Author name used in this publication: Chi K. TseRefereed conference paper2005-2006 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe

Lai, YM

Tan, SC

Tse, CKM

Author name used in this publication: Chi K. TseRefereed conference paper2005-2006 > Academic research: refereed > Refereed conference paperVersion of RecordPublishedVoR allowe

PolyU Institutional Repository

A Family of PWM Based Sliding Mode VoltageControllers for Basic DC-DC ConvertersSiew-Chong Tan*, Y. M. Lai and Chi K. TseDepartment of Electronic and Information EngineeringHong Kong Polytechnic University, Hong Kong, China*E-mail: ensctan@polyu.edu.hkAbstract- This paper discusses a family of fixed- the current mode control is afterall not fully nonlinear. Itfrequency pulse-width-modulation based sliding mode volt- does not fully support converter applications with large-signalage controllers for basic DC-DC converters operating in disturbances.continuous conduction mode. An experimental compari- Thus, in this paper, we introduce a family of fixed-frequencyson is offered between the proposed controller and the nonlinear controllers, namely, the PWM based sliding modePWM peak current mode controller for the case of the (SM) voltage controllers to supplement the existing types ofboost converter. The performances and properties of the PWM controllers for applications in basic DC-DC converters.proposed controller, the conventional PWM voltage mode The idea is to facilitate the control support for the class ofcontroller, and the PWM current mode controllers are also converters operating with wide operating ranges. The methodcompared. of deriving these controllers and their preliminary simulationresults have been provided in a previous paper [3]. ThisI. INTRODUCTION paper complements [3] with an experimental validation and aRequiring only the sensing of the output voltage and a detailed discussion of the practical aspects of the controllers.single stage compensation, linear PWM voltage mode control A comparison of the general aspects of the performancesis by far the most convenient method of controlling DC- and properties between the proposed controller and variousDC converters. However, the effectiveness of this control conventional PWM controllers is also provided.methodology is often limited to converters operating in discon-tinuous conduction mode (DCM) and the buck-type convert- II. A FAMILY OF PWM BASED SM CONTROLLERSers. Boost-type and buck-boost-type converters operating in SM controllers are well known for their robustness andcontinuous conduction mode (CCM), which inherit the right- stability. Particularly in converter applications requiring a widehalf-plane-zero (RPHZ) characteristic in their duty-cycle-to- operating range, SM controllers are understandably better can-output-voltage transfer functions, typically restrict designers to didates than conventional PWM controllers due to their abilitychoosing low gain bandwidth types of compensation network in handling large-signal perturbations in nonlinear systems [4],for their voltage controllers. This makes the performance of [5]. Among the various proposed systems, the fixed-frequencythe converters sluggish and often unsatisfactory [1]. Moreover, PWM based SM controllers are more suited for practicalthe performance will be further deteriorated in applications implementation in power converters [3], [5]-[9]. The mainrequiring wide operating conditions, since the compensation operating mechanism of these controllers is a pulse-widthnetwork is only optimized for a fixed operating condition. modulator that employs a control signal derived from SMA solution to achieving fast dynamical response in RPHZ control technique. Detailed discussion of the control strategyconverter systems is to employ the current mode control can be found in [3], [9].