Modern Control Engineering

490 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Method

This transfer function is tentative because we have not examined the phase-angle curve yet.

Once the corner frequencies are noted on the log-magnitude curve, the corresponding phase-

angle curve for each component factor of the transfer function can easily be drawn. The sum of

these component phase-angle curves is that of the assumed transfer function. The phase-angle

curve for G(jv)is denoted by in Figure 7–88. From Figure 7–88, we clearly notice a dis-

crepancy between the computed phase-angle curve and the experimentally obtained phase-

angle curve. The difference between the two curves at very high frequencies appears to be a

constant rate of change. Thus, the discrepancy in the phase-angle curves must be caused by

transport lag.

Hence, we assume the complete transfer function to be G(s)e–Ts. Since the discrepancy be-

tween the computed and experimental phase angles is –0.2vrad for very high frequencies, we can

determine the value of Tas follows:

or

The presence of transport lag can thus be determined, and the complete transfer function deter-

mined from the experimental curves is

G(s)e-Ts=

320(s+2)e-0.2s

s(s+1)As^2 +8s+ 64 B

T=0.2 sec.

vlimSq

d

dv

/G(jv)e-jvT=-T=-0.2

/G

40

20

0

• 20


• 40


• 60

dB

• 80


• 100
  0.1 0.2 0.4 0.6 1 2 4 6 10 20 40


• 500 °


• 400 °


• 300 °


• 200 °


• 100 °

0 °

v in rad/sec

G

Magnitude

(asymptotic)

Magnitude (K= 10)

(experimental)

Phase angle

(experimental)

Figure 7–88

Bode diagram of a

system. (Solid curves

are experimentally

obtained curves.)

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