# Block diagram reduction feedforward loop.

Discussion in 'Homework Help' started by Electromech man, Feb 2, 2011.

1. ### Electromech man Thread Starter New Member

May 2, 2009
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I have come across a block diagram that has me stumped. What has me stumped is the loop with no block on it.

Obviously if it had a block it would simply be G/(1+-GH). I am referring to the simplification of the first block of course...

Can anyone offer me any assistance?

Regards.

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2. ### Georacer Moderator

Nov 25, 2009
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1,271
The diagram doesn't have a loop and even if it had a block, you couldn't use the feedback formula.

When there's a simple line, you can always make one with H=1.

Notice that in this example, you don't have feedback, the signal keeps going forward and never returns.

Thus you have two systems in parallel. One that is H1=2/(s+1) and one that is H2=1.

Is that clear?

3. ### Electromech man Thread Starter New Member

May 2, 2009
8
0
Yes I believe so.

So does that make the parallel loop H1 + H2 = 2/(s +1) + 1?

Then I go on to find the transfer function with G(s) = 2/(s + 1) + 1 and Gc(s) = K/s(s + 2)?

Regards.

4. ### Georacer Moderator

Nov 25, 2009
5,150
1,271
Yes... almost.

The H2=1 is subtracted, so it it H=2/(s+1)-1.
The final system will be H*Gc.

And just remember that a parallel path is different than a loop. The loop refers to feedback.

5. ### Electromech man Thread Starter New Member

May 2, 2009
8
0
T(s) = Y(s)/R(s) = G(s)Gc(s)/[1 + G(s)Gc(s)] is it not?

G(s) = 2/(s+1)-1.

I have Gc(s) = K/[s(s + 2)

With your information I get a Transfer Function of

K - sK/[s^3 + 3s^2 + s(2 - K) + K]

Can these be done on Matlab?

Regards.

6. ### Georacer Moderator

Nov 25, 2009
5,150
1,271
The formula $T(s)=\frac{G(s)}{1 \pm G(s)H(s)}$ is valid only for a feedback loop, where signal goes backwards. This isn't the case as the signal goes only forwards.

Thus the TF is simply $T(s)=\left( \frac{2}{s+1}+1\right) \cdot \left( \frac{K}{s(s+2)} \right)$.

In Matlab that would be
Code ( (Unknown Language)):
1.
2. K=10 %you need to define a value for K, in order to use it
3. G1=tf(2,[1 1]);
4. G2=tf(1,1);
5. G=parallel(G1,G2);
6. Gc=tf(K,[1 2 0]);
7. T=series(G1,Gc)
8.
I 'm not currently able to test the code I provided as Matlab isn't installed in this computer yet.