2024年3月7日发(作者：)

外文原文

Principle, Modeling and Control of DC-DC

Convertors for EV

ZHAN G Cheng-ning , SUN Feng-chun , ZHAN G Wang

(School of Vehicle and Transportation Engineering , Beijing Institute of

Technology , Beijing 100081)

Abstract : DC-DC convertors can convert the EV’s high-voltage

DC power supply into the lowvoltage DC power supply. In order to

design an excellent convertor one must be guided by theory of

automatic control. The principle and the method of design, modeling

and control for DC-DC convertors of EV are introduced. The method

of the system-response to a unit step-function input and the

frequency-response method are applied to researching the convertor’s mat- hematics model and control characteristic. Experiments

show that the designed DC-DC convertor’s output voltage precision

is high , the antijamming ability is strong and the adjustable

performance is fast and smooth.

Key words: EV ; DC-DC convertors ; automatic control ;

mathematics model ; Bode drawing

CLC number : U 469-72

Document code : A

Generally there are two power supplies in EV. One is the DC

high-voltage power supply that is used by high power devices such as

traction motors and air conditioners etc. The other is the DC

low-voltage power supply that is usually used in some control circuit

and low-voltage electrical devices such as the inst- rument and

lighting. It s rating voltage is 24 V or 12 V. The low-voltage power

supply can be gained from the high-voltage power supply by a

DC-DC conver-

tor.

In this paper, the main performance of the designed convertor is

that the input voltage range is from DC 250 V to DC 450 V , the

output voltage is DC 24 V , the maximum output current is DC 20 A ,

and the output precision is 1 %.

1 Principle of the Convertor

1.1 The Block Diagram of the DC-DC Convertor

The block diagram of the DC-DC convertor is showed in Fig. 1.

The battery series provide the DC high-voltage input Us. The

low-voltage output of the con-

vertor is Uo. The setting value Ui of the convertor is equal to or is in

proportion to the demanded output voltage Uo. The convertor is a

closed-loop negative feedback-system with voltage feedback.

1.2 Power Switch Circuit

The power switch circuit with semi-bridge mode is showed in

Fig. 2. L1 and C1 constitute an input filter to avoid high-frequency

impulses flowing bac- kwards. Capacitors C2and C3 constitute the

partial-voltage circuit while resist-

ances R1 and R2do so. IGBT1 and IGBT2 are semiconductor switch

devices. C6 is a separation DC capacitor. T1 is a transformer that

reduces the voltage. L2 and C7 constitute an output filter. RL is the

load resistance. When the PWM signals

in the reverse semi-waves are inputted onto IGBT1 and IGBT2’s

control poles , the corresponding DC voltage can be yielded from the

convertor.

Fig. 2 Principle circuit of power switch with semi-bridge mode

1.3 Control Circuit

The chip SG3525 is used in the PWM control circuit showed in

Fig. 3. V cc is the power voltage applied to the chip, it is 12.0 V. A

base-voltage of 5.1 V is yielded on pin16 of the chip that is partially

used as parameter voltage input Ui. The chip includes a

sawtooth-wave generator. Rt and Ct are the external resis-

tance and capacity that determine the sawtooth-wave’s

2 of the chip is a positive-phase input port. Voltage

input Ui is putted to the port, here Ui =2. 5 V. Pin1 of the chip is the

negative-phase input port where the feedback voltage is 9

of the chip is the output end of the inside amplifier of the chip. The

proper resistance and capacitor are connected between the pin1 and

pin9 to realize compensation of the DC-DC convertor.C8 is the

integral capacitor. The integral compensator is adopted as the

system-compensation of the system. The PWM impulses are yielded

from pin11 and pin14 of the chip. When the PWM control circuit

operates normally, Ui on the pin2 and Ub on the pin1 should be

balanced. When Ub is not equal to Ui , the PWM width can be

automatically adjusted by the PWM control circuit to make Ub equal

to Ui. By this way we can control the output voltage of the convertor.

Fig. 3 The connection circuit for the PWM control chip SG3525

1.4 Drive Circuit

The drive circuit of IGBT usually adopts a pulse-transformer or

an opto-

coupler to isolate the power circuit from the control circuit. An

individual power supply is needed if an opto-coupler is used, which

increases the complexity of the system. So the isolation-circuit adopt

s a pulse-transformer showed in Fig. 4. Transistors BG1 and BG2 in

Fig. 4 compose a complementation power amplification circuit. T2 is

the pulse-transformer that isolates the power circuit from the control

circuit. R5 and C8 compose the acceleration circuit. The diode D6

eliminates negative impulses. The diode D7 and transistor BG3

compose the rapid discharge circuit of the distributing capacitor at the

control pole of IGBT.