[2]. This is a two-loop control methodology that uses an Fig. 1 shows the schematic diagrams of the family ofinternal current loop in addition to the voltage loop. In a PID PWM based SM voltage controller to be discussed incertain sense, this introduces a nonlinear state feedback term this paper. Here, C, L, and rL denote the capacitance, in-which makes the current mode control semi-nonlinear, since ductance, and instantaneous load resistance of the convertersthe voltage loop of its control is maintained linear. This respectively; ic, 'L, and ir denote the instantaneous capacitor,is unlike the PWM voltage mode control which is entirely inductor, and load currents respectively; Vref, vi, and /3volinear. Hence, the current mode control supports converter denote the reference, instantaneous input, and instantaneousapplications with a wider range of operating condition than output voltages respectively; Q denotes the feedback networkthe linear PWM voltage mode control. Additionally, since the ratio; and u = (0,1) is the state of power switch Sw.Overall system's stability (phase) margin is increased by theadoption of a fast inner-current loop compensator, a higher A. Control Equationsgain bandwidth compensator over a comparable voltage mode The control equations required for the implementation ofcircuit can be achieved. This leads to fast dynamical response the PWM based SM voltage controllers for the respective basicin RHPZ systems. However, despite such excellent properties, DC-DC converters were derived in [3], and are illustrated in0-7803-9390-2/06/$20.00 ©2006 IEEE 257 ISCAS 2006Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on December 14, 2008 at 22:51 from IEEE Xplore.  Restrictions apply.tc R R, "tc~~~~~~~~~~~~~~~~~~~~~~~ R1 ,2 R,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,plC icIvi plC~~~~~~~~~~~~~~~~~~~vIC~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ PM /3ICTABLE IlySliding Mode Contermann's Frml fodsgnnisaiccntrollersC[10,ltheConverteruk covereb SVCramp s condirtion ofthcyse iSatMatibcallyosatisfived.eBuck 3v0 - piic + K~ Vref -TABLE IermaThe conroulle circut (refestig.in1tti aondtabllerI) basicallEQUATONS F PWBASD SMVOLTGE CNTROLERSadoptsted samerac istructureca thePW Pldin linearccontrol buteBoos ~3(v0v~ - Kiic+ K2 (Vef ~3v) ~ (v0- v onwtheaddsitiona conmiponntronsriestIng ofi wytehinstataneousyConverter vc 'Namp co~~~~~~nputiovoltage sysndortheinsatoantianeousaotputvolagedv.Buck-os /3v0 - Kplic + Kp2 (Vre-f -,3Vo) 'J3v0 Thsarthectomponenrcuts conteribtoing. to the nonlie aritylof________ _____________________________adop_thefheedback cotrol,urand are threor thekieyr ponroperbtieBoost 3L (Vo - Vi~) anKpli + LCaVref fixed parameters. Wthatdkepthena controllertsrobu isttongload and linesrguantinonsunder widtaeoperain ranges. Incseohlredisatneusotpurbolance, theBuck-boos3vo Kplc + Kp2 (ref 0vo componeenvreise highlyntinluntrialtingothe ontrl.iHoever,toTable I. The ~ ~~~ ~ ~ ~ hefedbc control,gisK adandr hcntna a taysat,v eoe ar fixredfoint.he kequationerthenrameter tha can befondin term of covrter'sxe parameters. reduckeset the PM Dlircontroller form.olodadie eultoL,C,an r, ndseecedvaue o sidngcoffcint fl O te thr an, hee onrolesranbeviwe aa2, ad .Thismpliies te desgn prcedur.utyerofdnonlieratigrsatge-feebac caeontlroler desigrbned fromB. ExistenceConditions n~onlinear average modelsonfluethelconveter.Te mainol diffver-Tabl .The ontol ginsKpland re te cnstat enceabtead ttweenvtheetomesapproaces pisntha The SMuapproacth,nThmetr compliancbe fofuth eistenceo condirtinen'supraesther whiuchsavraetheP MoPDelduingacotholerimplmenaino.hoCcurrnce of SMd opleration Thlesmtoofdldngcerfiviengs , Otheotrllr,retainsduc,othes poweronlerrtcnerdynamicas.ThiB.Existence Conditionistoisetteooanecailt o- rsltsinea avsetagof mdesign fretrictons: rtherexs.Tene coinditions,dition of the controlled system. The existence conditions of whulsich ar sevolvdedigfrom stheicinstantaneoustdynamcscofdithensthe proposed family of controllers were derived in [3] and are whcnverter Suchvedesgfrestrhicinstareasntaeu froamithe nonlin-shown in Table II. Selection of the sliding coefficients must erPMcon trollSuherigndestrcignaponsach [11].tSince theabnidncecomply wittherespctive ineualities,of the existence