Example: F$16$ Longitudinal Model

$\frac{dx}{dt}=f(x,u)$

State vector $x$

$x_1-$ velocity $V[f\frac{t}{sec}]$

$x_2-$ angle of attack $[$rad$]$

$x_3-$ pitch angle $[rad]$

$x_4-$ pitch rate $q[ra\frac{d}{sec}]$

Control input

$u-$ elevator deflection ${}_e[deg].$

$1-$ Fer the F$-16$ model of airplane give in the slides, derive the state space model if$"$

a$)y=V$ elocity

b$)$ Velocity, AOA