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GATE ECE 2007 | Question-57

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. $\frac{1}{s^{2}+s+1}$
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