# Quiz 8 (Root Locus Analysis)

## 3 thoughts on “Quiz 8 (Root Locus Analysis)”

1. In response to a student’s question:

I am unable to understand what D (s) is as it’s not explicitly mentioned?

Yes, $D(s)$ is a disturbance.

Do we consider it to be zero for part 1?

Do you have to? Counter-question: If a system is unstable for one of its inputs (e.g., $X(s)$), do you think it can be stable for a different input ($D(s)$)?

If you insist, assume $D(s)=0$, but it does not make any difference. Therefore, it was not specified.

But part 2 says it has same denominator as X (s).

Yes, indeed. If you have the two transfer functions and you obtain the form

$$Y(s) = H_1(s) \cdot X(s) + H_2(s) \cdot D(s)$$

then $H_1(s)$ and $H_2(s)$ will have the same denominator. If at tny point you find that they haven’t, this should raise a red flag and you should check your work.