We consider the same DC motor as of Lab 1 and 2 for Speed Control with parameters K = 0.1, R = 1, L = 1 mH, B = 0.001 N. m. sec/rad; J = 0.001 N. m. s^2/rad Note that the rated current for the motor is 5A input current with a pic of 50A. The maximum speed that the motor can reach is 100 rad/sec (~1000 rpm) 1. Write the transfer function G(s) = (w(s))/(V(s)) of the DC motor. 2. Get the reduced representation of the transfer function PART I: We consider in this part a P-type controller Ge(s) = Kp 3. Show that with such a controller, the steady state error can never reach zero. 4. Show that the stability of the system is not altered with such a controller. 5. What is the maximum allowed value of the gain Kp by the hardware? 6. 7. Demonstrate the results in c-e) by simulation What would be the effect of a torque disturbance of 0.2 N.m on the steady state performance of the system. Would you maintain the same value of Kp? If not fine-tune the design. 8. Conclude about this part