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Question Figure 1 shows a DC motor with Ra = 20, Jm 4kg - m2, Dm 12kg- mm2/s, K 25mV-sec, K 7N-mm/A, and Km 0 Fixed field Ra w 0000 Rotor Armature ea T() circuit Figure 1: DC motor a) Find the transfer function, G(s) ( for L 10mH and find the pole(s) and Zero(s) of the system. b) Find the transfer function, G(s) ( for La OmH and find the pole(s) and Zero(s) of the system using the answer for (a). How can you compare them with your solutions to (a)?

please steps

Answer 1

Ra La (971 VIt) ealt) Trmit) ( X Pm, Dm m field wrrent 1,4 is fea om constant is conctant Cus it 40uice 80 consteunt Constant flue emt motor fnducedl Const ant dom 1 dt

olcveloteol by moter torgue com tent T ia Kr ia 2. T t0 writing dynamic equafion armeture cincuit .dia La Ra ia Ca ,ftn dnamie eguation mechanical iceit ナ Do. don olt + Km Bn dt2 from 2 & dep KT-La +Km Om dt 2 ia (. Jm d Om Dm dOm KT at2 KT dt

dla J d8m Dm dem KT dlt3 K T dt 2 dt By utting valus ia dia in eg 3 dt Jm d'on dlt2 Ra 1 d Om Ca -+Dm Kイ dt 3 La dEm KT +Dm dom dt2 + K dom At d Om Ra Jm dim Dm dlm t ea dt KT La -+ Dan d2m + K m dlt KT Loplace taneform JmLa a Jm S +Dm. Ra KT Eals) KT KT Kb mls) + La Dm S KT

utting valus Ea cs) 8 24 +La stt12a s+251A) -[ Ea 1s) 2 -a S 7 199 8 nls) +S m(s) 7 Ea(s) 4La s (12 La+8)s+199 La Ea Cs) 4S 20S 199 aeros 00 -2.5 tj 6.59 poles =7 La 7 Ea(s) 8S +199 -199 /8 pole => S
in a) system has two poles , both poles are imaginary and conjugate .

In b) there is only one pole that is real .

There is no zero in both the caese