Department of Electrical & Electronics Engineering1 | P a g eVJIT-HYD AMain Project report on DOUBLE-FREQUENCY BUCK CONVERTER Submitted In partial fulfillment of the requirements for the award of the degree of B.TECH inElectrical & ElectronicsEngineering BY 1.N.SAI SRINIVASYASASWI 08911A0285 2.S.SRAVAN KUMAR 08911A0296 3.G.SANTHOSH09915A0208 UNDER THE GUIDANCE OF Prof. S.M. ZAFARULLAH (H.O.D, EEE)

Department Of Electrical &Electronics Engineering VIDYA JYOTHI INSTITUTE OF TECHNOLOGY (Affiliated to JNTU) AZIZNAGAR, C.B.POST, MOINABAD, HYDERABAD 500075 Department of Electrical & Electronics Engineering2 | P a g eVJIT-HYD Vidya Jyothi Institute of Technology Approved by AICTE, New Delhi & Affiliated to Jawaharlal Nehru Technological University, Hyderabad DEPARTMENT OF ELETRICAL AND ELECTRONICS ENGENEERING CERTIFICATE ThisistocertifythatMainProjectWorkentitled DOUBLE-FREQUENCYBUCKCONVERTERisabenefited workofN.SAISRINIVASYASASWI,S.SRAVANKUMAR,and G.SANTHOSHBearingRoll.nos08911A0285,08911A0296and 09915A0208submittedinpartialfulfillmentfortheawardof BACHELOROFTECHNOLOGYinELECTRICALANDELECTRONICS ENGINEERINGtoVIDYAJYOTHIINSTITUTEOFTECHNOLOGY affiliated to JNTU university, Hyderabad. The result embodied in this project has not been submitted to any other university or institute for the award of any degree or diploma. Internal GuideHead of the DepartmentT.K SRINIVAS Prof. S.M. ZAFARULLAH Assistant professor, EEE Dept Professor and HOD, EEE Dept VJIT-HYDVJIT-HYD EXTERNAL EXAMINER Department of Electrical & Electronics Engineering3 | P a g eVJIT-HYD A C K N O W L E D G E M E N T We are very much thankful to our internal Guide Sri T.K SRINIVAS Sir, Lecturer in Electrical & ElectronicsEngineeringDepartmentforhisexcellentguidanceanddeepencouragementin every step in to this project DOUBLE-FREQUENCY BUCK CONVERTER successfully. WeconveyourspecialthankfultoSriZafarullahsir,HeadofElectrical& ElectronicsEngineeringDepartmentforallthosevaluablehourstheyhasspentwithusin every possible aspect to make our project a success. We are thankful to Sri D.Srinivas, SriJyoshna and Sri Geshma , Lecturer in Electrical & electronics Engineering Department who inspired us by his enthusiastic advises from time to time and also responding for successful completion of our project. WeareveryhappytooursincerethankstoourPrincipalSrivenugopalsir,forhis valuable co-operation in the successful completion of his project. Finally I am grateful to all the staff members and lab demonstrators of EEE Dept. and those who are directly and indirectly helpful in completion of this project. By: STUDENTS OF THIS PROJECT DOUBLE-FREQUENCY BUCK CONVERTER VIDYA JYOTHI INSTITUTE OF TECHNOLOGY. During the Academic Year 2011-2012 Department of Electrical & Electronics Engineering4 | P a g eVJIT-HYD CONTENTS Abstract i List of symbols. iiList of figures. iii List of Tables.iii Chapter- 1(Introduction) 1.1Introduction. 1 1.2Organization of thesis.3 1.3Overview of thesis. 3 Chapter-2 (Basics of dc-dc converters) 2.1 Introduction. 5 2.1.1 Basics of dc-dc converters.6 2.1.2 Buck converter.92.3 Average model of Buck converter.15 2.5 Conclusion.16 Chapter-3 (Double Frequency Buck converter) 3.1 Introduction.17 3.1.1 Proposed Double frequency buck converter.19 3.2 Performance evaluation of DF buck converter.24 3.2.1 Steady state response.25 3.2.2 Transient response. 25 Department of Electrical & Electronics Engineering5 | P a g eVJIT-HYD 3.3 Proposed double frequency buck converter fed with dc motor 26 3.3.1 Buck-converter Driven Dc Motor System 27 3.3.2 Modelling of Buck-converter Dc Motor System28 chapter-4 (mat lab) 4.1 simulink:31 4.2 connecting blocks33 4.3 continuous and discrete systems: 35 4.4 making subsystems39 Chapter-5(Simulation and Simulation result) 5.1 Introduction.405.2 PI controllers40 5.2.1Limitations ofPI controllers. 46 5.3 Simulation.475.3.1 Simulation diagrams.47 5.3.2 Simulation result.525.4 Efficiency analysis.57 Chapter-6 (Conclusion and future work) 6.1 Conclusion. 60 6.2 Scope of future work. 60 References 61 Department of Electrical & Electronics Engineering6 | P a g eVJIT-HYD ABSTRACT Improvingtheefficiencyanddynamicsofpowerconvertersisaconcernedtradeoffin powerelectronics.Theincreaseofswitchingfrequencycanimprovethedynamicsofpower converters,buttheefficiencymaybedegraded.Adouble-frequency(DF)buckconverteris proposedtoaddressthisconcern.Thisconverteriscomprisedoftwobuckcells:oneworksat high frequency, and another works at low frequency. It operates in a way that current in the high-frequency switch is diverted through the low-frequency switch. Thus, the converter can operate at very high frequency without adding extra control circuits. Moreover, the switching loss of the converterremainssmall.Theproposedconverterexhibitsimprovedsteadystateandtransient responseswithlowswitchingloss.Anacsmall-signalmodeloftheDFbuckconverterisalso given to show that the dynamics of output voltage depends only on the high-frequency buck cell parameters,andisindependentofthelow-frequencybuckcellparameters.Simulationresults demonstratethattheproposedconvertergreatlyimprovestheefficiencyandexhibitsnearlythe same dynamics as the conventional high-frequency buck converter. Furthermore, the proposed topology can be extended to other dcdc converters by the DF switch-inductor three-terminal network structure. Department of Electrical & Electronics Engineering7 | P a g eVJIT-HYD List of symbols

Uin,Uon.Input and output voltage of the converter. iL,ila.Current through the high, low frequency inductor. iSD. iS .... Current through the active, diode. S, SD .High frequency active switches. Sa, Da .low frequency switch and diode. L,La.. . inductors of the double frequency buck converter. Fh, f1 high, and low frequency of the switches. Ts1,Tsh ..low and high switching time periods. MMultiple integers. Uref .Reference voltage. Uon .On state voltage of the active switch. Uf .Total time periods of the switches and diodes. IR.Load current of the converter. RLoad resistance of the converter. Ton , Toff .turn on and turn off times of the switches and diode. C ..capacitor of the converter. Psf..... the total losses of the single frequency buck converter. Pscon, Pss conduction , switching losses of the active switch.Pdcon, Psdconduction and switching of the diode. IL inductor average current in efficiency analysis. Fs ..switching frequency. Ilapk..peak to peak low frequency inductor current ripple. PconDf total conduction losses in the double frequency buck converter.PsDf total switching losses in the double frequency buck

