Today I was asked a question in control lecture.

There are extra questions about this block diagram but I need to find;

  • the transfer function of this foreforward block diagram and find the roots
  • the state functions of this system

I am a bit newbie at block diagrams but not too bad.

I have found some examples at internet, but could not find. I followed the diagram: "X2= (U-X1)1/(s+1)" and "X1 = U(1/s+2)".

Therefore I found Y/U = (1-1/(s+2))*(1/(s+1)). then >>> Y/U= (s+1)/(s^2+3s+2).


the roots of the system are s1 = -2 and s2= -1

But this answer was wrong as assistant said. I could not understand why!

enter image description here

Thank you for helps.


1 Answer 1


$$ \frac{Y}{U} = \frac{(s+1)}{s^2+3s+2} = \frac{\color{red}{(s+1)}}{(s+2)\color{red}{(s+1)}} = \frac{1}{(s+2)} $$

This may be why the assistant said you were wrong.

  • $\begingroup$ But the answer was 1/( s*(s+1)) and I could not understand how. $\endgroup$ Jan 16 at 18:15
  • $\begingroup$ I too cannot imagine how they arrived at that answer. Perhaps there is more context to this question which you have not provided in the above question? I guess you can ask the (teaching?) assistant to explain it step by step (or ask the professor). $\endgroup$
    – AJN
    Jan 17 at 13:06

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