高级控制设计By Ridley

AdvancedControlDesignPresentedbyDr.RaymondB.RidleyAPEC2014WhatdoestheEiffelTowerhaveincommonwithPowerSupplyDesign?Whatisnewinpowersupplycontrol?PointofLoadConvertersVeryHighFrequencyOperation(MHz)CapacitorswithVeryLowESRVeryHighCrossoverFrequenciesFullyIntegratedControlandPowerSemiconductorsAdvancedCurrent-ModeSensingInternallyCompensatedPartsDigitalControllers2StatesAnalyzedinDepthTheProblemsofPowerSupplyAnalysisBasicTopology+-+-5StateswithControllerLogicAddingControllerStates+-7StateswithNoiseFilterSecond-StageFilter–OrPowerDistribution+-12StateswithInputFilterInputEMIFilter+-20StateswithSecondPowerStageandControlMultiplePowerSuppliesThemathisalreadyintractable.Thenaddcomplicationsof:High-noiseenvironmentInadequatemodelsformagneticsInadequatemodelsforcapacitorsInadequatemodelsforboardlayoutSwitchingeffectonmodelingOthersystemnonlinearitiesnotaccountedforinmodeling.High-OrderSystemAnalysisVorpérianswitchmodelstoexaminecoreconvertersLaplaceTransformstoeliminatecalculusBodeplotsto“see”complexhigh-orderfunctionsandeliminatethemathMiddlebrookcriteriatoseparateblocksHumanintelligencetoseepracticalsolutionsLoopgainsandotherBodeplotstodesignsystemsandassesspolelocationsSteploadstoverifyperformanceandseelarge-signaleffects.High-OrderSystemDesignVorpérianSwitchModeltoLinearizeCircuit+-apcPWMSwitchesDifferentFormsofVorpérianSwitchModelapACModel+-+-1DcapDCModel1Dcap1dcNonlinearModelapcPWMSwitchesˆapVdDˆcIdVorpérianSwitchModelinConverters+-apACModel+-+-1DcˆapVdDˆcId+apcPWMSwitches+ACModelpD1+-+-ac+-apcˆapVdDˆcIdPWMSwitchesBoostConverterBuckConverterVorpérianSwitchModelinHigh-OrderCircuits+-ap+-+-1DcˆapVdDˆcIdap+-+-1DcˆapVdDˆcIdLaplaceTransformstoEliminateCalculusLZsL1CZsC+-apACModel+-+-1DcˆapVdDˆcIdLdivLdtCdviCdt+-apACModel+-+-1DcˆapVdDˆcIdCircuitAnalysistoDeriveTransferFunctionsLZsL1CZsC+-apACModel+-+-1DcˆapVdDˆcIdESRZeroKVL,KCLResonantFrequencyDCGainBodePlotsSoWeCan“See”theResultsESRZeroDCGainResonantFrequency-80-60-40-2002040101001000100001000001000000Frequency(Hz)PowerSupplyTransferFunctions-200-180-160-140-120-100-80-60-40-200101001000100001000001000000Frequency(Hz)Gain(dB)Phase(deg)POWER4-5-6BuckConverterQCalculation-80-60-40-2002040101001000100001000001000000Frequency(Hz)PowerSupplyTransferFunctions-200-180-160-140-120-100-80-60-40-200101001000100001000001000000Frequency(Hz)Gain(dB)Phase(deg)CalculatingQincludingRcandRlCalculatingQincludingRswandRdPOWER4-5-6BuckConverterAudiosusceptibilityTransferFunctionESRZeroDCGainResonantFrequency-80-60-40-20020101001000100001000001000000Frequency(Hz)PowerSupplyTransferFunctions-200-180-160-140-120-100-80-60-40-200101001000100001000001000000Frequency(Hz)Gain(dB)Phase(deg)DPOWER4-5-6BuckConverterOutputImpedanceTransferFunctionCRcRZo(s)-60-50-40-30-20-1001020101001000100001000001000000Frequency(Hz)PowerSupplyOutputImpedancePOWER4-5-6BuckConverterInputImpedanceTransferFunctionCRcRZi(s)-60-50-40-30-20-1001020101001000100001000001000000Frequency(Hz)PowerSupplyInputImpedanceBuckConverterControlTransferFunctionDCMandCCM-80-60-40-2002040101001000100001000001000000Frequency(Hz)PowerSupplyTransferFunctions-200-180-160-140-120-100-80-60-40-200101001000100001000001000000Frequency(Hz)Gain(dB)Phase(deg)POWER4-5-6BoostConverterTransferFunctionsESRZeroDCGainResonantFrequencyRHPZero+ACModelpD1+-+-acˆapVdDˆcIdBoostConverterBodePlotsRHPZeroResonantFrequency-50-40-30-20-1001020304050101001000100001000001000000Frequency(Hz)PowerSupplyTransferFunctions-300-250-200-150-100-500101001000100001000001000000Frequency(Hz)LowLineFullLoadLowLineFullLoadHighLineLightLoadHighLineLightLoadHighLineFullLoadHighLineFullLoadPhase(deg)Gain(dB)POWER4-5-6Time-DomainResponseWithaRHPZeroOutputVoltage(V)InductorCurrent(A)D=0.5D=0.8SwitchOnLongerSwitchOnLongerSwitchOnSwitchOffSwitchOffSwitchOnDutycycleincreasesInductorcurrentincreasesimmediatelyVoltagedropsimmediatelyTime-DomainResponseWithaRHPZeroOutputVoltage(V)2302342382422462500.0000.0500.1000.1500.2000.2500.3000.3500.4000.450InductorCurrent(A)0204060801000.0000.0500.1000.1500.2000.2500.3000.3500.4000.450Time(ms)D=0.5D=0.8-50-40-30-20-1001020304050101001000100001000001000000Gain(dB)Frequency(Hz)-300-250-200-150-100-500101001000100001000001000000Phase(deg)Frequency(Hz)LowLineFullLoadLowLineFullLoadHighLineLightLoadHighLineLightLoadBoostConverterBodePlotswithDCMPOWER4-5-6LoopGainDefinitionsPhaseMargin:measureofphaseangleabove-180degreeswhengaincrossesunity(0dB)forthefinaltimePhasemarginisameasureofrelativestability.Shouldbeaminimumof50degreesforpowersupplydesignGainmarginisameasureofsensitivitytoparametervariation.Shouldbeatleast10dB101001000100001000001M-350-300-250-200-150-100-50010100100010000100000Frequency(Hz)102030-20-1001M-180GainmarginPhasemarginGainMargin:measureofgainwhenphaseisbelow-180degreesConditionallyStableLoopGainMultiple-CrossingLoopGain“Conventional”ConverterDesign+-00.511.522.50.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000Time(ms)InductorCurrent(A)37µH200µF400kHzPOWER4-5-6“Conventional”ConverterDesign+-37µH200µF400kHz-100-80-60-40-