The transfer function for an AFTI$/$F$-16$ aircraft relating angle of attack, $(t),$ to elevator de$-$

flection, ${}_e(t),$ is given by

$G(s)=\frac{0\mathrm{.}072(s+3)(s^2+0\mathrm{.}05s+0\mathrm{.}04)}{(s+0\mathrm{.}7)(s+1\mathrm{.}7)(s^2+0\mathrm{.}08s+0\mathrm{.}04)}$

Assume the block diagram shown in Figure $2$ for controlling the angle of attack, $,$ and do

the following:

a$)$ For $G_c=1,$ find the following:

What is the system type and the appropriate error constant associated with the

system type?

What are the Gain$-$Margin and Phase Margin?

Plot the s$-$plane and define if the system is stable or not.

b$)$ Use MATABL to design a PD controller to have a percent overshoot $3\%,$ rise time

$0\mathrm{.}2$ second.

c$)$ Use MATLAB to simulate your controlled system. Compare the results of the simula$-$

tion with the requirements in Part $($b$).$

Figure $2$: Simplified block diagram for angle of attack control.