Question

1. If an actuator input saturated at +12 and +3 volts. Given the duty cycle of a PWM signal with 35% (on/off), what is the average output voltage during one update period? 2. If an ADC has a sampling rate of 10k Hz, theoretically speaking, what would be the maximum frequency of the closed-loop system bandwidth? 3. Summarize two facts from the practical system that will limit the closed-loop control system bandwidth. (hint: based on question 1 & 2) 4. Explain the advantages/reasons of using PWM technique to design the controller signal. 5. Under the fact of an ADC that has fixed sampling rate, if the observer is designed with a high bandwidth, what effect would have from the sensor measurement? Also, suggest one general method to reduce that effect.

Answer 1

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          Please find the answer to Q1-3 attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

1. Average output = (12*0.35) + (3*0.65) = 6.15 volts

2. According to the Nyquist sampling criteria, the sampling frequency should be set to a minimum value of twice the highest frequency content in the signal. In this case, since fs = 10KHz, the maximum system bandwidth would be 5KHz.

3. The closed loop control system bandwidth is limited by the ADC sampling frequency, as seen in answer 2, and by the non-linearity of the PWM controller. Since the PWM controller operates on high frequency, there might be high frequency noise, which might limit nthe bandwidth.

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