Curret Progred Cotrol.e. Pek Curret-Mode Cotrol eture lde prt More Aurte Model ECEN 5807 Drg Mkovć
Sple Frt-Order CPM Model: Sury Aupto: CPM otroller operte delly, Ueful reult t low frequee, well uted for oervtve reltvely low bdwdth deg of voltge feedbk loop roud CPM otrolled overter tto: The ple odel doe ot dte poble tblty of the urret otroller, or the eed for opeto rtfl rp Doe ot lude hgh-frequey dy, whh relevt for wdebdwdth voltge loop deg Doe ot orretly odel le-to-output repoe CPM buk or buk-derved overter eve t low frequee t orretly predt oplete rejeto of le dturbe
More Aurte CPM Model: Outle Spled-dt odelg of dutor dy urret progred ode Itblty of the urret loop d the eed for opeto rtfl rp Iproved odelg of hgh-frequey dy to eble deg of wde-bdwdth voltge loop More urte verged odel rge-gl d ll-gl verged odultor odel Aurte verged ll-gl odel, ludg hgh-frequey dy Aurte odelg of le-to-output repoe Duo of reult for b overter CPM odel for ulto Deg exple 3
4
5
Idutor urret tret t t t dt d T dt d T 6
7 Hgh-frequey ll-gl dutor-urret dy Aue tht voltge perturbto re eglgbly ll t hgh frequee: the lope d be odered ott Apply pled-dt odelg: * t t z z jk T k ω
Sll-gl perturbto - t dt t 8
9 Drete-te dy T d T d
0 Drete-te dy T d T d ' D D M M
Itblty for D > 0.5 M M D D'
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4
Sll-gl perturbto wth opeto rp t - t dt t 5
6 Drete-te dy wth opeto rp: T d T d
7 T d ' D D Drete-te dy wth opeto rp: T d
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9
0
Drete-te dy: z z Z-trfor: z z z z z z z Drete-te z-do otrol-todutor urret trfer futo: T j T e e ω Dfferee equto: Pole t z Stblty odto: pole de the ut rle, < Frequey repoe ote tht z orrepod to dely of T te do:
Equvlet hold: t, z t - t dt t t T
Equvlet hold The repoe fro the ple of the dutor urret to the dutor urret perturbto t pule of pltude d legth T Hee, frequey do, the equvlet hold h the trfer futo prevouly derved for the zeroorder hold: e T 3
4 Coplete pled-dt trfer futo T T T e e ' D D Cotrol-to-dutor urret ll-gl repoe:
5 Exple CPM buk overter: V g 0V, 5 µh, C 75 µf, D 0.5, V 5 V, I 0 A, R V/I 0.5 Ω, f 00 khz Idutor urret lope: V g V/ A/µ V/ A/µ ' D D D 0.5: CPM otroller tble for y opeto rp, / > 0 T T T e e
Cotrol-to-dutor urret repoe for everl opeto rp / preter gtude db 0 0 0-0 -0-30 MATAB fle: CPMfr. / gtude d phe repoe / 0. / 0.5 / / 5-40 0 0 3 0 4 0 5 phe deg 0-50 -00 0.5 0. 5-50 0 0 3 0 4 0 5 frequey Hz 6
7 Frt-order pproxto hf T T T e e ω π ω / / / π ω π ω T e π π hf f D D f f Cotrol-to-dutor urret repoe behve pproxtely gle-pole trfer futo wth hgh-frequey pole t
Cotrol-to-dutor urret repoe for everl opeto rp / 0., 0.5,, 5 0 / gtude d phe repoe 0 gtude db 0-0 -0-30 -40 0 0 3 0 4 0 5 t -order trfer-futo pproxto 0 phe deg -50-00 -50 0 0 3 0 4 0 5 frequey Hz 8
9 Seod-order pproxto / / T T T e e ω ω π / / / / T e ω ω π ω ω π D D Q π π Cotrol-to-dutor urret repoe behve pproxtely eodorder trfer futo wth orer frequey f / d Q-ftor gve by
Cotrol-to-dutor urret repoe for everl opeto rp / 0., 0.5,, 5 0 / gtude d phe repoe 0 gtude db 0-0 -0-30 -40 0 0 3 0 4 0 5 d -order trfer-futo pproxto 0 phe deg -50-00 -50 0 0 3 0 4 0 5 frequey Hz 30
Coluo I CPM overter, hgh-frequey dutor dy deped trogly o the opeto rtfl rp lope Wthout opeto rp 0, CPM otroller utble for D > 0.5, reultg perod-doublg or other ub-hro or eve hot ollto For 0.5, CPM otroller tble for ll D Reltvely lrge opeto rp > 0.5 prtl hoe ot jut to eure tblty of the CPM otroller, but lo to redue etvty to oe For reltvely lrge vlue of, hgh-frequey dutor urret dy be well pproxted by gle hgh-frequey pole Seod-order pproxto very urte for y Next: ore urte verged odel, ludg hgh-frequey dy 3