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Problem $3$:

The open$-$loop pitch motion of a commercial transport aircraft can be approximated by the

following equations of motion:

$\backslash$theta $^()=$q

q$^()=-9\backslash$theta $-(1)/(2)$q$+\backslash$delta $\_($e$)$

where

q : pitch rate ra$($d$)/($s$)$

$\backslash$theta : pitch attitude $[$rad$]$

$\backslash$delta $\_($e$)$ : elevator deflection $[$rad$].$

Complete the following analysis and design tasks:

avec$($x$)^()=$Avec$($x$)+$Bvec$($u$)$

given that the state vector is vec$($x$)=[[\backslash$theta $],[$q$]]$ and the input vector is vec$($u$)=\backslash$delta $\_($e$).$

Clearly write down and box the A and B matrices.

bA matrix in this problem is not a

triangular matrix.

cK$,$ where

u$=-$Kx$^(),$ so that the closed$-$loop system poles are located at s$\_(1,2\_($cL$))=-6+-$i$2,$ where

i$=\backslash$sqrt$(-1).$