Actuators problem (DC motor) Duty Cycle, speed.

Consider a DC motor with separated excitation (or permanent magnets)
which is supplied with a voltage of 200v and a duty cycle of a. Consider that the machine
is under constant torque and it requires a constant current of 50A.
Consider Ra= 0.1 ohms, kaphi = 0.099 V/rpm. Find:

a)The possible range of the duty cycle under the constant torque conditions.
b)The range of the speed under the constant torque conditions.
c)The exact duty cycle so that the machine spins at 1000 rpms.

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