Department of Electrical & Electronics Engineering8 | P a g eVJIT-HYD List of figuresFig.2.1.1Simple DC DC Converter. Fig:2.1.2: output voltage as a function of time. Fig2.1.3:ThetwocircuitconfigurationsofaBuckconverter:(a)Onstate,whentheswitchis closed, and (c) Off-state, when the switch is open. Fig 2.1.4: Naming conventions of the components, voltages and current of the Buck converter. Fig: 2.3.1Average model of buck converter with the added CCS. Fig(3.1.1 )Schematic of the proposed DF buck converter. Fig 3.1.2(a)Equivalent circuit ofDF buck converter when s-on,sa=on. Fig 3.1.2(b)Equivalent circuit ofDF buck converter when s-off,sa=on; Fig 3.1.2(c)Equivalent circuit of DF buck converter when s-on,sa=off; Fig 3.1.2(d)Equivalent circuit ofDF buck converter when s-off,sa=off. Fig 3.2.1 current programmed mode control circuit. Fig4.1 Simulink library browser Fig 4 .2 Connectung blocks Fig.4.2.1 Sources and sinks Fig.4.3 Continous and descrete systems Fig.4.3.1 simulink blocks Fig4.3.2 Simulink math blocks Fig4..3.3 Signals and systems Fig:4.4.1 setting simulation parameters: Fig:5.2.1 discrete PI controller. Fig 5.3.1(a)simulation model of a double frequency buck converter. Fig5.3.1(b)simulation model of a high frequency buck converter. Fig 5.3.3simulation model of a low frequency buck converter. Fig 5.3.2.(b)output voltage steady state response comparison of the double frequency, single high and low frequency buck converter. Fig5.3.2.(b)outputvoltagetransientresponsecomparisonofthedoublefrequency,singlehigh and low frequency buck converter when load is step up. Fig5.3.2.(c)outputvoltagetransientresponsecomparisonofthedoublefrequency,singlehigh and low frequency buck converter when load is step down. Fig 5.3.2(a) Switch current waveforms. List of tables, TABLE I: SWITCHING STATES. TABLE 2.1: PI CONTROLLER TUNING METHOD. TABLE 2.2: EFFECTS INCREASING PARAMETER IN PI CONTROLLER. Department of Electrical & Electronics Engineering9 | P a g eVJIT-HYD 1.INTRODUCTION 1.1Introduction TheDemandofhigh-performancepowerconverterisincreaseddramaticallywiththe broadening of power converters application elds.In order to improve the transient and steady state performance of power converters and to enhance power density, high switching frequency isaneffectivemethod.However,switchingfrequencyrisecauseshigherswitchinglossesand greater electromagnetic interference. This, in turn, limits the increase of switching frequency and hinderstheimprovementofsystemperformance.Activeandpassivesoft-switchingtechniques havebeenintroducedtoreduceswitchinglosses.Whilethesecancreatemorefavorable switchingtrajectoriesforactivepowerdevices,theywillgenerallyincreasethecomplexityof control and sometimes are affected by the variable input and output condition. In the trends of using power modules, space is limited for placing the added elements. Thecomplexityofpowerstageandcontrolcircuitalsoreducesthereliabilityofsoft-switched converters.Multiconverterparallelingmethod,whichemployslow-powerconvertersinparallel toenhancethepowerrating,hasbeenproposedtoenhancethepowerprocessingcapability. However, parallel operation has interaction problem that causes circulating current. To avoid the circulatingcurrent,approachessuchasisolation,highimpedance,andone-converterapproach are utilized. These efforts increase the control complexity. The interleaving operation employs N converters to operate inparallel with interleavedclocks, so the total dynamics can reach higher performanceduetothefactthattheequivalentfrequencyisNtimesthesingleconverter frequency. Nevertheless, the circulating current phenomenon also exists. Asingleboost-typezero-voltage-transition(ZVT)pulsewidthmodulatedconverter proposedinadoptsanadditionalshuntresonantnetworktoformanadditionalBoostcell torealizesoftswitchingofthemainswitches.However,theauxiliaryswitchesoperateinhard switchandhighfrequency.Asimilartopologyofsingle-phaserectierisgivenin,wheretotal harmonic distortion of the input line current is reduced and the efficiency improved. Its operation is different from the ZVT circuit. Department of Electrical & Electronics Engineering10 | P a g eVJIT-HYD Theboost-typetopologyhowever,isnotveryeffectivetoenhancetheoutputvoltage performancethatthecapacitorripplevoltageisdeterminedbythelowfrequency.Hence,this topology is not in suitable for improvement of dc output transient and steady state performances. Moreover, the mainBoost circuit and the added cell are coupled, and the added Boostcell has aneffectontheinductorcurrentinput.Splittingthelterinductorofbuckconverterintotwo partswithaddedauxiliaryactiveswitchanddiodehasbeenproposedtoimprovetheoutput voltageresponseatloadcurrentstep-downtransientsituation,butnotatloadcurrentstep-up transient situation. Additional transformer and switches are needed to realize the improvement at step-uptransienttomakethecircuits.functionasdesigned,itisrequiredtodetecttheload transient event, then to trigger or shut down the auxiliary switch. This increases the complexity of the control circuit. Moreover,oscillationsattheoutputvoltageoccurduetothefrequentonandoff operationsateachtransientevent.Ontheotherhand,high-frequencyswitchingconverteror linear power supply in parallelwith low-frequencyconverter proposed and enhances the output voltageresponse. Paralleling high-frequency converterapproach also requires the load transient information,whilelinearpowersupplymethodsuffersfromlowefficiency.Moreover,the parallel structure brings about the circulating current problem. Additional current sharing control is needed to overcome this problem. Morevertoovercomethisproblemsweareproposesanovelconvertertopologyto achievehighdynamicresponseandhighefficiencyofbuck-typeconverters.Thistopology consists of a high-frequency buck cell and a low-frequency buck cell; and we call it the double- frequencybuckconverter(DFbuck).Thecurrentowingthroughthehigh-frequencycellis divertedbythelowfrequencyone,whichalsoprocessesthemajorityoftheconverterpower. This current decreases rapidly so that the high-frequency cell can work at very high frequency to improvethedynamicresponse.Furthermore,theefficiencyisenhancedduetothelow-current processing requirement of the high-frequency cell in the DF buck converter. Unlike the parallel structure, the proposed converter does not incur the circulating current problem. Moreover, it is notrequiredtodetecttheloadtransienteventforcontrol.Thecircuitcongurationandcontrol strategywillbedescribedindetail.Thefrequency-domainandtime-domainanalysesaregiven Department of Electrical & Electronics Engineering11 | P a g eVJIT-HYD to show that the proposed topology has the same transient and steady state performance with the single high-frequency buck converter. 1.2Organization of thesis: Chapter 2: This chapter deals with basics of DC DC Converters, Buck Converter, Average model of Buck Converter. Chapter 3: This chapter deals with Double Frequency Buck Converter. Chapter 4: This chapter deals withMat lab introduction Chapter 5: This chapter deals with Simulation model,Results and Efficiency Analysis. Chapter 6: This chapter deals with Conclusion and Future Scope. 1.3 Overview of Project: The buck converter works in the continuous conduction mode, then the inductor current iL can be regarded as a current source. In each switching cycle, both the current flowing through the switch and the voltage across the diode are averaged. To enhance the steady-state response and the transient response of the buck converter, the switching frequency should be increased; but higher switching frequency steps up theswitching loss dramatically. An CCS, which is in parallel with the load terminal, is added to tackle this loss problem. Fig.2 shows such modication.The load current through the active switch is diverted by the CCS. The propose to use a buck cell working at lower frequency to realize the CCS. The proposed converter is called the DF buck converter, because these buck cells work at two different frequencies. Schematic of this DF buck converter is shown in Fig. 3. The cell containing L, S , and SD works at higher frequency, and is called the high-frequency buck cell. Another cell containing La, Sa, and Da works at lower frequency, and is called the low-frequency buck cell. The high frequency buck cell is used to enhance the output performance, and the low-frequency buck cell to improve the converter efficiency. An Department of Electrical & Electronics Engineering12 | P a g eVJIT-HYD active switch, instead of a diode as in the conventional unidirectional buck converter, is employed to realize SD in the high frequency buck cell. This active switch transfers the energy stored in the low-frequency cell to the source during the transient stage of load step-down. It works complementarily with high-frequency cell stage of load step-down. It works complementarily with high-frequency cell switch S , and improves the transient response. The efficiency expression is analyzed in the double frequency buck converter. The analysis is also applied to the single high frequency buck and low-frequency buck converters. A simple loss model is adopted here in that we just want to show the efficiency relationship between the DF buck and single high-frequency buck, not to develop a new loss model. In the analysis, we have the following assumptions; 1.Theconductionlossesofactiveswitchanddiodeareestimated,respectively, according to their conduction voltages Uon and UF. 2.Theswitchingtransientprocessesareassumedtosatisfythelinearcurrentand voltage waveforms. Moreover, the turn-on time ton is the same for all switches and diodes, so is the turn-off time to . 3.Sincetheswitchinglossusuallydominatesthetotalloss,lossesoftheoutput capacitor and output inductor are not calculated here. This result also can be reasoned from the fact that the total currents owing through the DF buck switches and diodes are the same as that through a single-frequency buck. On the other hand, the total switching loss is nearly the same as the single low-frequency buck, and is much smaller than that of the single high-frequency buck. Hence, the DF buck converter im proves the efficiency by current diversion to the low-frequency cell. Although assumptions and approximations are made in the aforementioned analysis, it reveals the efficiency mechanism of the DF buck converter. Department of Electrical & Electronics Engineering13 | P a g eVJIT-HYD Chapter--2 (Basics of DC to DC Converters): 2.1 Introduction: Adc-to-dcconverterisusedtochangethedcvoltagefromoneleveltoanother.Inthis case,thedcinputvoltageisfixedandthelevelofthedcoutputvoltagedependsuponthe converters topology. The dc output voltage can be higher or lower than the input voltage since the advent of diodes; the techniques have been developed to obtain the dc voltage from the time-varying sinusoidal (ac) supply. The half-wave rectifier and the bridge rectifier are used to obtain dc voltage from a single-phase time-varying source. To control the ripple of the rectified output voltage,largecapacitorfiltersareused.Thesecircuitsnowreferredtoasthelinearregulators, operateatthefrequencyoftheacvoltage,whichisusuallyeither50Hzor60Hz.Untilabout twoorthreedecadesago,thelinearregulatorsweretheonlyreliablemethodstomeetalldc requirements.Someofthemajorproblemsassociatedwiththelinearregulatorisitssizeand weight of its components such as the transformer. The voltage regulator element in these circuits hasacomparativelyhighvoltageacrossitsterminalsanddissipateslargeamountsofpower, which results in low efficiency. For this very reason, the use of linear regulators is now limited to low power applications. Asthepowersemiconductordevicesbecamemorereliableandefficientintheir operation, the switchedmode power suppliescame into existence.In the design of these power supplies,thesemiconductordevicesareeitherswitchedonorswitchedoff.Duetothelow voltagedropacrossthesemiconductordevicewhenitison,itspowerconsumptionislow.For thisreason,theswitchedmodepowersuppliesarehighlyefficient.Sincetheswitchingaction, whichsimplymeanstoturnapowersemiconductordeviceeitheronoroff,isusuallydoneat highfrequencies,therelativesizeandweightofthecomponentsneededforitsdesignis comparativelysmall.Inthischapter,ouraimistoobtainadcoutputvoltage,whichmaybe higher or lower, from a fixed dc input voltage. A very simple scheme that illustrates the principle is shown in Figure. In this case, the dc voltage applied to the resistor is controlled via a switch, which is usually a power semiconductor device such as an SCR, a BJT, a MOSFET, an IGBT, etc.

