Introduction to Switched-Mode Converter Modeling using MATLAB/Simulink

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1 Introduton to Swthed-Mode Conerter Modelng ung MATLAB/Smulnk MATLAB: programmng and rptng enronment Smulnk: blok-dagram modelng enronment nde MATLAB Motaton: But*: Powerful enronment for ytem modelng and mulaton More ophtated ontroller model, analy and degn tool Blok-dagram baed Smulnk model, undretonal gnal Not a tradtonal rut mulator; pealzed phy-baed Spe dee model or omponent lbrare are not readly aalable *Varou add-on to Smulnk are aalable to allow tradtonal rut dagram entry and rut mulaton (e.g. SmPowerSytem, PLECS), or to embed Spe wthn MATLAB/Smulnk enronment. Thee add-on are not requred and wll not be ued n ECEN5807. ECEN5807

2 Introduton through an example g Synhronou buk onerter R on L _ Load L R L R er g R on2 C out C dt T PWM V M Ma agntude (db) Bode Dagram From: To: SynBuk/out Phae (deg) Swthng model Aeraged model 5 Vg g Frequeny (Hz) Small-gnal lnearzaton and frequeny repone 0.36 V out out See MATLAB/Smulnk page on the oure webte ( Materal page) for omplete tep-bytep detal, and to download the example fle ECEN Load Load SynBuk g g Sope Smulnk model: ynbuk_ol.mdl

3 Synhronou Buk Conerter g R on L _ Load g L R L R er out R on2 C C dt T PWM V M Input: g, Load, Output: out, g State arable:, ECEN5807 3

4 Conerter tate equaton g R on L _ Load g R on2 C out C L R L R er dt T PWM V M State equaton Output equaton L d L dt g Ron RL out ( ) R R ( 0) on2 L out g ( ) 0 ( 0) d C out Rer Load dt C Load ECEN5807 4

5 Smulnk model 5 Vg SynBuk ubytem blok g 0.36 V out out 0 Load Load SynBuk g g Sope g 2 3 Load PWM u u CCMbuk y y d /dt d/dt apator ntegrator ndutor ntegrator 2 SynBuk ubytem blok nternal CCM buk out 3 out g 4 g ECEN5807 5

6 Synhronou buk (SynBuk) ubytem Input g 2 3 Load PWM ubytem PWM u u CCMbuk y y d /dt d/dt Integraton of tate arable apator ntegrator ndutor ntegrator 2 Output CCM buk Conerter tate equaton out g 3 out 4 g ECEN5807 6

7 PWM operaton and model Add Comparator PWM ramp Smulnk PWM model ECEN5807 7

8 Conerter tate equaton: embedded MATLAB rpt g 2 3 Load PWM u u u CCMbuk y CCM buk y y Conerter tate equaton d /dt d/dt out g apator ntegrator ndutor ntegrator 2 3 out 4 g u = nput = [g Load ] y = output = [/C L/L out g] out g R er ( ) 0 ( 0) Load d C dt C Load L d L dt g R on R L out ( ) R R ( 0) on2 L out ECEN5807 8

9 Numeral example g g R on R on2 L L _ R L R er C C _ Load out _ Swthng frequeny: f = MHz I out = 0 V g = 5 V dt T PWM V M L = H R L = 0 m 5 Vg g 0.36 V out out 0 Load g g Load SynBuk Sope Smulnk model: ynbuk_ol.mdl R on = R on2 = 20 m C = 200 F R er = 0.8 m PWM ramp ampltude V M = V ECEN M V = 0.36, D = 0.36

10 Numeral example: ynhronou buk onerter model 5 g Vg 0.36 V out out 0 Load Load SynBuk g g Sope Makng a Smulnk ubytem allow parameterzaton Same ubytem model an be re-ued Model and MATLAB rpt an be olleted n a lbrary ECEN5807 0

