Transfer function algebraic manipulation

[gfd43tg]

Homework Statement

Homework Equations

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.

 

[Ray Vickson]

Homework Statement

View attachment 91494

Homework Equations

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.

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 $g_p(s)$.

 

[gfd43tg]

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!

 

[SteamKing]

Homework Statement

View attachment 91494

Homework Equations

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.

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

Hint: k_p ≠ -1.43 in the final form.