$($Please use MATLAB and simulink, show code and make sure it works$)$ Given the following data for the Learjet $24$ aircraft:

$g=32\mathrm{.}17405[A{t}^2]($gravitational

acceleration on Earth$)$

$s=0[t]($sta level$)$

$U_1=169\mathrm{.}98[$t ts $]$

$x_0=-0\mathrm{.}0589[\frac{1}{3}]$

$x_n=11\mathrm{.}3367[t{s}^2]$

$x_{0+}=0[t{t}^2]$

s$]$

$z_a=-103\mathrm{.}5160[f^2{s}^2]$

$Z_t=-7\mathrm{.}8184[f{t}^2]$

$M_9=-0\mathrm{.}0002[1t{t}_3]$

$M_a=-19408[\frac{1}{s^2}]$

$M_a=-03027[\frac{1}{s}]$

$M_4=-0\mathrm{.}8174[1s]$

$M_{46}=-28818[{15}^2].$

a$)($Computational$,5$ points$)$ Set up the longitudinal state$-$space system for this zircratt as

follews:

Clearly show the A$,$ B$,$ C$,$ and D matrix in your MATLAB code. Here we can assume C

is a $4$ by $4$ identity matrix and $D$ is a rull $($zero$)$ matrix.

b$)($Computational$,5$ points$)$ Check open$-$loop pole locations and damping characteristics

of the aircraft system from part $($a$).$ Is the open$-$loop aircraft system stable or unstable?

Clearly explain why. You may write your explanation as comments in your MATLAB

program.

c$)($Computational$,10$ points$)$ Write a MATLAB$-$Simulink program to simulate the open$-$

loop responses of the aircraft to an elevator input taken as a doublet as shown below:

Plot $u(t)$ vs$.t,(t)$ vs$.t,q(t)$ vs$.$ t $,$ and $(t)$ vs$.t$ Please remember to label the axes

and title the plots.