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Chapter 6

Q. 6.EX.26

Nichols Chart for PID Example
Determine the bandwidth and resonant peak magnitude of the compensated system whose frequency response is shown in Fig. 6.71.

Step-by-Step

Verified Solution

The magnitude and phase information of the compensated design example seen in Fig. 6.71 is shown on a Nichols chart in Fig. 6.85. When comparing the two figures, it is important to divide the magnitudes in Fig. 6.71 by a factor of 20 in order to obtain |D(s)G(s)| rather than the normalized values used in Fig. 6.71. Because the curve crosses the closed-loop magnitude 0.70 contour at ω = 0.8 \text{ rad/sec }, we see that the bandwidth of this system is 0.8 \text{ rad/sec }. Because the largest-magnitude contour touched by the curve is 1.20, we also see that M_r = 1.2.