ch4-DCDC變換器反饋控制設(shè)計(jì)課件

1、Introduction Modeling of CCM DC/DC ConverterModeling of DCM DC/DC ConverterCurrent Programmed ControlFeedback Control DesignModeling and Control of Single Phase InverterContents 第1頁(yè)，共76頁(yè)。 Chapter 4Feedback control design 第2頁(yè)，共76頁(yè)。第3頁(yè)，共76頁(yè)。Typical variation in vg(t): 100Hz ripple, produced by rectifi

2、er circuit.Load current variations: a significant step-change in load current, such as from 50% to 100% of rated value.Circuit elements are constructed to some specified tolerance. Effects to poor output第4頁(yè)，共76頁(yè)。Negative feedback: switching regulator systemObjective: maintain constant output voltage

3、 v(t) = V, in spite of disturbances in input and loadA typical output voltage regulation specification: 2% for example 5V 0.1V.Introduce feedback control第5頁(yè)，共76頁(yè)。Negative feedbackconverter第6頁(yè)，共76頁(yè)。Small signal model of converterOutput voltage can be expressed asLoad disturbance model第7頁(yè)，共76頁(yè)。DC/DC c

4、onverter system dynamic modelUse small-signal converter modelPerturb and linearize remainder of feedback loop第8頁(yè)，共76頁(yè)。DC/DC converter system small-signal block diagram疊加原理求解第9頁(yè)，共76頁(yè)。Solution of block diagramLoop gain T(s) = products of the gains around the negative feedback loop.Changed into form第10

5、頁(yè)，共76頁(yè)。Terminology: open-loop vs. closed-loopOriginal transfer functions, before introduction of feedback (open-loop transfer functions):Upon introduction of feedback, these transfer functions become(closed-loop transfer functions):The loop gain:第11頁(yè)，共76頁(yè)。Feedback improve the line regulationopen-loo

6、p line-to-output transfer function:With addition of negative feedbackFeedback reduces the line-to-output transfer function by a factor ofIf T(s) is large in magnitude, then the line-to-output transfer functionbecomes small.第12頁(yè)，共76頁(yè)。Closed-loop output impedanceOriginal (open-loop) output impedance:W

7、ith addition of negative feedback, the output impedance becomes:Feedback reduces the output impedance by a factor of- 第13頁(yè)，共76頁(yè)。Closed loop gainClosed-loop transfer function If the loop gain is large in magnitude, i.e., | T | 1, then T/(1+T) T/T = 1. The transfer function then becomeswhich is indepe

8、ndent of the gains in the forward path of the loop.This result applies equally well to dc values:Output is not sensitive to parameter variation in the forward path第14頁(yè)，共76頁(yè)。Open loop gain example 第15頁(yè)，共76頁(yè)。Approximating 1/(1+T) and T/(1+T)第16頁(yè)，共76頁(yè)。Example: construction of T/(1+T)第17頁(yè)，共76頁(yè)。At freque

9、ncies sufficiently less that the crossover frequency, the loopgain T(s) has large magnitude. The transfer function from thereference to the output becomesThis is the desired behavior: the output follows the reference according to the ideal gain 1/H(s). The feedback loop works well at frequencies whe

10、re the loop gain T(s) has large magnitude.At frequencies above the crossover frequency, | T | 1. The quantity T/(1+T) then has magnitude approximately equal to 1, and we obtainAt frequencies where | T | 1, the loop has essentially no effect on the transfer function from the reference to the output.D

11、iscussion第18頁(yè)，共76頁(yè)。Example: construction of 1/(1+T)第19頁(yè)，共76頁(yè)。How does the loop reject disturbances?Below the crossover frequency: f 1 Then 1/(1+T) 1/T, anddisturbances are reduced in magnitude by 1/| T |Above the crossover frequency: f fc and | T | 1 Then 1/(1+T) 1, and The feedback loop has essenti

12、ally no effect on disturbances第20頁(yè)，共76頁(yè)。inputoutputTransfer functionTransfer function第21頁(yè)，共76頁(yè)。Factorize the denominator and nominatorPoles:Zeros:Fold freq.Fold freq.第22頁(yè)，共76頁(yè)。Frequency characteristicsBode plots:Amplitude plotAngle plotUnit: dBAmplitude plot is a Folding line graphMultiplying factor

