结果中进行模拟，就像在负荷周期中的两极转换一样。输出电流过滤器被当做为线性板块。控制电路通常有一个增长板块——错误发大器——和宽脉冲波调幅器所组成，用来定义电压转换。

图4 一般电源稳压

四、降压转换器：

上述一般动力的最简单形式降压稳压器- 或降压- 拓扑它的功率级，如图6所示在这配置，直流输入电压起动，有些重复率，因为它是适用于输出过滤器。该过滤器的占空比平均输入电压的调制建立输出直流电压比输入值低。变量的传递函数定义如下

其中

tON为开关时间

T 为重复周期（频率的倒数）

D为占空比

图5.降压转换器

由于我们假设开关和过滤器组件是无损的，理想的效率这个转换过程是100％，与规制输出电压的水平是通过控制占空比。在波形图。6假设连续传导模式（CCM）这意味着电流始终流经当它从封闭开关- 电感从二极管当开关处于打开状态。该在这个主题提出的分析会强调CCM工作，因为正是在这一模式小信号稳定，一般比较困难来实现。在非连续导通模式（DCM）的，有三分之一的开关状态，其中电感器，开关和二极管电流都为零。每个开关周期开始从同一状态（零电感电流），从而有效地该系统减少了一个顺序，使小信号性能稳定，更容易实现。虽然超出了本专题的范围，可能有专门的情况是，大信号的DCM 系统的稳定性是更令人关注的比小信号稳定。

也有几种形式的PWM控制降压稳压器，包括

?固定频率和开关变量

?修正开的变量和变量频率关变量

?可变开和变量频率固定关变量

?迟滞与开、关频率变量，

所有的变量和fS这些形式各有各的一套优势和局限性，并已全部成功使用，但因为所有的开关模式监管机构产生的开关频率组件及其相关谐波以及如预期的直流输出，电磁干扰和噪声问题作出迄今为止最固定频率操作受欢迎。

随着滞后，所有其他异常PWM控制形式基本上相同小信号的行为。因此，没有太多

的损失在一般性的，固定的fS将是我们的基础讨论古典，小信号稳定。滞回控制是根本不同的在该职责的因素得不到控制，本身。开关关断时，会发生输出纹波电压达到一个上限触发点和开启发生在一个较低的门槛。根据定义，这是一大信号控制器的小信号稳定的考虑并不适用。在小信号某种意义上说，它已经是不稳定的，并且在一数学意义上，它更快速的反应，是由于比前馈反馈。

参考文献

[1]米切尔四米，“DC - DC开关调节分析”，麦格劳希尔，1988年，DMMitchell顾问，锡达拉皮兹，保险业监督，1992年（重印版）。

[2]四米米切尔，“小信号的Mathcad设计辅助“，（视窗95 / 98版），电子/日本布卢姆Associates公司，1999。

[3]乔治Chryssis，“高频交换式电源供应“，麦格劳希尔预订公司，1984。

[4]雷里德利“一个更精确的电流模式控制模式“，Unitrode研讨会手册，扫描电镜- 1300，附录A2。

[5]劳埃德迪克逊，“控制回路设计“，Unitrode研讨会手册，扫描电镜- 800。

[6]劳埃德迪克逊，“控制回路设计 -SEPIC型前置稳压器设计“，Unitrode研讨会手册，扫描电镜- 900，题目7。