Department of Electrical & Electronics Engineering14 | P a g eVJIT-HYD Fig.2.1.1Simple DC DC Converter switch is closed for a fraction of the time period T and is kept open for the remainder period. Let us say that the switch is turned on at t = 0 and remon time thedutycycle.Theoutputvoltageobtainedbyopeningandclosingoftheswitchisshownin Figure 2.1.1

Fig:2.1.2: output voltage as a function of time Thetimeduringwhichtheswitchremainsclosediscustomarilyreferredtoastheofftime (period). We can express the off time in terms of the duty cycle as Toff = (1-D) T. 2..1.1 The average output voltage may be computed as 2.1.2 Substituting, D = Ton/T, the output voltage in terms of the duty cycle isV0 = D Vs2.1.3 Inthiscase,theoutputvoltageisdirectlyproportionaltothedutycycle.Itis thereforeevidentthattheoutputvoltageislessthantheinputvoltage.Foranidealswitch,the efficiency of the dc-to-dc converter is 100%. This simple circuit can be designed to meet the dc Department of Electrical & Electronics Engineering15 | P a g eVJIT-HYD output-voltagerequirements.However,ithasonemajordrawback.Itspercentvoltagerippleis 100%. The output voltage with such a high ripple content may be satisfactory for electric heaters, lightdimmingcircuits,etc.,itiscertainlynotsuitablefortheoperationofamplifiersandother circuitsrequiringalmostconstantdcvoltage.Thehighvoltageripplecanbecontrolledby placing a capacitor across the load. Thecapacitorislargeenoughsothatitsvoltagedoesnothaveanynoticeable change during the time the switch is off. Somewhat better circuit can be developed by including an inductor, which is in series with the switch when the switch is on (closed), to limit the current in rush. However, this creates another problem. Since the current in the inductor cannot change suddenly, we have to provide at least one moreswitch, such a freewheeling diode, to provide a pathfortheinductorcurrentwhentheswitchisoff(open).Insummary,agooddc-to-dc converter may have, an inductor, a capacitor, and a freewheeling diode, and an electronic switch. Theplacementoftheseelementsinacircuitdictatestheperformanceofthecircuit.Thethree configurationsthatutilizethesecircuitelementsare(a)BuckConverter(loweringtheoutput voltage,step-downapplication),(b)BoostConverter(raisingtheoutputvoltage,step-up application), and (c) Buck-Boost Converter (lowering or raising the output voltage, step-down or step up application). But in these configurations, the energy transfer is not continuous. In the Buck converter, the energy transfer fromthe input to the output side occurs when the static switch is in the ON state.IntheBoost&Buck-Boostconverters,thistransfertakesplacewhenthestaticswitchis turnedOFF.Weovercomethislimitationbyprovidingadequatefiltering.Thefilterconsistsof energystorageelementssuchasaninductororcapacitororboth,whichserveasreservoirsof energy and ensure that the flow of energy into the load is continuous and ripple-free Incontrasttotheabove,threemoreconfigurationsweredevelopedinwhich energy transfer from input to the output occurs both during the ON time and the OFF time of the static switch. They are: Cuk converter, Sepic converter, Zeta converter. Theconverterhasbeenrealizedusinglosslesselements.Totheextentthatthey are ideal, the inductor, capacitor, and switch do not dissipate power. Hence, the efficiency of the converterapproaches100%.Butinrealcase,noneofthecomponentsareideal,thereforeto reachtherealefficiencyoftheDC-DCconverterthelossesofeachcomponentshouldbe Department of Electrical & Electronics Engineering16 | P a g eVJIT-HYD considered.DutyratioDisthecontrolparameterinDC-DCconverterelectronics.Inmostcases,Dis adjusted to regulate the output voltage, Vout. 2.1.1 Types of DC to DC Converters: Buck Converter Boost Converter Buck Boost Converter Cuk Converter

Buck converter: A buck converter is a step-down DC to DC converter. Its design is similar to the step-upboostconverter,andliketheboostconverteritisaswitched-modepowersupplythat uses two switches (a transistor and a diode) and an inductor and a capacitor. ThesimplestwaytoreduceaDCvoltageistouseavoltagedividercircuit,but voltagedividerswasteenergy,sincetheyoperatebybleedingoffexcesspowerasheat;also, outputvoltageisn'tregulated(varieswithinputvoltage).Abuckconverter,ontheotherhand, can be remarkably efficient (easily up to 95% for integrated circuits) and self-regulating, making it useful for tasks such as converting the 12-24V typical battery voltage in a laptop down to the few volts needed by the processor. Buck Converter Operation:

(a)Buck Converter circuit

(b)On state, when the switch is closed Department of Electrical & Electronics Engineering17 | P a g eVJIT-HYD (c)Off-state, when the switch is open Fig 2.1.3: The two circuit configurations of a Buck converter: (a)On state, when the switch is closed, and (c) Off-state, when the switch is open. Theoperationofthebuckconverterisfairlysimple,withaninductorandtwoswitches (usuallyatransistorandadiode)thatcontroltheinductor.Italternatesbetweenconnectingthe inductortosourcevoltagetostoreenergyintheinductoranddischargingtheinductorintothe load. Fig 2.1.4: Naming conventions of the components, voltages and current of the Buck converter. Continuous mode: ABuckconverteroperatesincontinuousmodeifthecurrentthroughtheinductor(IL) neverfallstozeroduringthecommutationcycle.Inthismode,theoperatingprincipleis described by the chronogram in figure 2.1.5

Department of Electrical & Electronics Engineering18 | P a g eVJIT-HYD Fig2.1.5:Voltages&currentswaveformswithtimeinanidealBuckconverter continuous mode-When the switch pictured above is closed, the voltage across the inductor is VL = Vi Vo. Thecurrentthroughtheinductorriseslinearly.Asthediodeisreverse-biasedbythe voltage source V, no current flows through it;-When the switch is opened, the diode is forward biased. The voltage across the inductor is VL = Vo (neglecting diode drop). The current IL decreases.The energy stored in inductor L is