11 Swthng mulaton: open-loop tart-up tranent out g 20 /d Zoom n, /d ECEN5807

12 d g L L dt d C dt ( ) g 0 ( 0) out C Load R er d L T dt d C C T dt d g out T T T Aeraged model Ron RL out ( ) R R ( 0) Load on2 L out Swthng model State-pae aeragng g (reew Textbook Seton ) R R d R R L d g T on L T out on T 2 T T T R er T T Load Load T T Large-gnal aeraged model L T out T ECEN5807 2

13 Conerter aeraged tate equaton: MATLAB The MATLAB funton tay exatly the ame, exept d (duty-yle) replae (wth ontrol) ECEN5807 3

14 Synhronou buk (SynBuk) ubytem: wthng or aeraged model 2 Input Aeraged model of the PWM PWM /VM PWM Gan g w ontant d 3 Load Swth d u CCMbuk y u CCM buk Conerter tate equaton y d /dt d/dt out g Integraton of tate arable apator ntegrator ndutor ntegrator 2 3 out 4 g Output ECEN5807 4

15 Start-up tranent mulaton Swthng model Aeraged model out g ECEN5807 5

16 Lnearzaton of the large-gnal aeraged model Large-gnal (nonlnear) aeraged model Lnearzaton at an operatng pont V g d R L L L R g D L D g I o d C R er Small-gnal aeraged model The mall-gnal model an be oled for all mportant onerter tranfer funton: ˆ ˆ ˆ G d ( ) Gg ( ) Zout ( ) dˆ ˆ ˆ g load Control-to-output Lne-to-output Output mpedane ECEN5807 6

17 Reew textbook Chapter 8 Synhronou buk onerter example Buk SSM V g d g D L D g I o d dˆ R L G d () L L R er C R G d ( ) G d V g ( ) ˆ o dˆ Q o er o 2 Par of pole: Low-frequeny gan: f o khz 2 CL 5V 4dBV G do L / C R Qlo db Q load 5 R R L / C Q Q lo er L Qlo Qload Qload db Q Q lo load f ESR zero: er 2CR er MHz ECEN5807 7

18 Magntude and phae Bode plot of G d 80dB 60dB (/V M )G d () 40dB 20dB G ( / ) 5 4dB do V M Q dB 0dB f o khz 40dB/de -20dB 0 / 2Q f o 0 o f er MHz 20dB/de -90 o 0 / 2QQ f o /0 f er 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz ECEN o 8

19 Lnearzaton and frequeny repone n MATLAB/Smulnk 5 g g. Set tranfer funton nput and output pont Vg 0.36 V out out 0 Load Load g g Load Sope SynBuk 2. MATLAB rpt (BodePlotter_rpt.m) ompute DC operatng pont, lnearze the model, ompute and plot the tranfer funton magntude and phae repone ECEN5807 9

20 Magntude and phae Bode plot of G d 40 Bode Dagram From: To: SynBuk/out 20 Ma agntude (db) Pha ae (deg) Frequeny (Hz) ECEN

21 Reew Textbook Chapter 9 Cloed-loop (oltage-mode) ontrol L (t) I out L V g C R o Dead-tme ontrol f = MHz duty-yle ommand error PWM Compenator G () /V M V ref =.8 V _ Pont-of-Load (POL) Synhronou Buk Regulator ECEN5807 2

22 Reew Textbook Chapter 9 Cloed-loop SMPS blok dagram Control objete: tght output oltage regulaton Stat or dynam dturbane Input (lne) oltage g Load urrent load Component tolerane ECEN

23 Small-gnal model: loop gan T T() ( ) Loop gan: T() = H()G ()(/V M )G d () ECEN

24 Small-gnal model: loed-loop repone T() ( ) ECEN

25 Feedbak loop degn objete T() ( ) To meet the ontrol objete, degn T a large a poble n a wde frequeny range a poble,.e. wth a hgh f a poble Lmtaton: tablty and qualty of loed-loop repone ECEN

