Environmental Engineering Reference
In-Depth Information
Returning to (3.
1
a), the closed-loop transfer function results as
where
is the DC closed-loop gain and
is the closed-loop pole, each
given by
The foregoing approximations hold for large loop gains which are
required for an adequate desensitisation of the closed-loop response with
respect to open-loop parameters. It is seen that increasing from zero shifts
the pole along the negative real axis, as illustrated in Fig. 4.2 1 . Since the pole
is located in the negative s -plane for any value of f , the system is termed
absolutely or unconditionally stable. This denotes an attractive condition
indicating that a one-pole amplifier is stable under all input signal conditions
1 This plot is called the root locus diagram. Its construction can become tedious for
higher order systems and we do not make use of this tool to examine stability. The
interested reader is referred to [SS91], [G85], or any feedback control text e.g.
[FPE94],
 
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