2.1.4 Therefore,itcanbeseenthattheenergystoredinLincreasesduringOn-time(asIL increases) and then decrease during the Off-state.L is used to transfer energy from the inputto the output of the converter. The rate of change of IL can be calculated from:

2.1.5 WithVLequaltoViVoduringtheOn-stateandtoVoduringtheOff-state.Therefore,the increase in current during the On-state is given by:

(

)

2.1.6 Identically, the decrease in current during the Off-state is given by:

(

)

2.1.7 Ifweassumethattheconverteroperatesinsteadystate,theenergystoredineach componentattheendofacommutationcycleTisequaltothatatthebeginningofthecycle. That means that the current IL is the same at t=0 and at t=T (see figure 2.2.3). Department of Electrical & Electronics Engineering19 | P a g eVJIT-HYD Therefore,

2.1.8 So we can write from the above equations as:

(

)

(

)

2.1.9It is worth noting that the above integrations can be done graphically: In figure 4, is proportionaltotheareaoftheyellowsurface,andtotheareaoftheorangesurface,as thesesurfacesaredefinedbytheinductorvoltage(red)curve.Asthesesurfacesaresimple rectangles,theirareascanbefoundeasily:fortheyellowrectangleandfor the orange one. For steady state operation, these areas must be equal.As can be seen on figure 3, ton = DT&toff = D DT. D is a scalar called the duty cycle with a value between 0 and 1. This yields: (

)

()2.1.10 This equation above can be rewritten as:V0 = D.Vi2.1.11 That yields a duty cycle being: 2.1.12 From this equation, it can be seen that the output voltage of the converter varies linearly with the duty cycle for a given input voltage. As the duty cycle D is equal to the ratio between ton andtheperiodT,itcannotbemorethan1.Therefore,.Thisiswhythisconverteris referred to as step-down converter. So,forexample,stepping12vdownto3v(outputvoltageequaltoafourthoftheinput voltage) would require a duty cycle of 25%, in our theoretically ideal circuit. Department of Electrical & Electronics Engineering20 | P a g eVJIT-HYD Discontinuous mode: Insomecases,theamountofenergyrequiredbytheloadissmallenoughtobe transferred in a time lower than the whole commutation period. In this case, the current through the inductor falls to zero during part of the period. The only difference in the principle described above is that the inductor is completely discharged at the end of the commutation cycle. This has, however, some effect on the previous equations. Fig 2.1.6: Voltages and currents with time in an ideal Buck converter discontinuous mode. We still consider that the converter operates in steady state. Therefore, the energy in the inductoristhesameatthebeginningandattheendofthecycle(inthecaseofdiscontinuous mode, it is zero). This means that the average value of the inductor voltage (VL) is zero, i.e., that the area of the yellow and orange rectangles in figure 2.1.6 are the same. This yields: (

)

2.1.13Sothevalueofis:

2.1.14 Department of Electrical & Electronics Engineering21 | P a g eVJIT-HYD Theoutputcurrentdeliveredtotheload(Io)isconstant;asweconsiderthattheoutput capacitorislargeenoughtomaintainaconstantvoltageacrossitsterminalsduringa commutationcycle.Thisimpliesthatthecurrentflowingthroughthecapacitorhasazero average value. Therefore, we have: IL = I0 2.1.15 Where is the average value of the inductor current. As can be seen in figure 2.2.6, the inductor currentwaveformhasatriangularshape.Therefore,theaveragevalueofILcanbesortedout geometrically as follow:

(

)

()

2.1.16 TheinductorcurrentiszeroatthebeginningandrisesduringtOnuptoILmax.Thatmeansthat ILmax is equal to:

(

)

2.1.17 Substituting the value of ILmax in the previous equation leads to:

(

) ()

2.1.18 Substituting in the above expression yields:

(

) (

)

2.1.19 This latter expression can be written as: Department of Electrical & Electronics Engineering22 | P a g eVJIT-HYD

2.1.20 ItcanbeseenthattheoutputvoltageofaBuckconverteroperatingindiscontinuous modeismuchmorecomplicatedthanitscounterpartofthecontinuousmode.Furthermore,the output voltage is now a function not only of the input voltage (Vi) and the duty cycle D, but also of the inductor value (L), the commutation period (T) and the output current (Io). 2.2 Average model of buck converter with the added CCS: ThetopologyofaconventionalbuckconverterInthesteadystate,theinput(uin)andthe output (uin) of the converter are governed by Uo = D Uin(2.2.1) Fig: 2.3.1 Average model of buck converter with the added CCS where D is the duty ratio .If the buck converter works in the continuous conduction mode, then theinductorcurrentiLcanberegardedasacurrentsource.Ineachswitchingcycle,boththe currentflowingthroughtheswitchandthevoltageacrossthediodeareaveraged.Theaverage model of buck converter is, shown in Fig.(2.3.1), excluding the added controlled current source (CCS) ILa, and its governing equations are, IS = D IL (2.2.2) UD = D Uin (2.2.3) ISD = (1 D) IL (2.2.4) Department of Electrical & Electronics Engineering23 | P a g eVJIT-HYD To enhance the steady-state response and the transient response of the buck converter, the switching frequency should be increased; but higher switching frequency steps up theswitching loss dramatically. An CCS, which is in parallel with the load terminal, is added to tackle this loss problem. Fig.2 shows such modication.The load current through the active switch is diverted by the CCS. The currents through the active switch and the diode can be expressed as, I

S = D (IL ILa)(2.2.5) I'SD=(1D) (ILILa). (2.2.6) It can be seen from (5) and (6) that when the load current and the CCS are the same, both the currents through the active switch and the diode are nearly zero. 2.3 Conclusion: To enhance the steady-state response and the transient response of the buck converter, theswitchingfrequencyshouldbeincreased;buthigherswitchingfrequencystepsupthe switchinglossdramatically.AnCCS,whichisinparallelwiththeloadterminal,isaddedto tackle this loss. ButthedisadvantageofCCS(controlledcurrentsource),whichisinparallelwiththe loadterminalcausesacirculatingcurrentproblem.Toovercomethisprobleminsteadof ccs the method proposed to use a buck cell working at lower frequency to realize the CCS. The proposed converter is called the Double Frequency buck converter. Department of Electrical & Electronics Engineering24 | P a g eVJIT-HYD Chapter-3 3 Proposed double frequency buck converter3.1 Introduction Improving the efficiency and dynamics of power converters is a concerned tradeoff in powerelectronics.Theincreaseofswitchingfrequencycanimprovethedynamicsofpower converters,buttheefficiencymaybedegraded.Adouble-frequency(DF)buckconverteris proposedtoaddressthisconcern.Thisconverteriscomprisedoftwobuckcells:oneworksat high frequency, and another works at low frequency. It operates in a way that current in the high-frequency switch is diverted through the low-frequency switch. Thus, the converter can operate at very high frequency without adding extra control circuits. Moreover, the switching loss of the converterremainssmall.Theproposedconverterexhibitsimprovedsteadystateandtransient responseswithlowswitchingloss.Anacsmall-signalmodeloftheDFbuckconverterisalso given to show that the dynamics of output voltage depends only on the high-frequency buck cell parameters,andisindependentofthelow-frequencybuckcellparameters.Simulationand experimental results demonstrate that the proposed converter greatly improves the efficiency and exhibits nearly the same dynamics as the conventional high-frequency buck converter To enhance the steady-state response and the transient response of the buck converter, theswitchingfrequencyshouldbeincreased;buthigherswitchingfrequencystepsuptheswitchinglossdramatically.Forthesepurposeanovelconvertertopologyusedtoachievehigh dynamic response and high efciency of buck-type converters. This topology consists of a high-frequencybuckcellandalow-frequencybuckcell;andwecallitthedouble-frequencybuck converter (DF buck) Department of Electrical & Electronics Engineering25 | P a g eVJIT-HYD 3.1.1Proposed double frequency buck converter:

Fig(3.1.1 )Schematic of the proposed DF buck converter.

