# Transfer function algebraic manipulation

1. Nov 7, 2015

### Maylis

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. Nov 7, 2015

### Ray Vickson

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 $g_p(s)$.

3. Nov 7, 2015

### Maylis

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!

4. Nov 7, 2015

### SteamKing

Staff Emeritus
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.