Section 7–12 / Lag Compensation 503In the complex plane, a lag compensator has a zero at s=–1/Tand a pole at
s=–1/(bT).The pole is located to the right of the zero.
Figure 7–101 shows a polar plot of the lag compensator. Figure 7–102 shows a Bode
diagram of the compensator, where Kc=1andb=10.The corner frequencies of the
lag compensator are at v=1/ Tandv=1/(bT).As seen from Figure 7–102, where
the values of Kcandbare set equal to 1 and 10, respectively, the magnitude of the lag
compensator becomes 10 (or 20 dB) at low frequencies and unity (or 0 dB) at high fre-
quencies. Thus, the lag compensator is essentially a low-pass filter.
Lag Compensation Techniques Based on the Frequency-Response Approach.
The primary function of a lag compensator is to provide attenuation in the high-
frequency range to give a system sufficient phase margin. The phase-lag characteristic
is of no consequence in lag compensation.
The procedure for designing lag compensators for the system shown in Figure 7–93
by the frequency-response approach may be stated as follows:
1.Assume the following lag compensator:
Gc(s)=Kc b
Ts+ 1
bTs+ 1
=Kc
s+
1
T
s+
1
bT
(b 7 1)
Im0Rev =` v = 0Kc KcbFigure 7–101
Polar plot of a lag
compensator
Kcb(jvT+ 1 )(jvbT+ 1 ).
3020v in rad/sec1000 °- 90 °
dB0.01
T0.1
T1
T10
TFigure 7–102
Bode diagram of a
lag compensator
b(jvT+1)/(jvbT+1),
withb=10.