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Modern Control System Theory and Design, 2nd Edition by Stanley M. Shinners

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6.12.  RELATIONSHIP BETWEEN CLOSED-LOOP FREQUENCY RESPONSE AND THE TIME-DOMAIN RESPONSE

Section 6.10 has illustrated how the closed-loop frequency-domain response may be obtained from the open-loop transfer function. The next logical question to ask is how to determine the relationship between Mp and the peak overshoot one obtains in the time domain. In Chapter 4, we defined the time at which the peak overshoot occurs as tp in terms of ζ and ωn [see Eq. (4.29)]. For example, does an Mp of 1.3 mean a 30% transient overshoot in the time domain?

Table 6.20. MATLAB Program to Obtain the Nichols Chart for the System whose Open-Loop Transfer Function is shown in Eq. (6.121)

num = [780    1344.8273] den = [1    30.5747    217.2414    114.9425    0] a = −[.25:.25:1    2    5    10:10:170    179.99]; b = [−24      − 18      − 12      − 9    − 7      − 5: − 1     −.5:.25:.5    1:5    7    9    12]; [x,y] = nichgrid([−360    0    − 24    36],a,b,3); [mag, ph] = bode(num,den,logspace(-1,2)); plot(ph,20 * log10(mag)); W = [5   1   2   5   7   9   12]; [mag, ph] = bode(num,den,w); plot(ph,20 * log10(mag),‘ * g’) title(‘Nichols Frequency Response Plot’)

Image

Figure 6.52   Nichols chart with Image superimposed.

This problem has been analyzed for the general, unity-feedback system of Figure 6.45 [22 ...

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