The proposedconverter is called the Double Frequency(DF) buck converter, because these buck cells work at two different frequencies. Schematic of this DF buck converter is shown in Fig. 3.1.1. ThecellcontainingL,S,andSDworksathigherfrequency,andiscalledthehigh-frequencybuckcell.AnothercellcontainingLa,Sa,andDaworksatlowerfrequency,andis calledthelow-frequencybuckcell.Thehighfrequencybuckcellisusedtoenhancetheoutput performance,andthelow-frequencybuckcelltoimprovetheconverterefficiency.Anactive switch,insteadofadiodeasintheconventionalunidirectionalbuckconverter,isemployedto realizeSDinthehighfrequencybuckcell.Thisactiveswitchtransferstheenergystoredinthe low-frequencycelltothesourceduringthetransientstageofloadstep-down.Itworks complementarilywithhigh-frequencycellstageofloadstep-down.Itworkscomplementarily with high-frequency cell switch S , and improves the transient response. The switch S is controlled to operate at the high frequency fh, and the corresponding switchingperiodisTsh.Ontheotherhand,theswitchSaiscontrolledtoworkatalow frequency fl ,and the corresponding switching period is Tsl. Assume that the high frequency is an integer multiples of the low frequency, i.e., fh = M f1. (3.1.1) Ateachlow-frequencycycle,fourswitchingstatesexistTableIliststheswitching states according to the status of switches S and Sa The state a denotes that both switches S and Sa Department of Electrical & Electronics Engineering26 | P a g eVJIT-HYD areon.TheequivalentcircuitisshowninFig.3.1.2(a).Inasimilarmanner,theequivalent circuits of states b, c, and d are shown in Fig.3.1.2(b)(d), respectively.

TABLE I SWITCHING STATES State Active Switches SSa aONON bOFFON cONOFF dOFFOFF

State a :

Fig 3.1.2(a)Equivalent circuit ofDF buck converter when s-on,sa=on. In this state, the voltage uL across the inductor L is positive, and the voltage uLa across La is zero. Hence, the current iLowing throughLrises,and thecurrent iLaowing throughLa does not change. The governing equations of statea are expressed as uL =UinU0(3.1.2)

(3.1.3) uLa=0 (3.1.4) Department of Electrical & Electronics Engineering27 | P a g eVJIT-HYD

(3.1.5)

State b : Fig 3.1.2(b)Equivalent circuit ofDF buck converter when s-off,sa=on; Atthisstate,thevoltageuLacrossLisnegative,sothecurrentiLdecreases.The voltage uLa across La is positive, and the current iLaowing through La rises. The governing equations of state bcan be described byuL=-U0 (3.1.6)

(3.1.7) uLa = Uin(3.1.8)

(3.1.9) State c :

Fig 3.1.2(c) Equivalent circuit of DF buck converter when s=on, sa=off; Department of Electrical & Electronics Engineering28 | P a g eVJIT-HYD The voltage uL across L is positive, so the current iL rises. Since the voltage uLa across La is negative, the current iLa through La decreases.In state c, the equivalent circuit equations are derived as, uL =UinU0 (3.1.10)

(3.1.11) uLa =- Uin (3.1.12)

(3.1.13)

State d : Fig 3.1.2(d)Equivalent circuit ofDF buck converter when s-off, sa=off;

In state d, the equivalent circuit equations are derived as uL = - U0(3.1.14)

(3.1.15) ULa = 0(3.1.16)

(3.1.17) The voltage uL across L is negative, so the current iL owing through L decreases. The voltage uLa across La is zero, and the current iLa owing through La remains the same. ThecurrentiLaowingthroughLaremainsthesamecelldoesnotaffecttheoutput inductorvoltage,whichhasthesamewaveformandvalueasthatoftheconventionalbuck converter. That is, the voltage across the output inductor is Uin Uo when the switch is on, and is Uo when the switch is off. The voltage and current waveforms of DF buck in one low frequency Department of Electrical & Electronics Engineering29 | P a g eVJIT-HYD cycle Tsl are shown in Fig. 5, where M = 4. In the conduction mode of low-frequency switch, the voltage across the low-frequency inductor La alternates between zero and Uin.Thus, the equivalent slope of the current iLa is positive. At the switch-off interval, uLa varies from zero to Uin, the equivalent slope of iLa becomes negative. As a result, if we employ propercontrolmethod,thelow-frequencyinductorcanbecontrolledtofollowtheoutput inductor current. Fig3.1.3: Voltage and current waveforms in one switching period Tsl. Department of Electrical & Electronics Engineering30 | P a g eVJIT-HYD 3.2Performance evaluation of double frequency buck converter: Thecurrentprogrammedmode(CPM)controlcircuitusedtocontroltheproposedDF buck converter is shown in Fig.3.2.1. In the control diagram, the output voltage is fed back and compared with Uref . The quantity Rf ic is used as the current reference for the buck cells. The currentsowingthroughinductorsLandLaareexpectedtobeequaltothisreferencevaluein the steady state. The low-frequency buck cell diverts the current owing through high-frequency switchesSandSD.Thiscontrolcircuit,likestandardcurrentmodecontrol,doesnotneed additional load transient information, which is not the case in other methods. Since no specic control circuit is required, complexity of the control circuitry of the DF buckconverterissimilartothatoftheconventionalbuckconverter.Theimplementationis simple and can be done by commercial CPM chips. Fig 3.2.1 current programmed mode control circuit Department of Electrical & Electronics Engineering31 | P a g eVJIT-HYD 3.2.1 Steady state performance: PerformanceoftheDFbuckconverterisevaluatedbylookingatthesteady-stateand transientresponsesofthreecircuitsaDFbuck,asinglehigh-frequencybuckconverterwhose switching frequency is the same as the higher frequency of DF buck, and a single low-frequency buckconverterwhoseswitchingfrequencyisequaltothelowerfrequencyofDFbuck. Parameters used in the simulation are uin = 48 V,Uo = 10 V, C= 470 F DF buck : L = 100 H, La = 1 mH, fl = 10 kHz fh = 100 kHz High-frequency buck : L = 100 H,f= 100 kHz Low-frequency buck :La = 1 mH,f= 10 kHz. Inthesteadystatewecanobservethatoutputvoltagewaveformsofvariousbuck converters. It can be seen that the steady state performance of DF buck and that of single high-frequency buck converter are almost the same 3.2.2 Transient Performance Analysis ThissectioninvestigatesthetransientresponseoftheDFbuckconverter.Iftheload resistanceisreducedfrom2RtoR,theloadcurrentwillincreasefrom0.5IRtoIR.Sincethe currentsthroughinductorLandLacannotchangeabruptly,atthistransientinstant,theoutput voltagedecreasesduetotheincreasedloadcurrentthatispartiallysuppliedbytheoutput capacitor.Thefeedbackcontrolloopregulatesthedutyratioofeachbuckcelltocontrolthe currentofinductorL,iL,andthecurrentofLa,iLa.Itincreasesthedutyratioofthehigh frequencyswitchsothatiLrisesThen,iLarisestoo.Notethatthelow-frequencyinductanceis selected to be larger than the high-frequency one to reduce the current ripple of iLa .Department of Electrical & Electronics Engineering32 | P a g eVJIT-HYD Iftheinductorhaslargerinductance,thecurrentowingthroughitwillhave lower dynamic response speed with the same voltage excitation. As shown in Fig. 5, when low-frequency switch is on, the averagevoltage applied to low-frequency inductor is(1d) times the inputvoltageUin.Thisisthesameasthevoltageacrossthehigh-frequencyinductor,UinUo, when high-frequency switch is on. On the other hand, when the low-frequency switch is off, the averagevoltageacrosslowfrequencyinductorisdtimesUin.Thisaveragevoltageisalsothe sameasthatacrossthehigh-frequencyinductorwhenhigh-frequencyswitchisoff.Hence,iLa risesslowerthaniL.Moreover,thecurrentthroughthehigh-frequencyswitchincreases momentarily, but soon back to the steady state level due to the current feedback loop. IftheloadresistanceisincreasedfromRto2R,thentheloadcurrentwill decrease from IR to 0.5 IR , so is the low-frequency inductor current iLa . At this moment, iLa can freewheel through SD when the switch S is off. When S is on, the energy stored in La can be fed back to the source via the switch S .Asaresult,theimpacttooutputresponsebythelow-frequencyinductoris largely alleviated. it is observed that the DF buck and the single high-frequency buck converters exhibitalmostthesametransientresponsesduringloadchanging,andmuchbetterthanthe singlelow-frequencybuckconverterdoes.Theeffectofswitchcurrentdiversionofthehigh-frequency cell and the low frequency cell is also investigated 3.3 Proposed double frequency buck converter fed with dc motorDcmotorhasgoodspeedcontrolrespondence,widespeedcontrol range. It is widely used in speed control systems which need high control requirements, such asrollingmill,double-hulledtanker,andhighprecisiondigitaltools.Whenitneedscontrolthe speed stepless and smoothness, the mostly usedway is to adjust the armature voltage of motor. One of the most common methods to drive a dc motor is by using PWM signals with respect to the motor input voltage. However, theunderlying hard switching strategy causes unsatisfactory dynamic behavior. The resulting trajectories exhibit a very noisy shape. This causes large forces actingonthemotormechanicsandalsolargecurrentswhichdetrimentallystresstheelectronic components of the motor as well as of the power supply. Since it is usuallynecessary to add a power supply component, anyway, this contribution shall present a control for the entire systemDepartment of Electrical & Electronics Engineering33 | P a g eVJIT-HYD ofbuck-converter/dcmotor.Thecombinationofdctodcpowerconverterswithdcmotorshas been reported. In particular, the composition of a buck converter with adc motor has been proposed. The buck typeswitcheddctodcconverteriswellknowninpower-electronics.Duetothefactthatthe converter contains two energy storing elements, a coil and a capacitor, smooth dc output voltages andcurrentswithverysmallcurrentripplecanbegenerated.Thecontrolissueofthe converter/motor is to design the controller sothat the dc motor can track a prescribed trajectory velocitypreciselywithminimumerror.Inordertoachievetheseobjectives,variousmethods usingdifferenttechniquehavebeenproposed.DCmachinesareextensivelyusedinmany industrialapplicationssuchasservocontrolandtractiontasksduetotheireffectiveness, robustnessandthetraditionalrelativeeaseinthedevisingofappropriatefeedbackcontrol schemes,especiallythoseofthePIandPIDtypes.Theincreasingavailabilityoffeedback controller design techniques and the rapid development of circuit simulations programs, such as PSpice,offermuchwiderpossibilitiestoanalyze,andredesign,currentlyuseddcmotordrivesystems..Thesmoothtrajectoryinputtrackingusingdynamicfeedbackcontrollerforbuck-converter 3.3.1 Buck-converter Driven Dc Motor System: The simplified model of the overall system buck-converter driven dc motor is shown in Figure 1. Theswitchingdeviceshavebeenreplacedbyanideallyswitchedvoltagesource.Thisis indicated by the multiplication of Ue withthe switching variableAn additional resistanceR Lcoil windings. The motor has been modeled byan inductanceL Mwith ohmic resistance R Mand electromagnetic voltage sourceK EAn input voltageU ehas been used which value is equal to the maximum voltage of the dc motor. In this st udy, the buck converter circuit with coil inductance, L, coil resistance,R Land capacitance,Cis considered. Department of Electrical & Electronics Engineering34 | P a g eVJIT-HYD 3.3.2 Modelling of Buck-converter Dc Motor System: This section provides a brief description on the modelling of the buck-converter driven dc motor, as a basis of a simulation environment for development and assessment of the proposed control techniques.Thedynamicsystemcomposedfromconverter/motorisconsideredinthis investigation and derived in the transfer function and state-space forms. Considering the dynamic system of the convert er/motor, the system can be modelled as Advantages of DC motor: Ease of control Deliver high starting torque Near-linear performance Disadvantages: High maintenance Large and expensive (compared to inductionmotor) Not suitable for high-speed operation due tocommutator and brushes Not suitable in explosive or very clean Environment

