Hello. Got this block diagram question the other day. Having a bit of trouble with the last part, and not sure of my answer to part b) either. I attach the question.

a) E = R - Y
but Y = GKR / (1 + GKH)

then E = R - GKR/(1+GKH)

For E = 0,

R = GKR/1+GKH

Rearrange for H = 1 - 1/KG

b) I just worked backwards to achieve:

Y = [ (0 - (1-1/KG)) + Td*P ] *G
= 1 - KG + Td*P*G

c) Not really sure about this one. Not come across Y(s) = 0 transfer functions before. Any general information would be appreciated.

 

I think you have done a mistake on b. You can disregard R and think of Td as the input of your feedback system.

I 'll rewrite it for you:
\(Y=\frac G {HK} \cdot P \cdot T_d\\
Y=\frac G {\frac {GK-1}{GK} K} \cdot PT_d\\
Y=\frac {G^2} {GK-1} PT_d\)

Now the question is if it is possible for this to happen:
\(\frac {G^2} {GK-1}=0\)
I think you can answer that.

 

Hi.

I don't really understand where your answer comes from initially.

If R = 0, then immediately after the first summing junction aren't we going to have 0 - Return Loop Gain?

 

If R=0, then it will only nullify its factor of the addition node. The feedback from the output is still there.

The new system has P*Td as input, G in the forward branch and H*K in the feedback branch.