The state-space representation of a separately excited DC servo motor dynamics is given by \[ \begin{bmatrix} \dfrac{d\omega}{dt} \ \dfrac{di_a}{dt} \end{bmatrix} = \begin{bmatrix} -1 & 1 \ -1 & -10 \end{bmatrix} \begin{bmatrix} \omega \ i_a \end{bmatrix} + \begin{bmatrix} 0 \ 10 \end{

Question

The state-space representation of a separately excited DC servo motor dynamics is given by $$ \begin{bmatrix} \dfrac{d\omega}{dt} \ \dfrac{di_a}{dt} \end{bmatrix} = \begin{bmatrix} -1 & 1 \ -1 & -10 \end{bmatrix} \begin{bmatrix} \omega \ i_a \end{bmatrix} + \begin{bmatrix} 0 \ 10 \end{bmatrix}u $$ where $\omega$ is the speed of the motor, $i_a$ is the armature current, and $u$ is the armature voltage. The transfer function $\omega(s)/U(s)$ of the motor is

Accepted Answer

10/(s²+11s+11). For the given state model, take $x=[\omega\ i_a]^T$, $A=\begin{bmatrix}-1&1\-1&-10\end{bmatrix}$, $B=\begin{bmatrix}0\10\end{bmatrix}$, and $C=[1\ 0]$. Using $G(s)=C(sI-A)^{-1}B$, the transfer function simplifies to $\omega(s)/U(s)=10/(s^2+11s+11)$.

Solution

Related GATE Technical questions