rg $=3//$b$1=0\mathrm{.}65//$ b$2=0\mathrm{.}371//$J$=0\mathrm{.}7//$ R $=260//$M $=40//$ Ja$=0\mathrm{.}35//$ Da $=0\mathrm{.}185//$K$1=13//$ K$2=8\mathrm{.}66(($I just want to solveMATLAB, nothing else$))$TF$=13/\{(1\mathrm{.}05$s$+1\mathrm{.}021)+((8\mathrm{.}66/$s$)+0\mathrm{.}185)\}$Perform the following using Matlab:

Derive the differential equations for the system in Figure $(1).$

Find the open loop transfer function. Plot the unit step response.

Plot the root locus of the open loop transfer function and comment on the stability.

Find the closed loop transfer function. Plot the unit step response.

For the closed loop response, calculate the system characteristics: percentage overshoot, rise time, peak time, settling time, and steady$-$state error from the response plot.

Design the required controller to improve the response of the system as you see convenient. $($Use the open loop transfer function$).$

Plot the new root locus $($use open loop with controller$)$ and the new system response $($use closed loop with controller$).$

For the closed loop response with controller, calculate the system characteristics: percentage overshoot, rise time, peak time, settling time, and steady$-$state error from the response plot.