13、s become addition operation in amplitude Bode plot.第23頁(yè)，共76頁(yè)。Meet a pole, Fold down with a rate of 20dB/dec Meet a zero, Fold up with a rate of +20dB/dec Amplitude Bode plot20dB/dec 40dB/dec 20dB/dec 第24頁(yè)，共76頁(yè)。If meet a pole , increase phase delay 90 degree occurring between fp/10 and 10fpIf meet a

14、zero ,lead phase angle with 90 degree occurring between fz/10 and 10fz Angle Bode plot-90-1800第25頁(yè)，共76頁(yè)。+-Closed loop transfer functionCharacteristic equationIf all roots are in the left half plane, stableIf a root in the right half plane, unstable.Root:Stability of closed loop第26頁(yè)，共76頁(yè)。Contains all

15、 the information about the roots of Therefore we can know the stability of the closed loop system by studying Bode plot is used to analysis the stability of the system相位裕量增益裕量增益交越頻率相位交越頻率Bode graph第27頁(yè)，共76頁(yè)。+-Oscillation conditionandOscillation conditionTo Break the oscillation condition, it is requ

16、iredwhenwhen第28頁(yè)，共76頁(yè)。gain margin: GM （dB） Relative stabilityphase margin: PM 相位裕量增益裕量增益交越頻率相位交越頻率回路增益函數(shù)的相位為180時(shí)的頻率稱為相位交越頻率 增益裕量是指當(dāng)回路增益函數(shù)的相位為180時(shí)，回路增益函數(shù)所能容許增加的回路增益 +-第29頁(yè)，共76頁(yè)。相位裕量增益裕量增益交越頻率相位交越頻率相位裕量:當(dāng)閉環(huán)系統(tǒng)達(dá)到不穩(wěn)定之前，其回路內(nèi)所能容許增加的相位。當(dāng)回路增益函數(shù)的幅值為零分貝（單位增益）時(shí)，回路增益函數(shù)的相移與180之差。 Phase margin+-第30頁(yè)，共76頁(yè)。相位裕量乃是在平面

17、上為了使軌跡的增益交越點(diǎn)通過(guò)（1，j0）點(diǎn)，則圖必須以原點(diǎn)為中心順時(shí)針?biāo)毿D(zhuǎn)角度.增益裕量就是在平面上相位交越點(diǎn)對(duì)（1, j0）點(diǎn)接近程度的一種量度 Naquist Graph相位裕量增益裕量增益交越頻率相位交越頻率-1第31頁(yè)，共76頁(yè)。 The relationship between phase marginand closed-loop damping factorHow much phase margin is required?A small positive phase margin leads to a stable closed-loop system, which has

18、 complex poles near the crossover frequency with high Q. The transient response exhibits overshoot and ringing.Increasing the phase margin reduces the Q. To obtain real poles with no overshoot and ringing requires a large phase margin.第32頁(yè)，共76頁(yè)。Consider the case where T(s) can be well-approximated i

19、n the vicinity of the Crossover frequencyA simple second-order system第33頁(yè)，共76頁(yè)。Closed-loop responseExpressed byWherewhereis substituted第34頁(yè)，共76頁(yè)。Low-Q case第35頁(yè)，共76頁(yè)。High-Q case第36頁(yè)，共76頁(yè)。Solve for exact crossover frequency, evaluate phase margin, express as function of QQ vs. phase margin 第37頁(yè)，共76頁(yè)。Q

20、 vs. phase margin 第38頁(yè)，共76頁(yè)。Transient response vs. damping factorUnit-step response of second-order system T(s)/(1+T(s)where第39頁(yè)，共76頁(yè)。Transient response vs. damping factor第40頁(yè)，共76頁(yè)。Regulator designTypical specifications:Effect of load current variations on output voltage regulation, which is a limit

21、 on the maximum allowable output impedanceEffect of input voltage variations on the output voltage regulation, which limits the maximum allowable line-to-output transfer functionTransient response time, which requires a sufficiently high crossover frequencyOvershoot and ringing. An adequate phase ma

22、rgin must be obtainedThe regulator design problem: add compensator network Gc(s) to modify T(s) such that all specifications are met.第41頁(yè)，共76頁(yè)。+-反饋信號(hào)參考信號(hào)誤差信號(hào)DC/DC power converter systemPWM調(diào)制器的傳遞函數(shù)為 傳遞函數(shù)為至輸出的傳遞函數(shù)第42頁(yè)，共76頁(yè)。Buck變換器占空比至輸出的傳遞函數(shù)Buck變換器系統(tǒng)原始回路增益函數(shù) 原始回路增益函數(shù)是一個(gè)二階系統(tǒng)，有兩個(gè)極點(diǎn)。 幅頻圖在低頻段為水平線，幅值為高頻段以4

