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Transfer function algebraic manipulation

  1. Nov 7, 2015 #1


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    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    I don't know if I am just stupid, but I can't see how to make this manipulation. I tried factoring the denominator

    $$ g_{p} = \frac {-1.43}{(s-1.399)(s+5.086)} $$
    Then take out -1.399 and 5.086
    $$ g_{p} = \frac {-1.43}{-1.399(\frac {-1}{1.399}s + 1)5.086(\frac {1}{5.086}s+1)} $$
    But I know this won't work, and I am not clever enough right now to come up with the right way to manipulate this thing.
  2. jcsd
  3. Nov 7, 2015 #2

    Ray Vickson

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    Your manipulations are correct; it is just that one of your constants ##\tau_i## is negative. If that is not allowed, there must be something wrong with the original ##g_p(s)##.
  4. Nov 7, 2015 #3


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    The negative time constant is allowed, which is what makes it unstable. My algebra is weak, so for some reason I had it in my head that if I multiplied my result out, I would come up with something different from the original transfer function!
  5. Nov 7, 2015 #4


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    You've almost got the form of gp(s) that is specified, you just need to combine all the constants in the numerator and the denominator.

    Hint: kp ≠ -1.43 in the final form.
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