434 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Methoddenominator polynomial of G(jv)is greater than that of the numerator, then the G(jv)
loci converge to the origin clockwise. At v=q, the loci are tangent to one or the other
axes, as shown in Figure 7–34.
Note that any complicated shapes in the polar plot curves are caused by the nu-
merator dynamics—that is, by the time constants in the numerator of the transfer func-
tion. Figure 7–35 shows examples of polar plots of transfer functions with numerator
dynamics. In analyzing control systems, the polar plot of G(jv)in the frequency range
of interest must be accurately determined.
Table 7–1 shows sketches of polar plots of several transfer functions.
Im(^0) Re
v =
n–m= 1
n–m= 2
n–m= 3
G(jv)=
bo(jv)m+...
ao(jv)n+...
Figure 7–34
Polar plots in the high-frequency range.
Im
(^0) Re
0
v=`vIm0 Re0
v=`vFigure 7–35
Polar plots of transfer functions with numerator dynamics.Openmirrors.com