condition implies that the system's trajectoryTABLE II will strictly follow the desired sliding surface, the system'sSLIDING MODE CONTROL ExiSTENCE CONDITIONS dynamic response will strictly obey the designed dynamics.Such stringency is not present in the nonlinear PWM controllerBuck < 3O plic+ Kp (Vrf -,Vo) 3Vi design approach.Buck <i31~- Kiic K~2 Vref /317) <~Table III shows a comparison of the general aspects of theperformances and properties between the proposed controllerBoost 0 < Kplic - Kp2 (Vref - /3Vo) <j3(Vo - ¼i) and various conventional PWM controllers.III. EXPERIMENTAL RESULTS AND DiscusSIONSBuck-boost 0 < Kplic - Kp2 (Vref -/317o) <L3Vo The proposed PWM based SM voltage controllers haveAuthorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on December 14, 2008 at 22:51 from IEEE Xplore.  Restrictions apply.TABLE IIIA COMPARISON OF THE VARIOUS FIXED-FREQUENCY PWM CONTROL SCHEMESCategory of Comparison PWM Voltage Mode PWM Current Mode/Average Current Mode PWM Based SM Voltage Modetype of control linear some nonlinearity nonlinearcompensation design difficult moderate/difficult easysteady-state line and load regulation average good averagelarge-signal dynamic response consistency poor average goodgain bandwidth in RHPZ converter low relatively higher lowrequirement for current sensing no yes yesnoise-to-signal ratio low high/moderate moderatecurrent protection external circuit inherent external circuitaudiosusceptibility protection external scheme inherent existingTABLE IVSPECIFIC TIONOFBOOST CONVERTER it changes from RL 240 Q and RL = 24 Q. This isexpected since the peak current mode controller is designedDescription Parameter Nominal Value under a linearized small signal model that is only optimal for aInput voltage vi 24 V specific operating condition. Thus, when a different operatingCapacitance C 2000 ,uF condition is engaged, the responses varies.Capacitor ESR Cr 69 mQInductance L 300,H On the other hand, with the PWM based SM voltageInductor resistance ir 0.14 Q controller, the dynamic behavior of the output voltage rippleSwitching frequency fs 200 kHz is basically similar (i.e. critically damped) for all operatingMinimum load resistance (full load) rL(min) 24 QMaximum load resistance (10 % load) rL(max) 240 Q input and load conditions. Moreover, the transient setting time,Desired output voltage Vod 48 V which is around 3.4 ms, is also independent of the directionof the step load change. This coincides with our design, whichbeing a 1.5 krad/s bandwidth controller, is expected to haveof wo, = 1.5 krad/s, i.e., T = 0.66 ms. The sliding coefficients a settling time of 5T = 5 3.33 ms. This demonstratesal13 ~~~~~~~~~~~~~~~~~~~~~~~~~~1.5are = 3000 and 0 2250000 (full-load condition the strength of the SM controller in terms of robustness indesign) according to the design equations in [9]; the reference the dynamic behavior under different operating conditions andvoltage is Vref 8 V, Q = 6; and control parameters uncertainties. Additionally, the example also illustrates a majorKpl = 13L - 0.149 and Kp2 = '3LC = 1.35. difference between a large-signal controlled system (SM) anda small-signal controlled system (PWM), that is, the formerA. Regulation Performance complies to the design with a similar response for all operatingA tabulation of the data in terms of the load and line conditions, while the response of the latter will only complyregulation properties is also given in Tables V and VI respec- to the design at a specific operating condition.tively. According to Table V, the maximum load-regulation IV. CONCLUSIONerror occurs at vi = 20 V, with a deviation of 1.75 %from Vo(nominal condition)- Similarly, it can be found from We provide a detailed discussion on a newly proposed fam-Table VI that the maximum line-regulation error occurs at ily of fixed-frequency pulse-width-modulation based slidingminimum load rL = 240 Q, with a deviation of 1.42 % from mode voltage controllers for basic DC-DC converters. AnVo(nominal condition) experimental comparison between the proposed