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The problem is the one at the top of the page. I was able to reduce the first block diagram into the feedback loop block and I got H(s) = 4s + 1 using the identities in the book. I've spent hours playing with the 5 identities to try and reduce it to the 3rd G(s) block with a feedback loop gain of 1 but I haven't been successful.

The closest I've gotten was in combining the feedback loop block of G and H into one block and trying to find some parallel combination with a gain of 1 but it hasn't worked.

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"Linear control systems" Charles Rohrs, James Melsa, Donald Schultz McGraw Hill, 1993

Pwestm
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1 Answers1

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First, we need to name each node:

enter image description here

Now, let's write down the equations for each node:

  • $$\text{S}_1=\text{U}-\text{S}_3\tag1$$
  • $$\text{S}_2=\text{S}_1\cdot\frac{5}{\text{s}+2}\tag2$$
  • $$\text{Y}=\text{S}_2\cdot\frac{1}{\text{s}}\tag3$$
  • $$\text{S}_3=\text{S}_2\cdot4+\text{Y}\tag4$$

So, combinding gives:

$$\text{Y}\cdot\text{s}\cdot\frac{\text{s}+2}{5}=\text{U}-\left(\text{Y}\cdot\text{s}\cdot4+\text{Y}\right)\space\Longleftrightarrow\space\frac{\text{Y}}{\text{U}}=\frac{5}{5+\text{s}\left(22+\text{s}\right)}\tag5$$

Jan Eerland
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