$\frac{Y(s)}{R(s)} = \frac{3s+4}{s^2 +4s +3}$

Mumbai University > Electronics Engineering > Sem 4 > Linear Control Systems

Topic : State Variable Models

Difficulty : High

Marks : 10M

The given transfer function can be written in the form of: $T(s)=\cfrac{X_{1}(s)}{R(s)}\cdot \cfrac{Y(s)}{X_{1}(s)}$

Let, $\cfrac{X_{1}(s)}{R(s)}=\cfrac{1}{s^{2}+4s+3}$ --------(1)

$\cfrac{Y(s)}{X_{1}(s)}=3s+4$ --------(2)

From equation (1), we get,

$X_{1}(s)[s^{2}+4s+3]=R(s)$

$s^{2}X_{1}+4s X_{1}+3X_{1}=R(s)$

Taking inverse laplace transform,

$\cfrac{d^{2}}{dt^{2}} x_{1}(t)+4 \cfrac{d}{dt} x_{1}(t)+3x_{1}(t)=r(t)$

$\ddot { { x }_{ 1 } } (t) +4 \dot { { x }_{ 1 …