Fig. 4 Principle circuit for IGBT drive

2 Modeling and Control

2.1 Modeling

The DC-DC convertor is a voltage negative feedback-system.

Aiming to obtain the better dynamic and static characteristic we must

model and analyse it in theory. According to Ref. [ 1 ] ,DC-DC

convertors are the approximate second-order systems. In order to

obtain accurate parameters , the method of the system-response to a

unit step-function input is adopted in this paper.

2.1.1 Measuring the Open-Loop System’s Response to a

Unit Step-Function Input

The block diagram for measuring is shown in Fig. 5. The

concrete method is described as follows : ① The voltage feedback

signal is cut off ; ② The setting value of the chip SG3525 adopts the

middling value Ui0 to make the width of an impulse be about 0.5 T ;

③ Ui0 is superimposed with d Ui that is composed by positive and

negative rectangle wave impulses. The amplitude of d Ui is taken to

be equal to 0.2Ui0. It should make d Uo be easy to be observed to

select the rectangle wave frequency , adopting f 1 = 400 Hz ; ④ The

output waveform of Uo ( = Uo 0 + d Uo ) is shown in Fig. 6. As

shown in Fig. 6 when f 1 = 400 Hz , period T = 2.5 ms (5 grills) ,

the time for the maximum voltage value is about 0.2 grills. d Uo’s

stable voltage amplitude is - grills. Peak overshoot is 1 grill. Every

grill in the vertical direction represents 5 V. By this way the data of

system-response to a unit step-function input can be obtained as

follows :

peak time tp = 0.1 ms ; peak overshoot σp = 1/ 2 = 50 %;

output and input’s incremental ratio K0 = d Uo/ d Ui = 10/ 1 = 10.

Fig.5 The measuring block diagram of the open-loop system

Fig. 6 The system-response to a unit step-function input

2.1.2 Determining the Open-Loop Transfer Function

According to Ref s. [2,3 ] , we have the damping ratio ξ,

undamped natural frequency ωn and transfer function of controlled

object Gp ( s) as follows :

In order to ensure that when the output voltage Uo =24 V the

feedback voltage to pin1 of the SG3525 is 2.5 V to balance the input

voltage Ui = 2.5 V, we take the feedback and measuring factor as

Kb = Ub/ Uo = -15/ -4 = 01104.

( 4 )

2.2 Design of the PID Regulator

2. 2.1 The Principle Scheme and Transfer Function of the

PID Regulator

To resist the disturbance of the power supply voltage and load

current to the DC-DC convertor so as to improve control precision ,

an integral compensator is adopted. The principle scheme of the

integral compensator is shown in Fig. 7.

Fig. 7 The principle scheme of the integral compensator

It s transfer function is

Gc ( s) = Ki/ s = 1/ ( RCs).

( 5 )

In Fig. 7 and Eq. (5), R = 10 kΩ, C = 0.1μF , Ki = 1/ ( RC) = 1/ (10

×103 ×011 ×10 - 6)= 1 000.

2. 2.2 The Bode Drawing of the System Open-Loop

Transfer Function

The system open-loop transfer function is the product of the

controlled object’s , feedback and measuring circuit’s and integral

compensator’s transfer functions. We have

G( s) = Gc ( s) Gp ( s) Gb ( s) =

The system Bode drawing is shown in Fig. 8 from Eq. (6). The

curves ①and ④are respectively the logarithmic gain-frequency

characteristic ,logarithmic phase-frequency characteristic of

controlled object Gp ( s). The curves ② and ⑤ are respectively the

logarithmic gain-frequency characteristic , logarithmic

phase-frequency characteristic of the feedback and measuring circuit

joint the integral compensator. The curves ③ and ⑥ are

respectively the logarithmic gain-frequency characteristic and

logarithmic phase-frequency characteristic of the compensated

open-loop system. By Fig. 8 we know that the system is I-model

system. When the input doesn’t change , there isn’t steady-state error.

It s original phase-margin frequency ωc = 1 016 rad/ s , phase

margin γ= 89.21°, so the adjustable performance of the

system is fast and smooth.

Fig. 8 The Bode drawing of the system open2loop transfer function

3 The Result and Conclusion of

Experiment

When the load resistance RL = 1.2Ω , the experiment data of

Us , I s , Uo , Io , η(ηis efficiency of the convertor) are shown in

Tab. 1. When the load resistance RL = 2.4Ω , the experiment data of

Us , I s , Uo , Io , ηare shown in Tab.2.

4 Conclusions

①Because the integral compensator is adopted , the output

voltage Uo of the convertor has quite high precision even if the input

power voltage and the load changes.

