Q$2,$ Consider the system

Using phase variable

$\frac{d^{3}y}{d{t}^3}+5\frac{d^{2}y}{d{t}^2}+3\frac{dy}{dt}+2y=u$

regulator whose characteristic polynomial is of the form

approach, design a state

It is desired $()=({}^2+2{}_n+{}_n^2)(+{}_n).$ natural

to have a damping factor $=0\mathrm{.}8$ and frequency of oscillation ${}_n=6ra\frac{d}{s}.$