Power Electronics Lab1Lecture 9ECEN 4517/5517Experiment 4Lecture 8: Step-up dc-dc converter Lecture 9: Design of analog feedback loopPart I—Controller IC:Demonstrate operating PWM controller IC (UC3525)Part II—Power Stage:Demonstrate operating power converter (cascaded boost converters)Part III—Closed-Loop Analog Control System:Demonstrate analog feedback system that regulates the dc output voltageMeasure and document loop gain and compensator designPower Electronics Lab2Due datesThis week in lecture (Mar. 9):Prelab assignment for Exp. 4 (one from every student)This week in lab (Mar. 9-11):Start Exp. 4Next week in lecture (Mar. 16):Midterm exam, to cover Exps. 1-3After Spring break, in lab (Mar. 30 – Apr. 1):Exp. 3 part 2 report duePower Electronics Lab3Exp. 4 Part IIIRegulation of output voltage via feedback•Model and measure control-to-output transfer function Gvd(s)•Design and build feedback loop•Demonstrate closed-loop regulation of vHVDCECEN 451711Negative feedback:a switching regulator system+–+v–vgSwitching converterPowerinputLoad–+CompensatorvrefReferenceinputHvPulse-widthmodulatorvcTransistorgate driverGc(s)H(s)veErrorsignalSensorgainiloadECEN 451712Transfer functions ofsome basic CCM convertersTable 8.2. Salient features of the small-signal CCM transfer functions of some basic dc-dc convertersConverterGg0Gd00Qzbuck D VD 1LC RCLboost 1D' VD' D'LC D'RCL D'2RLbuck-boost –DD' VDD'2 D'LC D'RCL D'2RDLwhere the transfer functions are written in the standard formsGvd(s)=Gd01–sz1+sQ0+s02Gvg(s)=Gg011+sQ0+s02Flyback: push L and C to same side of transformer, then use buck-boost equations. DC gains Gg0 and Gd0 have additional factors of n (turns ratio).ECEN 451713Bode plot: control-to-output transfer functionbuck-boost or flyback converter examplef0˚–90˚–180˚–270˚ Gvd Gd0 = 187 V 45.5 dBV Gvd Gvd0 dBV–20 dBV–40 dBV20 dBV40 dBV60 dBV80 dBVQ = 4 12 dBfz2.6 kHzRHP Gvd10-1/2Qf0101/2Qf00˚300 Hz533 Hz–20 dB/decade–40 dB/decade–270˚fz /10260 Hz10fz26 kHz1 MHz10 Hz 100 Hz 1 kHz 10 kHz 100 kHzf0400 HzECEN 451714The loop gain T(s)+–+v–vgSwitching converterPowerinputLoad–+CompensatorvrefReferenceinputHvPulse-widthmodulatorvcTransistorgate driverGc(s)H(s)veErrorsignalSensorgainiloadLoop gain T(s) = product of gains around the feedback loopMore loop gain ||T|| leads to better regulation of output voltageT(s) = Gvd(s) H(s) Gc(s) / VMGvd(s) = power stage control-to-output transfer functionPWM gain = 1/VM. VM = pk-pk amplitude of PWM sawtoothECEN 451715Phase MarginA test on T(s), to determine stability of the feedback loopThe crossover frequency fc is defined as the frequency where|| T(j2fc) || = 1, or 0 dBThe phase margin m is determined from the phase of T(s) at fc , as follows:m = 180˚ + (T(j2fc))If there is exactly one crossover frequency, and if T(s) contains no RHP poles, thenthe quantities T(s)/(1+T(s)) and 1/(1+T(s)) contain no RHP poles whenever the phase margin m is positive.ECEN 451716Example: a loop gain leading toa stable closed-loop system (T(j2fc)) = – 112˚m = 180˚ – 112˚ = + 68˚fcCrossoverfrequency0 dB–20 dB–40 dB20 dB40 dB60 dBffp1fzT0˚–90˚–180˚–270˚m T T T1 Hz 10 Hz 100 Hz 1 kHz 10 kHz 100 kHzECEN 451717Transient response vs. damping factor00.511.520 5 10 15ct, radiansQ = 10Q = 50Q = 4Q = 2Q = 1Q = 0.75Q = 0.5Q = 0.3Q = 0.2Q = 0.1Q = 0.05Q = 0.01v(t)ECEN 451718Q vs. m0 10 20 30 40 50 60 70 80 90mQQ = 1 0 dBQ = 0.5 –6 dBm = 52˚m = 76˚–20 dB–15 dB–10 dB–5 dB0 dB5 dB10 dB15 dB20 dBFundamentals of Power Electronics Chapter 9: Controller design429.5.2. Lag (PI) compensationGc(s)=Gc∞1+ωLsImproves low-frequency loop gainand regulationf|| Gc ||∠ GcGc∞0˚fL/10+ 45˚/decadefL– 90˚10fL– 20 dB /decadeFundamentals of Power Electronics Chapter 9: Controller design43Example: lag compensationoriginal(uncompensated)loop gain isTu(s)=Tu01+sω0compensator:Gc(s)=Gc∞1+ωLsDesign strategy:chooseGc∞ to obtain desiredcrossover frequencyωL sufficiently low tomaintain adequatephase margin0 dB–20 dB–40 dB20 dB40 dBf90˚0˚–90˚–180˚Gc∞Tu0fLf0Tu0∠ Tu|| Tu ||f0|| T ||fc∠ T10fL10f0ϕm1 Hz 10 Hz 100 Hz 1 kHz 10 kHz 100 kHzFundamentals of Power Electronics Chapter 8: Converter Transfer Functions948.4. Measurement of ac transfer functionsand impedancesNetwork AnalyzerInjection source Measured inputsvymagnitudevzfrequencyvzoutputvz+–inputvxinput+– +–vyvxvyvxData17.3 dB– 134.7˚Data busto computerFundamentals of Power Electronics Chapter 8: Converter Transfer Functions95Swept sinusoidal measurements•Injection source produces sinusoid of controllable amplitude andfrequency•Signal inputs and perform function of narrowband trackingvoltmeter:Component of input at injection source frequency is measuredNarrowband function is essential: switching harmonics and othernoise components are removed• Network analyzer measuresvzvxvy∠vyvxvyvxandFundamentals of Power Electronics Chapter 8: Converter Transfer Functions96Measurement of an ac transfer functionNetwork AnalyzerInjection source Measured inputsvymagnitudevzfrequencyvzoutputvz+–inputvxinput+– +–vyvxvyvxData–4.7 dB– 162.8˚Data busto computerDeviceunder testG(s)inputoutputVCCDCbiasadjustDCblockingcapacitor•Potentiometerestablishes correctquiescent operatingpoint•Injection sinusoidcoupled to deviceinput via dc blockingcapacitor• Actual device inputand output voltagesare measured asand•Dynamics of blockingcapacitor are irrelevantvxvyvy(s)vx(s)= G(s)Fundamentals of Power Electronics Chapter 9: Controller design649.6.1. Voltage injection• Ac injection source vz is connected between blocks 1 and 2• Dc bias is determined by biasing circuits of the system itself•Injection source does modify loading of block 2 on block 1+–H(s)+–Z2(s)Block 1 Block 20Tv(s)Z1(s) Zs(s)– ++vx(s)–vref(s)G1(s)ve(s)ve(s) G2(s)vx(s) = v(s)–vy(s)+vzi(s)Power Electronics Lab5Averaged switch modelingBasic approachSeparate switching elements from remainder of
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