ECEN 5807 eture 6 HW 8 due v D Frdy, rh, 0 S eture 8 on Wed rh 0 wll be leture reorded n 0 he week of rh 5-9 Sprng brek, no le ody: Conlude pled-dt odelng of hghfrequeny ndutor dyn n pek urrentode ontrolled onverter ore urte verged odel
Drete-te dyn wth openton rp: ] [ ] [ n n j e e z z z ] [ ] [ ] [ n n n Frequeny repone
Equvlent hold: [ n] t, z + t [n] [n] [n-] t d[n] t t [n] e
Coplete pled-dt trnfer funton e e ' D D Control-to-ndutor urrent ll-gnl repone:
Exple CP buk onverter: V g = 0V, = 5 H, C = 75 F, D = 0.5, V = 5 V, I = 0 A, R = V/I = 0.5, f = 00 khz Indutor urrent lope: = V g V/ = A/ = V/ = A/ ' D D D = 0.5: CP ontroller tble for ny openton rp, / > 0 e e
Control-to-ndutor urrent repone for everl openton rp / preter 0 / gntude nd phe repone / = 0. gntude [db] 0 0-0 -0 / = 0.5 / = / = 5-30 AAB fle: CPfr. -40 0 0 3 0 4 0 5 phe [deg] 0-50 -00 5 0. 5 0. -50 0 0 3 0 4 0 5 frequeny [Hz]
Frt-order pproxton hf e e / / / e hf f D D f f Control-to-ndutor urrent repone behve pproxtely ngle-pole trnfer funton wth hgh-frequeny pole t
Control-to-ndutor urrent repone for everl openton rp / = 0., 0.5,, 5 0 / gntude nd phe repone 0 gntude [db] 0-0 -0-30 -40 0 0 3 0 4 0 5 t -order trnfer-funton pproxton 0 phe [deg] -50-00 -50 0 0 3 0 4 0 5 frequeny [Hz]
Seond-order pproxton / / e e / / / / e D D Q Control-to-ndutor urrent repone behve pproxtely eond-order trnfer funton wth orner frequeny f / nd Q-ftor gven by
Control-to-ndutor urrent repone for everl openton rp / = 0., 0.5,, 5 0 / gntude nd phe repone 0 gntude [db] 0-0 -0-30 -40 0 0 3 0 4 0 5 nd -order trnfer-funton pproxton 0 phe [deg] -50-00 -50 0 0 3 0 4 0 5 frequeny [Hz]
Conluon In CP onverter, hgh-frequeny ndutor dyn depend trongly on the openton rtfl rp lope Wthout openton rp = 0, CP ontroller untble for D > 0.5, reultng n perod-doublng or other ub-hron or even hot ollton For = 0.5, CP ontroller tble for ll D Reltvely lrge openton rp > 0.5 prtl hoe not jut to enure tblty of the CP ontroller, but lo to redue entvty to noe For reltvely lrge vlue of, hgh-frequeny ndutor urrent dyn n be well pproxted by ngle hgh-frequeny pole Seond-order pproxton very urte for ny Next: ore urte verged odel, nludng hgh-frequeny dyn
ore Aurte Averged CP odel extbook Seton.3 wth updte ECEN 5807
Objetve ore Aurte Averged odel Effet of ndutor urrent rpple nd openton rtfl rp odelng of ll trnfer funton of nteret: ontrol-to-output, lne-to-output, nput nd output pedne ore urte odel t hgh-frequene to enble wdebndwdth degn Approh rge-gnl verged CP ontroller odel: reltonhp between ontrol nput, verge ndutor urrent, verged voltge, nd duty-yle d Sll-gnl verged CP ontroller odel Coplete CP ontrolled onverter odel norportng wellknown ll-gnl odel for duty-yle ontrol
Averged CP Controller odel t t t t d d Gol: fnd verge ndutor urrent funton of Control nput Duty-yle d Slope,,
Averged CP Controlled odel t p t t t d d p d p d d p d' d d d'?
d d t d d'? p t t t d d 6
Averged CP Controlled odel t t p d d t t d d' d d odel Coent Corret n tedy-tte DC Corret n tedy-tte DC 3 4 d d' d' d = verge over the entre perod: textbook = verge t the plng ntnt
Approhe to CP ndutor urrent vergng odel Coent [] ddlebrook Corret n tedy-tte DC [] Rdley Corret n tedy-tte DC 3 [3] extbook d d' = verge over the entre perod: textbook 4 [4] n d' d = verge t the plng ntnt [] ddlebrook, R.D., "op n ultple-oop Regultor nd Current-ode Progrng," Power Eletron, IEEE rnton on, vol.pe-, no., pp.09,4, Aprl 987 [] R.B.Rdley, "A new, ontnuou-te odel for urrent-ode ontrol," IEEE rnton on Power Eletron, Volue 6, Iue, Aprl 99, pp. 7-80. [3] Verghee, George C.; Bruzo, C.A.; hbr, K.N., "Averged nd pled-dt odel for urrent ode ontrol: re-exnton," Power Eletron Spelt Conferene, 989. PESC '89 Reord., 0th Annul IEEE, vol., no., pp.484,49 vol., 6-9 Jun 989 [4] F.D.n, R.D.ddlebrook, "A unfed odel for urrent-progred onverter," IEEE rnton on Power Eletron, Volue 0, Iue 4, July 995, pp. 397-408. h pper derbe verged CP odel tht produe hgh-frequeny dyn ontent wth ext pled-dt odelng.
Coent bout lrge-gnl verged CP odel All odel gve the e reult t DC All odel gve very lr reult t low-frequene All odel nlude ndutor urrent dyn odel 3 verge over the entre perod the textbook pproh Seton.3 d d' d d d' extbook Eq..59 odel 4 verge urrent t the plng ntnt reult n hgh-frequeny dyn ontent wth the pled-dt odel d d ' d dd'
Sll-gnl verged CP odel odel 3 textbook d d d d d ' ' ' ' D D d D D F v v F F d v g g F
odel 3 textbook
Sll-gnl verged CP odel odel 4 n dd d d d ' ' ' DD d D F v v F F d v g g D F D D F '
Sll-gnl verged CP odel odel 4 n d F F F v g g F v v Converter Buk Boot Buk-boot F g DD' 0 DD' odel 4 veron of ble. F v 0 DD' DD'