Determine the transfer function TsYsRs for thr system below

Determine the transfer function T(s)=Y(s)/R(s) for thr system below

Solution

forward paths k=1

T1=1*(1/S)*2*1*(1/S)=(2/S^2)

LOOPS ARE

L1=-1*(1/S)=(-1/S)

L2=-1*(1/S)=(-1/S)

L3=2*(1/S)*(-1)=(-2/S)

Q=1-(L1+L2+L3)=1+1/S+1/S+2/S=1+(4/S)

Q1=1

TRANSFER FUNCTION=(T1*Q1)/Q

TRANSFER FUNCTION=[(2/S)*1]/[1+4/S]=2/[S(S+4)]