23、0dB/dec斜率下降，轉(zhuǎn)折點(diǎn)由LC濾波器的諧振頻率決定。第43頁(yè)，共76頁(yè)。設(shè)Buck變換器系統(tǒng)的參數(shù)為：輸入電壓輸出電壓，輸出負(fù)載輸出濾波電感值，電容值開關(guān)頻率kHz，即開關(guān)周期PWM調(diào)制器中鋸齒波幅值反饋分壓網(wǎng)絡(luò)傳遞函數(shù)可求出工作占空比： Buck變換器占空比至輸出的傳遞函數(shù) 第44頁(yè)，共76頁(yè)。原始回路增益函數(shù) 幅頻圖的轉(zhuǎn)折頻率為： 幅頻圖低頻段為幅值約為20dB水平線,高頻段為斜率穿越0dB線的折線。Hz 第45頁(yè)，共76頁(yè)。幅頻圖相頻圖 增益交越頻率， 相位裕量 第46頁(yè)，共76頁(yè)。原始回路增益函數(shù)頻率特性的相位裕量太小。雖然系統(tǒng)是穩(wěn)定的，但存在較大的輸出超越量和較長(zhǎng)的調(diào)節(jié)時(shí)間。

24、通常選擇相位裕量在45左右，增益裕量在10dB左右。因此需要加入補(bǔ)償網(wǎng)路 一般原始回路增益函數(shù)不能滿足系統(tǒng)靜態(tài)和動(dòng)態(tài)特性的要求，為了使系統(tǒng)滿足靜態(tài)和動(dòng)態(tài)的指標(biāo)，需要加入補(bǔ)償網(wǎng)路。 雖然，補(bǔ)償網(wǎng)路只是系統(tǒng)中極小的一部分，但是，對(duì)系統(tǒng)靜態(tài)和動(dòng)態(tài)特性而言卻是非常重要部份，它會(huì)影響到系統(tǒng)的輸出精度、電壓調(diào)整率、頻帶寬度以及暫態(tài)響應(yīng)。第47頁(yè)，共76頁(yè)。最小相位系統(tǒng)的幅頻特性和相頻特性之間存在一一對(duì)應(yīng)關(guān)系，如幅頻圖中斜率為-20dB/dec折線對(duì)應(yīng)相頻圖中相移為斜率為-40dB/dec折線對(duì)應(yīng)相頻圖中相移為斜率為+20dB/dec折線對(duì)應(yīng)相頻圖中相移為知道了幅頻特性也就知道了相頻特性，反之也然。最小相位

25、系統(tǒng)理論水平線對(duì)應(yīng)相頻圖中相移為第48頁(yè)，共76頁(yè)。為使DC/DC變換器系統(tǒng)滿足穩(wěn)定性要求，可以通過(guò)外加補(bǔ)償網(wǎng)絡(luò)使DC/DC變換器系統(tǒng)的回路增益函數(shù)的幅頻圖在增益交越頻率處（增益為零dB）的斜率為-20dB/dec。相位裕量PM大于零 因?yàn)楦鶕?jù)最小相位系統(tǒng)的性質(zhì)，幅頻圖的斜率為-20dB/dec折線對(duì)應(yīng)相移為-90度第49頁(yè)，共76頁(yè)。還須驗(yàn)證在相位交越頻率處（相位在180時(shí)）若相位裕量與增益裕量的值，只是稍稍大于零時(shí)，雖然對(duì)系統(tǒng)而言也是穩(wěn)定的，不過(guò)卻會(huì)具有較大的超越量和調(diào)節(jié)時(shí)間。通常選擇相位裕量在45左右，增益裕量在10dB左右。 增益裕量必須大于零。回路增益函數(shù)第50頁(yè)，共76頁(yè)。補(bǔ)償網(wǎng)路

26、設(shè)計(jì) （1）超前補(bǔ)償網(wǎng)路（2）滯后補(bǔ)償網(wǎng)路；（3）超前滯后補(bǔ)償網(wǎng)路。 第51頁(yè)，共76頁(yè)。Lag (PI) compensationImproves low-frequency loop gain and regulationSuitable to the 1st order system第52頁(yè)，共76頁(yè)。Lag Compensation Examplecompensator:original loop gainis selected less than fo to maintain adequate phase margin is selectedPIFirst select crosso