26 Unompenated loop gan T u L (t) I out L V g C R o _ G d () _ f = MHz Dead-tme ontrol PWM duty-yle ommand Compenator error _ H ene = (n th example) /V M G () = V ref T u () = H ene (/V M )G d () Plot magntude and phae repone of T u () to plan how to degn G () ECEN

27 Magntude and phae Bode plot of T u 80dB 60dB T u () = H ene (/V M )G d () 40dB 20dB T uo G do ( / V ) H 5 4dB M ene Q dB 0dB -20dB f o khz 0 / 2Q f o 40dB/de T uo f f o 2 0 o target f 20dB/de f er MHz -90 o 0 / 2QQ f o /0 f er 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz ECEN o 27

28 Lead (PD) ompenator degn. Chooe: f 00 khz m 53 o 2. Compute: 33 khz 300 khz 3. Fnd G o to poton the rooer frequeny: T uo 2 f f o p Go Go f f z T uo f f o 2 f f z p db Magntude of T u at f Magntude of G at f ECEN

29 Lead (PD) ompenator ummary G ( ) G o z p p Lead ompenator 2 HF pole G o 5.45 f z 33 khz 5 db f p 300 khz f 00 khz (=/0 of f ) Hgh-frequeny gan of the lead ompenator: G o f p /f z = 49 (34 db) Added hgh-frequeny pole: f p2p 2 MHz (= f er = f n th example) ECEN

30 Loop gan wth lead (PD) ompenator 80dB 60dB 40dB 20dB 0dB T uo G o dB G ( ) G f o z p p 00 khz 2-20dB f z 0kHz f z 33kHz f p 300kHz 0 o -90 o 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz ECEN5807 m 53 o -80 o 30

31 Add lag (PI) ompenator Integrator at low frequene Chooe 0f L < f o that phae margn tay approxmately the ame: f L = 8 khz Keep the ame ro-oer oer frequeny: G G o G m db ECEN5807 3

32 Addng PI Compenator 80dB 60dB 40dB 20dB 0dB f L 8kHz f 00 khz -20dB 0 f L 0 o /0 f L PI ompenator phae -90 o 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz ECEN5807 m 53 o -80 o 32

33 Complete PID ompenator: ummary G m db f L 8 khz f z 33 khz f p 300 khz f p2 MHz Crooer frequeny: Phae margn: f 00 khz (=/0 of f ) m 53o ECEN

34 Magntude and phae Bode plot of T 80dB 60dB 40dB 20dB 0dB f 00 khz -20dB Phae of unompenated T u 0 o Phae of ompenated T -90 o 0 Hz 00 Hz KHz 0 KHz 00 KHz MHz ECEN5807 m 53 o -80 o 34

35 Cloed-loop oltage regulator n Smulnk Smulnk model: ynbuk_cl.mdl 5 g g Vg x out out Step Load Load SynBuk g g Sope H x y Injeton pont y 5.45 Gm /(2*p*8e3) /(2*p*8e3) Inerted zero /(2*p*33e3) /(2*p*300e3) PD Compenator /(2*p*e6) HF pole.8 Vref PID ompenator Input and output lnearzaton pont for fndng the loop-gan, T = - y / x The output pont (y) hould be Open Loop, a hown by an x ymbol next to the output arrow ECEN

36 Loop gan and tablty margn MATLAB rpt BodePlotter_rptT.m (ompute d op, lnearze, alulate and plot frequeny repone and tablty margn) 00 Bode Dagram Gm = Inf db (at Inf Hz), Pm = 5.6 deg (at.05e005 Hz) From: x To: Gm/y Magntude (db) Phae (deg) Frequeny (Hz) ECEN

37 Cloed-loop 0-5 Atep-load tranent repone Aeraged model Swthng model out g 5 /d 5 /d See MATLAB/Smulnk page on the oure webte ( Materal page) for omplete tep-by-tep detal, and to download the example fle ECEN