2. The data sheet for a wound field separately excited dc motor has the following parameters given: Rated Va=220V, Rated Ia=10A, Rated Vf=120V, La=100mH ; Ra=1.5, Rf=120, motor back emf constant is 0.215 V/RPM, torque constant is 1.5143 ft-lb/A, J=4 kg-m2 and rated speed =100rad/s. The friction and windage loss at rated conditions is 100 watts. 20% of that loss is due to friction and is constant over the entire speed range. 50% of that loss is due to drag and varies proportional to the speed. 30% of that loss is due to windage and varies proportional to the square of the speed. Calculate the following:

a) the armature current and torque being developed by the motor under rated conditions

b) No-load speed, Starting armature current, and starting torque.

c) Repeat part a and b if the armature voltage is reduced to 200V and determine the new Vf (if necessary) to ensure that operation up to rated speed is enabled.

d) Find the necessary Vf to ensure operation up to twice rated speed under the conditions of both a and c while operating at rated current

e) Plot the speed-torque characteristics of the motor from stall to twice rated speed for the rated conditions and the condition of c. Assume that the motor can be operated with sufficient current to achieve all conditions including those of b.

f) Determine the motor efficiency as a function of speed and then, using that efficiency, plot the speed versus input power characteristics for parts a, b, and c.

g) Determine appropriate drive current and voltage ratings and field supply current and voltage ratings to achieve the maximum torque-speed capability of the motor. Assume that overload torque capacity, i.e. to accelerate the motor from start-up, is maintained for a maximum of one minute. Therefore the drive can have a current overload capability equal to twice its rating.

h) On the same plot as e, plot the speed-torque characteristics and speed-input power characteristics limited by the maximum voltage and current capacity of the drive.

i) On the same plot as e, plot the speed-torque characteristics and speed-input power characteristics limited by the operation at the drive rated current.

3. Develop a MATLAB-Simulink model for DC motor described in (2.). Assume constant voltage power sources for both armature and field that are varied according to conditions described in (2.).

a. Use the simulation to validate your results to 2.(a)-(d). Provide supporting plots.

b. Add an affinity (pump) load to the simulation and ramp up the speed in open loop by using a variable DC source as the armature power supply. Ramp the speed up to the rated operational conditions of 2(a.). Plot the armature voltage, armature current, speed and torque