27、ver frequency of closed loop第53頁(yè)，共76頁(yè)。Lead (PD) compensatorImproves phase marginSuitable to the 2nd order system第54頁(yè)，共76頁(yè)。Lead compensator: maximum phase leadThe frequency with maximum phase leador55 deg第55頁(yè)，共76頁(yè)。Lead compensator designTo obtain a compensator phase lead of at frequency fc, the pole

28、and zero frequencies should be chosen as follows:If it is desired that the magnitude of the compensator gain at fc be unity, then Gc0 should be chosen as第56頁(yè)，共76頁(yè)。Lead compensation example第57頁(yè)，共76頁(yè)。超前滯后補(bǔ)償網(wǎng)絡(luò) （a）電路 （b）零極點(diǎn)分布超前滯后補(bǔ)償網(wǎng)絡(luò)的傳遞函數(shù) “超前滯后”補(bǔ)償網(wǎng)路輸出正弦信號(hào)的相位在不同頻率范圍有落后又有超前于正弦輸入信號(hào)的特性，它結(jié)合超前補(bǔ)償與滯后補(bǔ)償?shù)奶匦裕l(fā)揮滯后補(bǔ)

29、償特性提高靜態(tài)或穩(wěn)態(tài)性能，利用超前補(bǔ)償特性提高相對(duì)穩(wěn)定性和動(dòng)態(tài)性能。第58頁(yè)，共76頁(yè)。，項(xiàng)產(chǎn)生超前補(bǔ)償效果項(xiàng)產(chǎn)生滯后補(bǔ)償效果 (c)第59頁(yè)，共76頁(yè)。有源超前滯后補(bǔ)償網(wǎng)路1 RC網(wǎng)路所組成的超前滯后補(bǔ)償網(wǎng)絡(luò)的增益只能衰減不能增加，增益設(shè)計(jì)不便。因此，一般采用運(yùn)算放大器構(gòu)成有源的超前滯后補(bǔ)償網(wǎng)路。第60頁(yè)，共76頁(yè)。-20dB/dec20dB/dec補(bǔ)償網(wǎng)路增益 利用補(bǔ)償網(wǎng)絡(luò)幅頻特性圖低頻的積分特性，可以使經(jīng)補(bǔ)償后的系統(tǒng)成為無(wú)差系統(tǒng)，使靜差為零，同時(shí)減少了低頻誤差。利用補(bǔ)償網(wǎng)絡(luò)幅頻圖在 至 之間斜率為20 dec/dB上升特性，補(bǔ)償原始回路函數(shù) 以斜率 穿越0dB線的特性，使補(bǔ)償后的回路函數(shù)

30、 以 穿越0dB線，這樣才能使DC/DC變換器系統(tǒng)具有較好的相對(duì)穩(wěn)定性。因此，一般將補(bǔ)償后系統(tǒng)的增益交越頻率 設(shè)定在補(bǔ)償網(wǎng)路的 與 之間。第61頁(yè)，共76頁(yè)。有源超前滯后補(bǔ)償網(wǎng)絡(luò)2 零點(diǎn)為：極點(diǎn)為：與有源超前滯后補(bǔ)償網(wǎng)路1的差異是在高頻部份增加了一個(gè)極點(diǎn)fp3，而使其向下反折為20dB/dec。 第62頁(yè)，共76頁(yè)。頻率fz1與fz2之間的增益可近似為 在頻率 與 之間的增益則可近似為一般也將補(bǔ)償后系統(tǒng)的增益交越頻率 設(shè)定在補(bǔ)償網(wǎng)路的 與 之間 20dB/dec-20dB/dec-20dB/dec第63頁(yè)，共76頁(yè)。下面以有源超前滯后補(bǔ)償網(wǎng)絡(luò)2為例介紹補(bǔ)償網(wǎng)絡(luò)的設(shè)計(jì)方法。 補(bǔ)償網(wǎng)絡(luò)的設(shè)計(jì)方法選擇補(bǔ)償后的回路函數(shù) 的增益交越頻率fg 補(bǔ)償后的回路函數(shù)增益交越頻率fg愈大，變換器系統(tǒng)動(dòng)態(tài)響應(yīng)愈快。將補(bǔ)償網(wǎng)絡(luò) 兩個(gè)零點(diǎn)頻率設(shè)計(jì)為原始回路函數(shù)