MT$374-$ Modeling and Simulation

Assignment $3$

Class: BEMTS F$22$

Due Date: $05-12-2024$

Marks: $50$

CLO: $2$

Q$1$: Find the state space representation of the electrical network shown below if the output is $v_0.$

Q$2$: Represent the translational mechanical system shown above in state$-$space, where $x_1(t)$ is the output.

Q$3$: Represent the system shown below in state$-$space, where ${}_L(t)$ is the output.

Q$4$: For the transfer function given above, write the state equations and the output equation for the phase$-$variable representation. Also give the equivalent diagram. Verify your answer by finding step response for both models $($given and equivalent state$-$space$)$ in Simulink.

Q$5$: Find the transfer function $G(s)=\frac{Y(s)}{R(s)}$ for the following system represented in state space. Use MATLAB to verify your answer by finding step response.

$x^{}=\left[\begin{array}{ccccccc}3& -5& 2& -8& 7& -6& 2\end{array}\right]$

$-3$

$-3$

$1x+\left[\begin{array}{c}5\end{array}\right]$

$-3$

$2r$

$y=\left[\begin{array}{ccc}1& -4& 3\end{array}\right]x$