Fundamentals of Power Electronics1Chapter 12: Current Programmed ControlChapter 12Current Programmed Control+–Buck converterCurrent-programmed controllerRvg(t)is(t)+v(t)–iL(t)Q1LCD1+–AnalogcomparatorLatchTs0SRQClockis(t)RfMeasureswitchcurrentis(t)RfControlinputic(t)Rf–+vrefv(t)CompensatorConventional output voltage controllerSwitchcurrentis(t)Control signalic(t)m1t0 dTsTson offTransistorstatus:Clock turnstransistor onComparator turnstransistor offThe peak transistor currentreplaces the duty cycle as theconverter control input.Fundamentals of Power Electronics2Chapter 12: Current Programmed ControlCurrent programmed control vs. duty cycle controlAdvantages of current programmed control:• Simpler dynamics —inductor pole is moved to high frequency• Simple robust output voltage control, with large phase margin,can be obtained without use of compensator lead networks• It is always necessary to sense the transistor current, to protectagainst overcurrent failures. We may as well use theinformation during normal operation, to obtain better control• Transistor failures due to excessive current can be preventedsimply by limiting ic(t)• Transformer saturation problems in bridge or push-pullconverters can be mitigatedA disadvantage: susceptibility to noiseFundamentals of Power Electronics3Chapter 12: Current Programmed ControlChapter 12: Outline12.1 Oscillation for D > 0.512.2 A simple first-order modelSimple model via algebraic approachAveraged switch modeling12.3 A more accurate modelCurrent programmed controller model: block diagramCPM buck converter example12.4 Discontinuous conduction mode12.5 SummaryFundamentals of Power Electronics4Chapter 12: Current Programmed Control12.1 Oscillation for D > 0.5• The current programmed controller is inherently unstable forD > 0.5, regardless of the converter topology• Controller can be stabilized by addition of an artificial rampObjectives of this section:• Stability analysis• Describe artificial ramp schemeFundamentals of Power Electronics5Chapter 12: Current Programmed ControlInductor current waveform, CCMiL(t)icm1t0 dTsTsiL(0)iL(Ts)– m2buck converterm1=vg– vL– m2=–vLboost converterm1=vgL– m2=vg– vLbuck–boost converterm1=vgL– m2=vLInductor current slopes m1and –m2Fundamentals of Power Electronics6Chapter 12: Current Programmed ControlSteady-state inductor current waveform, CPMiL(t)icm1t0 dTsTsiL(0)iL(Ts)– m2iL(dTs)=ic= iL(0) + m1dTsd =ic– iL(0)m1TsiL(Ts)=iL(dTs)–m2d'Ts= iL(0) + m1dTs– m2d'TsFirst interval:Solve for d:Second interval:0=M1DTs– M2D'TsIn steady state:M2M1=DD'Fundamentals of Power Electronics7Chapter 12: Current Programmed ControlPerturbed inductor current waveformiL(t)icm1t0 DTsTsIL0– m2– m2m1Steady-statewaveformPerturbedwaveformIL0+ iL(0)dTsD + d TsiL(0)iL(Ts)Fundamentals of Power Electronics8Chapter 12: Current Programmed ControlChange in inductor current perturbationover one switching periodiL(Ts)icm1– m2– m2m1Steady-statewaveformPerturbedwaveformdTsiL(0)magnifiedviewiL(0) = – m1dTsiL(Ts)=m2dTsiL(Ts)=iL(0) –m2m1iL(Ts)=iL(0) –DD'Fundamentals of Power Electronics9Chapter 12: Current Programmed ControlChange in inductor current perturbationover many switching periodsiL(Ts)=iL(0) –DD'iL(2Ts)=iL(Ts)–DD'= iL(0) –DD'2iL(nTs)=iL((n –1)Ts)–DD'= iL(0) –DD'niL(nTs) →0 when –DD'<1∞ when –DD'>1D< 0.5For stability:Fundamentals of Power Electronics10Chapter 12: Current Programmed ControlExample: unstable operation for D = 0.6iL(t)ict0 TsIL0iL(0)2Ts3Ts4Ts– 1.5iL(0)2.25iL(0)– 3.375iL(0)α =–DD'=–0.60.4= – 1.5Fundamentals of Power Electronics11Chapter 12: Current Programmed ControlExample: stable operation for D = 1/3α =–DD'=–1/32/3= – 0.5–18iL(0)14iL(0)–12iL(0)iL(t)ict0 TsIL0iL(0)2Ts3Ts4Ts116iL(0)Fundamentals of Power Electronics12Chapter 12: Current Programmed ControlStabilization via addition of an artificial rampto the measured switch current waveform+–Buck converterCurrent-programmed controllerRvg(t)is(t)+v(t)–iL(t)Q1LCD1+–AnalogcomparatorLatchia(t)RfTs0SRQmaClockis(t)++RfMeasureswitchcurrentis(t)RfControlinputic(t)RfArtificial rampia(t)mat0 Ts2TsNow, transistor switches offwhenia(dTs)+iL(dTs)=icor,iL(dTs)=ic– ia(dTs)Fundamentals of Power Electronics13Chapter 12: Current Programmed ControlSteady state waveforms with artificial rampiL(dTs)=ic– ia(dTs)iL(t)icm1t0 dTsTsIL0– m2– ma(ic – ia(t))Fundamentals of Power Electronics14Chapter 12: Current Programmed ControlStability analysis: perturbed waveform– maiL(Ts)iL(0)icm1t0 DTsTsIL0– m2– m2m1Steady-statewaveformPerturbedwaveformIL0+ iL(0)dTsD + d Ts(ic – ia(t))Fundamentals of Power Electronics15Chapter 12: Current Programmed ControlStability analysis: change in perturbationover complete switching periodsiL(0) = – dTsm1+ maiL(Ts)=–dTsma– m2iL(Ts)=iL(0) –m2– mam1+ maiL(nTs)=iL((n –1)Ts)–m2– mam1+ ma= iL(0) –m2– mam1+ man= iL(0) αnα =–m2– mam1+ maiL(nTs) →0 when α<1∞ when α>1First subinterval:Second subinterval:Net change over one switching period:After n switching periods:Characteristic value:Fundamentals of Power Electronics16Chapter 12: Current Programmed ControlThe characteristic value α• For stability, require | α | < 1• Buck and buck-boost converters: m2 = – v/LSo if v is well-regulated, then m2 is also well-regulated• A common choice: ma = 0.5 m2This leads to α = –1 at D = 1, and | α | < 1 for 0 ≤ D < 1.The minimum α that leads to stability for all D.• Another common choice: ma = m2This leads to α = 0 for 0 ≤ D < 1.Deadbeat control, finite settling timeα =–1–mam2D'D+mam2Fundamentals of Power Electronics17Chapter 12: Current Programmed ControlSensitivity to noiseiL(t)ict0 DTsTsSteady-statewaveformPerturbedwaveformdTs(D + d)TsicWith small ripple: a small amount of noise in the control current icleads to a large perturbation in the duty cycle.Fundamentals of Power Electronics18Chapter 12: Current Programmed ControlArtificial rampreduces sensitivity to noiseiL(t)ict0 DTsTsSteady-statewaveformPerturbedwaveformdTs(D + d)TsicArtificialrampThe same amount of noise in the control current ic leads to a smallerperturbation in the duty cycle, because the gain has been reduced.Fundamentals of Power Electronics19Chapter 12: Current Programmed Control12.2 A Simple First-Order ModelCompensator+–+–R+v(t)–vg(t)Currentprogrammedcontrollerd(t)Convertervoltages andcurrentsSwitching convertervrefic(t) v(t)Fundamentals