②The width of the impulses is adjusted automatically in the

convertor to realize constant output voltage value. With the increase

of the input voltage the width of the impulses turn narrow , the

convertor’s efficiency drops. In the process of designing a DC-DC

convertor, we must diminish the adjustable range of the impulse

width and make the impulse width wider when the convertor

operates.

③ The reasonable value of the resistance and capacitor in the

feedback circuit must be selected so that the feedback-system has

enough gain margin and phase margin that can guarantee the

control-system to be adjusted smoothly.

References:

[1 ] Cai Xuansan , Gong Shaowen. High-frequency electronics (in Chinese)

[ M].Beijing : Science Press , 1994. 232 - 246.

[2] Zhang Wang , Wang Shiliu. Automatic control principle (in Chinese)[M].

Beijing: Beijing Institute of Technology Publishing House , 1994. 71 - 72.

[3 ] D’Azzo J J. Linear control system analysis and design [M]. San

Francisco: McGraw-Hill Book Company,1981. 83 - 92.

电动汽车DC-DC电源转换器的原理、建模和控制

张承宁, 孙逢春, 张 旺

(北京理工大学车辆与交通工程学院, 北京 100081)

摘要：为了设计出在电动汽车上把高压直流电源变换成低压直流电源的高品质DC-DC 变换器,采用自动控制理论进行指导. 介绍电动汽车DC-DC 变换器原理和设计,建模与控制方法. 应用阶跃响应法、频率法研究其数学模型和控制特性,并且进行分析和计算.

实验结果表明,用这种方法所研制的电动汽车DC-DC 变换器输出电压精度高,抗干扰能力强,调节特性快速、平稳.

关键词： 电动汽车; DC-DC 变换器; 自动控制; 数学模型; Bode

图

中图分类号U 469172 文献标识码A

通常有两种电源电动汽车。一个是直流高压电源采用高功率设备,如牵引电机和空调等。另一个是低压直流电源,通常被用在一些控制电路和低压电器设备,如仪表和照明。它的额定电压24 V或12 V低压供电,可由高电压供电直流-直流变换器得到在本文中,主要性能设计的是输入电压转换器,范围从直流250 V到直流450

V,输出直流电压24 V、最大输出电流是直流20 A,输出精度为1%。

1变换器原理

1·1直流-直流变换器的原理框图

直流-直流转换器的原理框图如图1所示，电池组提供直流高

压输入Us，低压变频器的输出是Uo。变频器的调定值Ui等于或者是按比例到要求的输出电压Uo。这个转换器是一个负电压反馈闭环系统。

1·2功率开关电路

图2所示电路的电源开关半桥接模式，L1和C1构成一个输入滤波器来避免高频脉冲反流，C2和C3电容器与电阻R1和R2分别构成部分电压回路，T1和T2是半导体开关，C6是一个分离直流电容器，T1是一个减少电压的变压器，L2和C7构成一个输出过滤器，RL是负载电阻。当逆向半波上的PWM信号均在T1和T2的控制限时，相应的直流电压可以从自己的变换器中产生。

图2电路的电源开关半桥接模式

1·3控制电路

用于PWM控制电路的SG3525芯片如图3所示，Vcc是芯片的电源电压，它是12V，在芯片脚16上5.1V的基极电压部分作为参数输入界面电压Ui，芯片包含一个锯齿波发生器，Rt和Ct是确定的锯齿波频率的外部电阻和电容，芯片的脚2是正的输入端口，输入电压Ui是针对端口，Ui=2.5V，芯片的脚1是输入反馈电压的负输入端，芯片的脚9是芯片内部放大器输出结果。连接在脚1和脚9之间适当的电阻和电容实现直流—直流变换器的补偿。C8是积分电容，采用整体补偿系统的补偿制度，PWM脉冲从脚11和脚4产生，当PWM控制电路正常运行时，脚2上的Ui和脚1上的Ub应该平衡，当Ui不等于Ub时，PWM技术宽度可自动调节PWM控制电路使Ui等于Ub，通过这种方法我们可以控制变压器的输出电压。

图3用于PWM控制电路的SG3525芯片

1·4驱动电路

IGBT驱动电路通常采用脉冲变压器或光耦合器通过控制电路隔离电源电路，如果光耦合器需要使用个人电源，就会增加系统的复杂度，所以隔离电路采用脉冲变压器如图4所示，如图4中晶体管BG1和BG2组成一个互补的功率放大电路，T2是控制电路中的脉冲变压器隔离电路，R5和C8组成加速电路，二极管D6消除负脉冲，二极管D7和晶体管BG3在IGBT的控制下组成快速放电电路分布电容。

