Environmental Engineering Reference
In-Depth Information
By normalising the module of the closed-loop transfer function and the
angular frequency to
and
respectively, we obtain the frequency
responses plotted in Fig. 4.6.
This figure helps to visualise that when is lower than a critical value
an overshoot in the frequency domain arises at a frequency,
with the (peak) amplitude,
both given below [MG9
1
]
It is apparent that the relative amplitude of the overshoot depends only on
the damping factor, For it can be shown that the module of the
frequency response is maximally flat (which is often referred to as the
Butterworth
condition). Specifically, this condition yields the largest
possible closed-loop 3-dB bandwidth within the constraint of a monotone
decreasing frequency response.