controller andthe PWM peak current mode controller is performed on theB. Proposed Controller Versus Peak Current Mode Controller boost converter. The general differences in terms of controlThe dynamic behavior of the proposed PWM controller performances and properties between the proposed controlleris compared to that of a UC3843 PWM peak current mode and the conventional PWM controllers are highlighted. Itcontroller that is optimally tuned to operate a boost converter at can be concluded that the PWM based sliding mode voltagestep load change from RL = 24 Q to RL = 240 Q for the input controllers possible control alternatives for DC-DC conversioncondition Vi = 24 V. Figs. 2(a)-2(f) show the experimental applications requiring wide operating conditions.waveforms of the boost converter under these control schemes.It can be seen that with the PWM peak current mode ACKNOWLEDGMENTcontroller, the dynamic behavior of the system differs for The authors would like to acknowledge the contribution ofdifferent operating conditions. Specifically, the response be- Mr. Chi-Kin Wu for developing the experimental prototype.comes more oscillatory at higher input voltages. Moreover,the dynamic behavior and transient settling time are also REFERENCESvery much different between the case when the load changes [1] F.A. Himmelstoss, J.W. Kolar and F.C. Zach, "Analysis of a Smith-from RL =24 Q and RL =240 Q and the case when predictor-based-control concept eliminating the right-half plane zero of259Authorized licensed use limited to: Hong Kong Polytechnic University. Downloaded on December 14, 2008 at 22:51 from IEEE Xplore.  Restrictions apply.TABLE VLOAD REGULATION PROPERTY: OUTPUT VOLTAGE AT NOMINAL OPERATING CONDITION Vi 24 V AND rL =24 Q is vo(nominal condition) =47.95 V.Input Voltage Voltage Deviation: Avo 020~ -V(4~ Percentage Change: x 100 %= Vo(240 Q)o(24 Q) Vo~~(nomninal condition)vi= 20 V 0.84 V 1.75 % of vo(nominal condition)vi= 24 V 0.61 V 1.27 % of Vo(norninal condition)vi= 28 V 0.56 V 1.16 % of vo(nominal condition)TABLE VILINE REGULATION PROPERTY: OUTPUT VOLTAGE AT NOMINAL OPERATING CONDITION vi 24 V AND rL =24 Q is vo(nominal condition) =47.95 V.Loading Codition Volage Deviaton: Av0 vov. -20 V)- Vo(v.i-28 V) Percentage Change: Ax 100 %Loadin CondiionVotage Dviatio: AVO Vo(vi20_V)Vo(norninal condition)Minimum load (240 Q) 0.68 V 1.42 % of vo(nominal condition)Half load (48 Q) 0.58 V 1.21 % of vo(nominal condition)Full load (24 Q) 0.40 V 0.83 % of vo(nominal condition)stop Te stop~~~~~~~~~~~~~~~~~~~~~~~~Tekst?pi_~~~~~~~~~~~~~ ~~~optimal'design _oL 2004V ms____MOOsA h4f14m 2200V ms____MQOsA h4f2LmV1 6-msm-A h I~0-0~~500mV M2O~ms~ A Ch4 fr 14.S My fJ20V ~ 20sAC4f1 m N 0m LOsAC 11.mCh4710.0 V Ch4[710.0 Ch4 10OmVj(d))vvi 20 V(Sekcretmodcontroller) (e)vvi 24 V(Sekcretmodcontroller) (fcvvi 28 V(Sekcretmodcontroller)Fig.2. xperimetalwaeomIf uptvltg Tipe stndoupuc rnI~ o hos cneTer,SwthpthIekcretmd cnrle a-cnth.ka/ anwdh W aedS onrle ()(),oeain tlodrsstnealentnga 4 mnmu)ad 447maiu)curenmoe"iEntoeDsg oe u 94 noe mutphs nliEarVMcnrle" nIE oelcrnc[3SCTa,Y>Li n .K s,"eino PW>ae ldn pcait ofrneRcr PS) p 1422,Jn04mod vltge onrolerfo D-DCcoveter oertin i cntiuos 9] .C Tn, .M Li, .K Te, ndM..H.Chun, " fxe-frqunccondutionmode, inProceding, 11h Euopea Conerenc on ower puls-widh-modlatin baed qasi-lidin mod conrollr fo bucElecrnc n plctos(P 05,Sptme 05 ovres,IE rnaton nPwrEetois o.2,n.6[4oVUtin J.Glnron ..Si,SiigMd Conrl ilcrmp.17-32 Nov 2005chnca yses.Lndn UK: alo ndFani, 99.[0]J Akrmn3adV.Uki,"Siin-od onrl eig asdoPowrlecroic Conference and Expsiio (AE),vl 1p311.her adDsin(CCD,vo.2,p.145129e.V93[7]gJ,Mahdravi,oAnEadiaondeecH.A Tolstiyat, "Aplicationis Cofntate sace i rceig,IE ofrneo Idsr plctos(A) o.2Insruenatin ECN, p.42-42, ov 191.pp 82-87,Oc26097Authorized licensed use limited to: Hong Kong Polytechnic University. 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A family of PWM based sliding mode voltage controllers for basic DC-DC converters

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