Department of Electrical & Electronics Engineering35 | P a g eVJIT-HYD CHAPTER-4 MATLAB Matlabisahigh-performancelanguagefortechnicalcomputing.Itintegrates computation, visualization, and programming in an easy-to-use environment where problems and solutionsareexpressedinfamiliarmathematicalnotation.TypicalusesincludeMathand computationAlgorithmdevelopmentDataacquisitionModeling,simulation,andprototyping Dataanalysis,exploration,andvisualizationScientificandengineeringgraphicsApplication development, including graphical user interface building. Matlab is an interactive system whose basic data element is an array that does not require dimensioning.Thisallowsyoutosolvemanytechnicalcomputingproblems,especiallythose with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar no interactive language such as C or Fortran.Thenamematlabstandsformatrixlaboratory.Matlabwasoriginallywrittentoprovide easyaccesstomatrixsoftwaredevelopedbythelinpackandeispackprojects.Today,matlab enginesincorporatethelapackandblaslibraries,embeddingthestateoftheartinsoftwarefor matrix computation.Matlabhasevolvedoveraperiodofyearswithinputfrommanyusers.Inuniversity environments,itisthestandardinstructionaltoolforintroductoryandadvancedcoursesin mathematics,engineering,andscience.Inindustry,matlabisthetoolofchoiceforhigh-productivity research, development, and analysis.Matlabfeaturesafamilyofadd-onapplication-specificsolutionscalledtoolboxes.Very importanttomostusersofmatlab,toolboxesallowyoutolearnandapplyspecialized technology.Toolboxesarecomprehensivecollectionsofmatlabfunctions(M-files)thatextend thematlabenvironmenttosolveparticularclassesofproblems.Areasinwhichtoolboxesare availableincludesignalprocessing,controlsystems,neuralnetworks,fuzzylogic,wavelets, simulation, and many others.The matlab system consists of five main parts:Department of Electrical & Electronics Engineering36 | P a g eVJIT-HYD Development Environment. This is the set of tools and facilities that help you use matlab functionsandfiles.Manyofthesetoolsaregraphicaluserinterfaces.Itincludesthematlab desktopandCommand Window,acommandhistory,aneditoranddebugger,andbrowsersfor viewing help, the workspace, files, and the search path. ThematlabMathematicalFunctionLibrary.Thisisavastcollectionofcomputational algorithms ranging from elementary functions, like sum, sine, cosine, and complex arithmetic, to moresophisticatedfunctionslikematrixinverse,matrixeigenvalues,Besselfunctions,andfast Fourier transforms. ThematlabLanguage.Thisisahigh-levelmatrix/arraylanguagewithcontrolflow statements, functions, data structures, input/output, and object-oriented programming features. It allows both "programming in the small" to rapidly create quick and dirty throw-away programs, and "programming in the large" to create large and complex application programs. Matlabhasextensivefacilitiesfordisplayingvectorsandmatricesasgraphs,aswellas annotatingandprintingthesegraphs.Itincludeshigh-levelfunctionsfortwo-dimensionaland three-dimensionaldatavisualization,imageprocessing,animation,andpresentationgraphics.It also includes low-level functions that allow you to fully customize the appearance of graphics as well as to build complete graphical user interfaces on your matlab applications.ThematlabApplicationProgramInterface(API).Thisisalibrarythatallowsyouto write C and Fortran programs that interact with matlab. It includes facilities for calling routines frommatlab(dynamiclinking),callingmatlabasacomputationalengine,andforreadingand writing MAT-files. Department of Electrical & Electronics Engineering37 | P a g eVJIT-HYD 4.1 SIMULINK: INTRODUCTION: Simulink is a software add-on to matlab which is a mathematical tool developed by The Mathworks,(http://www.mathworks.com)acompanybasedinNatick.Matlabispoweredby extensivenumericalanalysiscapability.Simulinkisatoolusedtovisuallyprogramadynamic system(thosegovernedbyDifferentialequations)andlookatresults.Anylogiccircuit,or control system for a dynamic system can be built by using standard building blocks available in SimulinkLibraries.Varioustoolboxesfordifferenttechniques,suchasFuzzyLogic,Neural Networks,dsp,Statisticsetc.areavailablewithSimulink,whichenhancetheprocessingpower of the tool. The main advantage is the availability of templates / building blocks, which avoid the necessity of typing code for small mathematical processes. CONCEPT OF SIGNAL AND LOGIC FLOW: InSimulink,data/informationfromvariousblocksaresenttoanotherblockbylines connectingtherelevantblocks.Signalscanbegeneratedandfedintoblocksdynamic/ static).Datacanbefedintofunctions.Datacanthenbedumpedintosinks,whichcouldbe scopes,displaysorcouldbesavedtoafile.Datacanbeconnectedfromoneblocktoanother, canbebranched,multiplexedetc.Insimulation,dataisprocessedandtransferredonlyat Discrete times, since all computers are discrete systems. Thus, a simulation time step (otherwise calledanintegrationtimestep)isessential,andtheselectionofthatstepisdeterminedbythe fastest dynamics in the simulated system. Department of Electrical & Electronics Engineering38 | P a g eVJIT-HYD Fig4.1 Simulink library browser Department of Electrical & Electronics Engineering39 | P a g eVJIT-HYD 4.2 CONNECTING BLOCKS: Fig 4 .2 Connectung blocks Toconnectblocks,left-clickanddragthemousefromtheoutputofoneblocktothe input of another block. 4.2.1 SOURCES AND SINKS: The sources library contains the sources of data/signals that one would use in a dynamic system simulation. One may want to use a constant input, a sinusoidal wave, a step, a repeating sequence such as a pulse train, a ramp etc. One may want to test disturbance effects, and can use the random signal generator to simulate noise. The clock may be used to create a time index for plottingpurposes.Thegroundcouldbeusedtoconnecttoanyunusedport,toavoidwarning messages indicating unconnected ports. Department of Electrical & Electronics Engineering40 | P a g eVJIT-HYD Thesinksareblockswheresignalsareterminatedorultimatelyused.Inmostcases,we wouldwanttostoretheresultingdatainafile,oramatrixofvariables.Thedatacouldbe displayed or even stored to a file. the stop block could be used to stop the simulation if the input tothatblock(thesignalbeingsunk)isnon-zero.Figure3showstheavailableblocksinthe sourcesandsinkslibraries.Unusedsignalsmustbeterminated,topreventwarningsabout unconnected signals. Fig.4.2.1 Sources and sinks Department of Electrical & Electronics Engineering41 | P a g eVJIT-HYD 4.3 CONTINUOUS AND DISCRETE SYSTEMS: Alldynamicsystemscanbeanalyzedascontinuousordiscretetimesystems.Simulink allowsyoutorepresentthesesystemsusingtransferfunctions,integrationblocks,delayblocks etc. Fig.4.3 Continous and descrete systems Department of Electrical & Electronics Engineering42 | P a g eVJIT-HYD 4.3.1 NON-LINEAR OPERATORS: AmainadvantageofusingtoolssuchasSimulinkistheabilitytosimulatenon-linear systems and arrive at results without having to solve analytically. It is very difficult to arrive at ananalyticalsolutionforasystemhavingnon-linearitiessuchassaturation,signupfunction, limited slew rates etc. In Simulation, since systems are analyzed using iterations, non-linearities are not a hindrance. One such could be a saturation block, to indicate a physical limitation on a parameter,suchasavoltagesignaltoamotoretc.Manualswitchesareusefulwhentrying simulationswithdifferentcases.Switchesarethelogicalequivalentofif-thenstatementsin programming. Fig.4.3.1 simulink blocks Department of Electrical & Electronics Engineering43 | P a g eVJIT-HYD 4.3.2 MATHEMATICAL OPERATIONS: Mathematicaloperatorssuchasproducts,sum,logicaloperationssuchasand,or,etc. .canbeprogrammedalongwiththesignalflow.Matrixmultiplicationbecomeseasywiththe matrixgainblock.Trigonometricfunctionssuchassinortaninverse(atan)arealsoavailable. Relationaloperatorssuchasequalto,greaterthanetc.canalsobeusedinlogiccircuits Fig4.3.2 Simulink math blocks Department of Electrical & Electronics Engineering44 | P a g eVJIT-HYD 4.3.3 SIGNALS & DATA TRANSFER: In complicated block diagrams, there may arise the need to transfer data from one portion toanotherportionoftheblock.Theymaybeindifferentsubsystems.Thatsignalcouldbe dumped into a goto block, which is used to send signals from one subsystem to another. Multiplexinghelpsusremoveclutterduetoexcessiveconnectors,andmakes matrix(column/row) visualization easier.

