Question

The transfer function (w(s) (va (s)) of the DC motor shown in the figure is:* DS (2 Points) ialt) Ra w w(t) valt) vio, da

Answer 1

given circuit is iact) Ra wat) J We know Volt)= Km wit) Valt) Apply Kul to electrical current than Valt)-Volt) = ialt). Ra Vitt o where Km = back emf Constant than T- Valt) - Km wit) altora Let us considere Ta motor torque Takti(t) where ке = motor torque constant. KH' (t) Laplace transform on both sides than T(S) =kt Pcs) From mechanical part we know Tai dwit) dt Taking Laplace transform on both sides than 105)= Jis: W(S) G 2 From equation ® & © We got Kt la(s) = = J.S. W(S) Jacs) - Season wes) CS Scanned with CamScanner

From equation o valt) - Km wit) = a(t): Ra Laplace transform on Bolk sides we get Vals)- km w(s) = Ra. Ta(s) We Know Ta(s) = TS wes) than K t Vals) - Km wes) JS WCS) Ra ses)) KA Va(s)- km W(S) = Ra JS Kt was) Vacs ) = (km + RAJS) ) weso Kt Wes) = Vacs Kont Ra IS Rays) kt kt W(S) Vacs) km kt & Rais where K+ = notor torque Constant mo km = Back emf constant CS Scanned with CamScanner