How do I find the closed loop transfer function?

Can anyone give me some hints?

Do I do the closed-loop for the small feedback(the one with -0.5) then follow by the big feedback(the one with -1)?

If so , the small feedback loop is it equal to z^-1 / (1-0.5z^-1) ?

 

The diagram is simply a way of expressing mathematical operations. So carry out the math operations shown. Do it node by node. Let's call the unlabeled node in the middle A(z).

You have

Y(z) = (-1)*E(z) + (2)*A(z)

Now you try to go from there. Show your work and we can look to see where you go wrong (if you do).

 

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How do I find the closed loop transfer function?

Can anyone give me some hints?

Do I do the closed-loop for the small feedback(the one with -0.5) then follow by the big feedback(the one with -1)?

If so , the small feedback loop is it equal to z^-1 / (1-0.5z^-1) ?

Hi,

I think you meant to ask, "How do i find the transfer function".
When you ask how to find the closed loop transfer function that implies that the loop is not yet closed, yet i think it is for this problem. You can verify this though.

Also, you can not simplify a feedback loop if there is a takeoff point in the middle somewhere. Just a hint.

 

The diagram is simply a way of expressing mathematical operations. So carry out the math operations shown. Do it node by node. Let's call the unlabeled node in the middle A(z).

You have

Y(z) = (-1)*E(z) + (2)*A(z)

Now you try to go from there. Show your work and we can look to see where you go wrong (if you do).

Hi Thanks for your reply.
So E(z) = R(z) - A(z)*0.5 and A(z) = z^-1 *E(z) then I proceed to sub it into the equation Y(z) = (-1)*E(z) + (2)*A(z) ? am i correct?

 

Hi,

You could use substitutions or just solve the two, three, or more equations simultaneously.
You could then double check your result by transforming the resulting equation and checking that result against a direct sequence calculation using the equations you find from the block diagram. Choose a convenient clock period like 1 second.

 

Hi. I have solved this question. This thread can be closed.

Thanks for all the help

 

Hi. I have solved this question. This thread can be closed.

Thanks for all the help

Hi,

Dont you want to post your result so it can be checked? Did you test your result with another method as suggested?