Fig4..3.3 Signals and systems Department of Electrical & Electronics Engineering45 | P a g eVJIT-HYD 4.4 MAKING SUBSYSTEMS DragasubsystemfromtheSimulinkLibraryBrowserandplaceitintheparentblock whereyouwouldliketohidethecode.Thetypeofsubsystemdependsonthepurposeofthe block.Ingeneralonewillusethestandardsubsystembutothersubsystemscanbechosen.For instance, the subsystem can be a triggered block, which is enabled only when a trigger signal is received. Open(doubleclick)thesubsystemandcreateinput/outputPORTS,whichtransfer signalsintoandoutofthesubsystem.Theinputandoutputportsarecreatedbydraggingthem fromtheSourcesandSinksdirectoriesrespectively.Whenportsarecreatedinthesubsystem, theyautomaticallycreateportsontheexternal(parent)block.Thisallowsforconnectingthe appropriate signals from the parent block to the subsystem.4.4.1 SETTING SIMULATION PARAMETERS: Runningasimulationinthecomputeralwaysrequiresanumericaltechniquetosolvea differentialequation.Thesystemcanbesimulatedasacontinuoussystemoradiscretesystem basedontheblocksinside.Thesimulationstartandstoptimecanbespecified.Incaseof variablestepsize,thesmallestandlargeststepsizecanbespecified.AFixedstepsizeis recommended and it allows for indexing time to a precise number of points, thus controlling the sizeofthedatavector.Simulationstepsizemustbedecidedbasedonthedynamicsofthe system.Athermalprocessmaywarrantastepsizeofafewseconds,butaDCmotorinthe systemmaybequitefastandmayrequireastepsizeofafewmilliseconds. Fig:4.4.1 setting simulation parameters: Department of Electrical & Electronics Engineering46 | P a g eVJIT-HYD Chapter-5 5 Simulation Results: 5.1 Introduction: Aproportional-integralcontroller(PIcontroller)isagenericcontrolloopfeedback mechanismwidelyusedinindustrialcontrolsystems.APIcontrollerattemptstocorrectthe errorbetweenameasuredprocessvariableandadesiredsetpointbycalculatingandthen outputting a corrective action that can adjust the process accordingly.

ThePIcontrollercalculationinvolvestwoparameters;theProportional,theIntegral values.TheProportionalvaluedeterminesthereactiontothecurrenterror,theIntegral determinesthereactionbasedonthesumofrecenterrorsandtheDerivativedeterminesthe reactiontotherateatwhichtheerrorhasbeenchanging.Theweightedsumofthesethree actions is used to adjust the process via a control element such as the position of a control valve or the power supply of a heating element. By"tuning" the three constants in the PI requirements. TheresponseofthecontrollercanbedescribedintermsofthecontrolleralgorithmthePIcan provide control action designed for specific process responsiveness of the controller to an error, the degree to which the controller overshoots the set point and the degree of system oscillation. 5.2 PI controllers: 5.2.1 Proportional term: Theproportionaltermmakesachangetotheoutputthatisproportionaltothecurrent error value. The proportional response can be adjusted by multiplying the error by a constant Kp, called the proportional gain. The proportional term is given by: Pout = Kp e(t) (4.1) Where -Pout : Proportional output Department of Electrical & Electronics Engineering47 | P a g eVJIT-HYD -Kp: Proportional Gain, a tuning parameter -e: Error = SP PV -t : Time or instantaneous time (the present) A high proportional gain results in a large change in the output for a given change in the error.Iftheproportionalgainistoohigh,thesystemcanbecomeunstable(Seethesectionon Loop Tuning)In contrast, a small gain results in a small output response to a large input error, andalessresponsive(orsensitive)controller.Iftheproportionalgainistoolow,thecontrol action may be too small when responding to system disturbances.

In the absence of disturbances pure proportional control will not settle at its target value, but will retain a steady state error that is a function of the proportional gain and the process gain. Despitethesteady-stateoffset,bothtuningtheoryandindustrialpracticeindicatethatitisthe proportional term that should contribute the bulk of the output change. 5.2.2 Integral term: Thecontributionfromtheintegraltermisproportionaltoboththemagnitudeoftheerror and the duration of theerror. Summing the instantaneous error over time (integrating theerror) gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by the integralgainand addedto the controller output.The magnitude of the contribution of the integral term to the overall control action is determined by the integral gain, Ki. The integral term is given by: I out=K ()

(4.2) Where Iout : Integral output Ki: Integral Gain, a tuning parameter e: Error = SP PV : Time in the past contributing to the integral response Department of Electrical & Electronics Engineering48 | P a g eVJIT-HYD

The integral term(when added to the proportional term) accelerates the movement of the processtowardssetpointandeliminatestheresidualsteady-stateerrorthatoccurswitha proportionalonlycontroller.However,sincetheintegraltermisrespondingtoaccumulated errors from the past, it can cause the present value to overshoot the set point value (cross over the set point and then create a deviation in the otherdirection). For furthernotes regarding integral gain tuning and controller stability, see the section on Loop Tuning.

