Question $1(50$ points$)$:

DC motors are widely used in various applications, including robotics, industrial automation, and home appliances, due to their ability to provide precise speed and position control. Understanding the modeling and control of DC motors is an essential skill for control engineers. In this project, you will model a DC motor in MATLAB Simulink, design various controllers $($P$,$ PI$,$ PD$,$ PID$),$ and analyze their performance. The motor parameters and specifications are provided below

$\backslash$table$[[$Parameter$,$Value,units$],[$Armature Resistance,$R_a=2,$