Environmental Engineering Reference
In-Depth Information
correspondence to the value of which nullifies the denominator of (4.35),
that is
For instance, assuming
K=
2 and
In [PP992] the model was validated for values of in a range from -1 to
0.5, meaning a doublet with its pole and zero spaced by a factor of two.
The time-domain closed-loop step response can be also approximately
represented through that of a pure two-pole amplifier. To evaluate the effect
of a pole-zero doublet, we calculate the relative deviation of
and
D
in a
two-pole amplifier given by (4.23) and (4.24)
For those cases in which is small, such as when a doublet arises from
process tolerances in a pole-zero compensation [BAR80], [PP95],
relationships (4.37) and (4.38) can be approximated to
The approximate relationships show that the relative variations of and
D
are linearly related to the spacing of the doublet. It can be seen that for
phase margins greater than 50° (i.e.
K >
1.2) the variation in
D
is much
greater than that of Besides, when the zero is lower than the pole, the
doublet has the effect of reducing overshoot (both in the frequency and in the
time domain).