The output from the three terms, the proportional, and the integral terms are summed to calculate the output of the PI controller.

Fig:5.2.1 Discrete PI controller

First estimation is the equivalent of the proportional action of a PI controller. The integral actionofaPIcontrollercanbethoughtofasgraduallyadjustingtheoutputwhenitisalmost right.Derivativeactioncanbethoughtofasmakingsmallerandsmallerchangesasonegets closetotherightlevelandstoppingwhenitisjustright,ratherthangoingtoofar.Makinga changethatistoolargewhentheerrorissmallisequivalenttoahighgaincontrollerandwill lead to overshoot. If the controller were to repeatedly make changes. Department of Electrical & Electronics Engineering49 | P a g eVJIT-HYD Thoseweretoolargeandrepeatedlyovershootthetarget,thiscontrolloopwouldbe termedunstableandtheoutputwouldoscillatearoundthesetpointineitheraconstant,a growing or a decaying sinusoid. A human would not do this because we are adaptive controllers, learning from the process history, but PI controllers do not have the ability to learn and must be setupcorrectly.Selectingthecorrectgainsforeffectivecontrolisknownastuningthe controller. If a controller starts from a stable state at zero error (PV = SP), then further changes by the controller will be in response to changes in other measured or unmeasured inputs to the process that impact on the process, and hence on the PV. Variables that impact on the process other than theMVareknownasdisturbancesandgenerallycontrollersareusedtorejectdisturbances and/or implement set point changes.Intheory,acontrollercanbeusedtocontrolanyprocesswhichhasameasurableoutput (PV), a known ideal value for that output (SP) and an input to the process (MV) that will affect therelevantPV.Controllersareusedinindustrytoregulatetemperature,pressure,flowrate, chemical composition, level in a tank containing fluid, speed and practically every other variable for which a measurement exists. Automobile cruise control is an example of a process outside of industrywhichutilizesautomatedcontrol.Kp:ProportionalGain-LargerKptypicallymeans faster response since the larger the error, the larger the feedback to compensate. An excessively large proportional gain will lead to process instability. Ki: Integral Gain Larger Ki implies steady stateerrorsareeliminatedquicker.Thetrade-offislargerovershoot:anynegativeerror integratedduringtransientresponsemustbeintegratedawaybypositiveerrorbeforewereach steadystate.Kd:DerivativeGain-LargerKddecreasesovershoot,butslowsdowntransient response and may lead to instability 5.2.3 Loop tuning: If the PI controller parameters (the gains of the proportional, integral terms) are chosen incorrectly, the controlled process input can be unstable, i.e. its output diverges, with or without oscillation, and is limited only by saturation or mechanical breakage. Tuning a control loop is the adjustment of its control parameters (gain/proportional band, integral gain/reset) to the optimum values for the desired control response. Department of Electrical & Electronics Engineering50 | P a g eVJIT-HYD Some processes must not allow an overshoot of the process variable beyond the set point if,forexample,thiswouldbeunsafe.Otherprocessesmustminimizetheenergyexpendedin reachinganewsetpoint.Generally,stabilityofresponse(thereverseofinstability)isrequired andtheprocessmustnotoscillateforanycombinationofprocessconditionsandsetpoints. Someprocesseshaveadegreeofnon-linearityandsoparametersthatworkwellatfull-load conditions don't work when the process is starting up from no-load. This section describes some traditional manual methods for loop tuning. There are several methods for tuning a PI loop. The most effective methods generally involve the development of some form of process model, and then choosing P, I, based on the dynamic model parameters. Manual "tune by feel" methods have proven time and again to be inefficient, inaccurate, and often dangerous. The choice of method will depend largely on whether or not the loop can be taken "offline" for tuning, and the response time of the system. If the system can be taken offline, the best tuning method often involves subjecting the system to a step change in input, measuring the output as a function of time, and using this response to determine the control parameters.

Department of Electrical & Electronics Engineering51 | P a g eVJIT-HYD Ifthesystemmustremainonline,onetuningmethodistofirstsettheIvaluetozero. IncreasethePuntiltheoutputofthelooposcillates,andthenthePshouldbeleftsettobe approximately half of that value for a"quarter amplitude decay" type response. Then increaseI untilanyoffsetiscorrectinsufficienttimefortheprocess.HowevertoomuchIwillcause instability.Finally,increaseD,ifrequired,untiltheloopisacceptablyquicktoreachits referenceafteraloaddisturbance.HowevertoomuchDwillcauseexcessiveresponseand overshoot. A fast PI loop tuning usually overshoots slightly to reach the set point more quickly; however,somesystemscannotacceptovershoot,inwhichcasea"criticallydamped"tuneis required,whichwillrequireaPsettingsignificantlylessthanhalfthatofthePsettingcausing oscillation. Department of Electrical & Electronics Engineering52 | P a g eVJIT-HYD 5.2.4 Limitations of PI control

While PI controllers are applicable to many control problems, they can perform poorly insomeapplications.PIcontrollers,whenusedalone,cangivepoorperformancewhenthePI loopgainsmustbereducedsothatthecontrolsystemdoesnotovershoot,oscillateor"hunt" aboutthecontrolsetpointvalue.Thecontrolsystemperformancecanbeimprovedby combining the PI controller functionality with that of a Feed-Forward control output as described inControlTheory.Anyinformationorintelligencederivedfromthesystemstatecanbe"fed forward" or combined with the PI output to improve the overall system performance. The Feed-Forward value alone can often provide a major portion of the controller output. The PI controller can then be used to respond to whatever difference or "error" that remains between the controller set point and the feedback value. Since the Feed-Forward output is not a function of the process feedback, it can never cause the control system to oscillate, thus improving the system response and stability.

Another problem faced with PI controllers is that they are linear. Thus, performance of PI controllersinnon-linearsystems(suchasHVACsystems)isvariable.OftenPIcontrollersare enhanced through methods such asgain scheduling or fuzzy logic.Further practical application issuescanarisefrominstrumentationconnectedtothecontroller.Ahighenoughsamplingrate and measurement precision and measurement accuracy (more relevant to FF and MPC). Aproblemwiththedifferentialtermisthatsmallamountsofmeasurementorprocess noisecancauselargeamountsofchangeintheoutput.Sometimesitishelpfultofilterthe measurements,witharunningaverage,alsoknownasalow-passfilter.However,low-pass filteringandderivativecontrolcanceleachotherout,soreducingnoisebyinstrumentation meansisamuchbetterchoice.Alternatively,thedifferentialbandcanbeturnedoffinmost systemswithlittlelossofcontrol.ThisisequivalenttousingthePIcontrollerasaPID controller. Department of Electrical & Electronics Engineering53 | P a g eVJIT-HYD 5.3 Simulation:

5.3.1(a) Simulation Model of a Double Frequency Buck Converter.

Fig 5.3.1(a) simulation model of a double frequency buck converter Department of Electrical & Electronics Engineering54 | P a g eVJIT-HYD 5.3.1(b)simulation model of a high frequency buck converter:

Fig5.3.1 (b) simulation model of a high frequency buck converter Department of Electrical & Electronics Engineering55 | P a g eVJIT-HYD 5.3.1(C) simulation model of a low frequency buck converter: Fig 5.3.1(c) simulation model of a low frequency buck converter \ Department of Electrical & Electronics Engineering56 | P a g eVJIT-HYD 5.3.1(D) Simulation model of a doublefrequency buck converter fed with dc motor Fig 5.3.1(d) simulation model of a double frequency buck converter fed with dc motor Discrete,Ts = 1e-006 s.powerguiv+-teTo Workspace3wmTo Workspace2i aTo Workspace1tTo WorkspaceStepScope6Scope3Scope2Scope1ScopeSRQ!QS-RFl i p-Fl op1SRQ!QS-RFl i p-Fl op