3 views

The state space representation of a separately excited DC servo motor dynamics is given as
$\left[\begin{array}{l} \frac{d \omega}{d t} \\ \frac{d i_{a}}{d t} \end{array}\right]=\left[\begin{array}{rr} -1 & 1 \\ -1 & -10 \end{array}\right]\left[\begin{array}{l} \omega \\ i_{a} \end{array}\right]+\left[\begin{array}{r} 0 \\ 10 \end{array}\right] u$
where $\omega$ is the speed of the motor, $i_{a}$ is the armature current and $u$ is the armature voltage. The transfer function $\frac{\omega(s)}{U(s)}$ of the motor is

1. $\frac{10}{s^{2}+11 s+11}$
2. $\frac{1}{s^{2}+11 s+11}$
3. $\frac{10 s+10}{s^{2}+11 s+11}$
4. $\frac{1}{s^{2}+s+1}$