图41GBT驱动电路原理

2建模和控制

2·1建模

直流—直流转换器是一个电压负反馈系统，以获得良好的动态和静态特性，我们必须理论上模型和分析，根据参考【1】，直流—直流转换器是近似二阶系统，为了获得正确的参数，本文采用对单位阶跃函数输入系统响应的方法。

2·1·1对单位阶跃函数输入的开环系统响应测量

测量原理框图如图５所示，基本方法是描述如下：①电压反馈信号被切断②调定值上的芯片SG3525采用中等价值Uio是每个脉冲密度达到大约0.5特，③Uio与Ui叠加产生正负矩形脉冲，使Ui振幅等于0.2倍Uio，它将会使Uo容易被观察去选择矩形波的频率，采用f1=400赫兹，④Uo的输出波形如图6所示，当f1=400赫兹时，周期T=2.5毫秒（5格），最大电压值的时间约为0.1毫秒，Uo为稳定电压幅值时为1ms,峰值超调为1格，每格在垂直方向代表5V，通过这种方法，系统响应的数据输入到一个单位阶跃函数可以得到如下：峰值时间tp=0.1ms 峰值超调σp = 1/

2 = 50 %;

输出和输入的增量的比Ko=dUo/ dUi=10/ 1=10.

图5开环系统测量原理框图

图6对单位阶跃函数输入系统响应

2·1·2开环传递函数的确定

根据参考【2、3】，我们有阻尼比ξ、被控制对象Gp (

s)、固有频率ωn无阻尼自由振动微分方程：

为了确保输出电压Uo=2.4V电压反馈给SG3525脚1的为

2.5V，来平衡输出电压Ui=2.5V时，我们采用反馈和测量的参数

Kb = Ub/ Uo = 2.5/ 24 = 0.104.

( 4 )

2·2 PID调节器的设计

2·2·1 PID调节器的原理方案及传递函数

直流—直流转换器的抗扰动电源电压和负载电流，以提高控制精度采用整体补偿、积分补偿器的原理如图7

图7整体补偿原则

它的传递函数

Gc(s)=Ki/s=1/(RCs)

( 5 )

由图7和公式5 ,

R

= 10 kΩ ,

C

= 0.1μF ,

Ki = 1/ (

RC)

= 1/ (10×0.1 ×0.001)= 1 000

2·2·2开环传递函数的绘制

该系统开环传递函数是被控制对象的产品，反馈和检测电路和整体补偿器的传递函数，我们有

G( s)

=

Gc

( s) Gp

( s) Gb

( s)

=104/s＊10/(s*s/32150*32150+2*0.2154*s*s/32150+1)

( 6 )

由公式6该系统图如图8所示，曲线①和④分别获得对数频率特性，对数相频特性的控制对象Gp

( s)，曲线②和⑤对数频率特性分别获得对数相频特性的反馈和测量电路的整体补偿关节。曲线③和⑥分别获得频率特性和对数相频特性的开环系统的补偿。由图8我们知道系统是自我模型系统，当输入不改变，没有稳态误差。它的初始阶段ωc = 1 016 rad/ s，相位边缘γ=

89.21°,所以可以调节系统性能的快捷顺畅。

图8系统开环传递函数图

3 实验结果和结论

当负载电阻RL = 1.2Ω时，表一显示实验数据Us ,

I

s ,

Uo ,

Io , η（效率的摸），当负载电阻RL = 2.4Ω时, 表二显示实

验数据Us ,

I

s ,

Uo ,

Io , η。

表一当负载电阻RL = 1.2Ω时

表二当负载电阻RL = 2.4

4总结

①由于采用的整体补偿法，即使输入电压和负载变化，转换器的输出电压Uo有很高的精度；

②脉冲的宽度自动调整来实现变频器输出电压不变，随输入电压的增加脉冲的宽度将缩小，转换器的效率下降，在设计DC-DC转换器的过程中，当转换器运作时我们必须减少脉冲宽度的可调范围和是脉冲宽度更宽；

③反馈电路中电阻和电容器合理的价值必须选择为能够使反馈系统有足够的增益和极限来保证控制系统可以顺利进行调整

5参考文献

[ 1 ] Cai Xuansan , Gong Shaowen. High2frequency

electronics ( in Chinese) [ M] . Beijing : Science Press ,

1994. 232 - 246.

[ 2 ] Zhang Wang , Wang Shiliu. Automatic control

principle (in Chinese) [M] . Beijing : Beijing Insti2 tute

of Technology Publishing House , 1994. 71 - 72.

[ 3 ] D’Azzo J J . Linear control system analysis and

design [M] . San Francisco : McGraw2Hill Book Company ,1981.

83 - 92.