Question

A geared dc motor uses a 13 kHz PWM signal to control its speed. It uses a 12 V supply voltage and requires a minimum duty cycle of 15% to overcome frictional forces in the motor/gearbox and start the motor rotating. As the duty cycle is increased, the motor speed follows a linear relationship with this PWM signal up to the maximum angular velocity of 2150 rad/s. a) What duty cycle is required to run the motor at 1311.5 rad/s? Give your answer as % (i.e.Oto 100) to the nearest integer. Expected answer: 67 Round your answer to the nearest integer. * Score: 0/3 X Unanswered What is the perceived (ie, average) voltage at this duty cycle? Give you answer in V to 2 decimal places. Expected answer: 8.02 Pound your answer to 2 decimal places. * Score: 0/2 * Unanswered Advice

Answer 1

As per the question, a dc motor uses a 13 kHz PWM signal where a 12V supply voltage has been used which requires at least 15% of the duty cycle to overcome frictional forces. With the increasing duty cycle, the angular velocity will be increased in a linear fashion. The max. angular velocity is 2150 rad/sec.
a)   Therefore, the required duty cycle to run the motor at 1311.5 rad/sec will be
Duty cycle = (req. speed*100)/(max. speed) = (1311.5*100)/2150 = 61 %
b)   Now, we need to find the average voltage at this duty cycle which can be calculated as

Avg. Voltage = (current duty cycle/100)* max. voltage = 0.61*12 = 7.32 V.