Problem: A PM DC motor has the following parameters:

Rated Power 10 hp;

Rated armature voltage 230 V-DC;

Rated RPM: 1800;

Armature Resistance: 0.2 Ohm

Armature Inductance: 0.005 H

Inertia (motor plus mechanical load): 0.1 kgm^2;

Viscous friction coefficient: 0.015 Nms

1. Compute the voltage constant of the motor. Also compute therated current and rated torque of the motor (obtained at the ratedRPM). If the motor is supplied by 230 V across the armature, andthe only torque from the load is friction, compute the motorarmature current and speed. Repeat, if in addition to friction, a30 Nm counter torque is present at the load.

2. Provide the mathematical equations that describe the motor.Also provide a block diagram (using sdomain TF blocks) to representthe mathematical equations. Reduce the block diagram to a singleblock TF from the armature voltage to the speed. Find the poles andzeros of the TF.

3. Use the previous block in MATLAB rltool and design a PIcontroller to control the motor speed. The target performanceparameters are:

a. Speed overshoot less than 5%

b. Settling time of speed response less than 1.5 s

4. If the above controller is implemented by a 4Q dc-dcconverter, what should be the dc voltage?

5. Simulate the complete closed-loop system (along with arepresentation of the dc-dc regulator) in

Simulink. Obtain the response to a speed reference step changefrom 0 to 188.5 r/s. Also obtain the

response to a load torque increase from 0 to 30 Nm while themotor speed reference is 188.5 r/s.

Provide plots of the speed, armature voltage and armaturecurr