Q2) (30 points) A block diagram for full state feedback control system is shown in the Fig. 2.
where
$x_1 = x_2$,
$x_2 = x_3$,
$x_3 = x_4$,
$x_4 = -12x_1 - 8x_2 - 5x_3 - 2x_4 + u$,
y = 3x1 + 5x2 - 2x3 + 4x4
a) Find A, B and C matrices of the system.
b) Find K matrix that will assign the poles at {-1+1.Xi, -1-1.Xi, -10, -20}
\textbullet X is the last digit of your number
c) When X increase, what will happen to Ts, Tp and \%OS? Explain briefly.
