A 10kW, 48V, 250A, 3663 min-1 PMDC motor is given. The armature resistance (Ra) and inductance (La) values of the motor are 0.003615 Ω and 24.6 μH, respectively. The overall rotor and load inertia (J) is 0.17 kgm2 and the viscous friction coefficient of the motor-load system (B) is 0.012 Nm.s/rad. (Brush-commutator and iron losses are neglected and assuming all mechanical losses are due to viscous friction.)

a. Build the mathematical model (block diagram) of the motor model by using the fundamental equations and Laplace transformation.
b. By means of a modelling software (Matlab/Simulink or other), simulate the operation of the motor from starting to the rated load (the load can be assumed as a constant load which is independent from the motor speed). And give the graphs of armature current-time, shaft speed-time, shaft torque-time, shaft torque-shaft speed.
c. Obtain the no-load slowing down characteristic (rotating speed versus time) of the motor (from the no-load speed to zero speed). Comment and explain that which behaviours can be understood from that characteristic?

d. Design a closed loop speed control system of the motor which provides constant motor speed for various loading conditions?

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