The motor parametrs are Ja$=0\mathrm{.}6,$ Da$=0\mathrm{.}1,$ Kt$/$Ra$=8,$Kb$=0\mathrm{.}2.$ As seen at its input shaft, the gear pair between the motor and load has mass moment of inertia J$1=1\mathrm{.}4$ and viscous damping D$1=0\mathrm{.}4.$ The tooth counts are N$1=50$ and N$2=1250.$ The load moment of inertia is JL$=1300.$ The load provides viscous damping, DL$=140.1)-$ Obtain the transfer fuction and the state space model of the system $($must use phase variable method based on transfur fuction$)$ considering that the input is voltage $($ea$)$ and output is load output shaft $($L$).$ You must show detail of your calculations. $(20\%)$

$2)-$ Design a controller using pole placement method for $25\%$ overshoot and $1$ second setteing time. $(20\%)$

$3)-$ Design an observer with its poles $10$ times futher away from imaginiry axis $($You much use observer canonical format here$).(20\%)$

$4)-$ Design an integral control to eliminate the steady state error with the overshoot of $25\%,$ and the setteing time of one second. $(20\%)$

$5)-$ Using Aukermann method obtain the observer gains for the phase variable state space model. Then use the observer to estimate the state variables for the controller. $(20\%)$