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## 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.

## 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 $M_r = 1.2.$