Root Locus Homework

A closed$-$loop system and its closed$-$loop transfer function, $C\frac{s}{R}(s),$ are given below:

$$

To find the closed$-$loop poles, s$\text{'}$s must be found that obey the following equations:

$1+G(s)H(s)=0$LongleftrightarrowG$(s)H(s)=-1$

So $G(s)H($s$)$ as a vector is equal to the $-1$ vector.

Therefore, the angle condition and the amplitude condition of $G(s)H(s)$ are as follows:

Therefore, the angle condition and the amplitude condition of $G(s)H(s)$ are as follows:

Angle Condifon