Topic: Control Systems
In the asymptotic bode plot of a transfer function of a closed loop system shown below, the number of poles and zeros are,
(The Bode plot starts from +40 dB at low frequency, slopes down to 10 dB at a frequency between 1K and 10K, then slopes up to 20 dB at 10K, and finally slopes down crossing 0 dB.)
- A. 3 pole, 2 zero
- B. 2 pole, 2 zero
- C. 2 pole, 1 zero
- D. 3 pole, 1 zero
Answer: A. 3 pole, 2 zero
Explanation: Since the plot is starting from 40 dB and decreasing at low frequencies, it indicates there are 2 poles at the origin (slope of -40 dB/dec).
At the frequency between 1k and 10k, the slope turns positive (+20 dB/decade), which means 2 zeros are added to change the slope by +40 dB/dec.
At the frequency 10k, a pole is added so that the slope is again -20 dB/decade.
Thus, there are $2+1=3$ poles and 2 zeros in total.