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The transfer function for this particular case is

(7.31) 
and it describes a system with delayed
behaviour. For the steadystate
error of the closed loop system it follows in the case of a stable loop
for a step and ramp input signal

(7.32) 
and for a parabolic input
signal

(7.33) 
From these results, especially from Eqs. (7.26),
(7.30) and (7.33) and from
Table 7.1 it follows, that the steadystate error
Table 7.1:
Steadystate error for different type of systems of
and different input signals
(command and disturbance signals if all disturbances will
act at the plant output)

, which characterises the static behaviour of the
control loop
is in all cases smaller the larger the loop gain given by
Eq. (7.24). In the case of delayed P behaviour of the open loop
the steadystate error
is much smaller the
smaller the value of the
static
control factor

(7.34) 
Often a large loop gain rapidly leads to
instability of the closed loop. For setting
usually a compromise is made unless selecting an
appropriate type of controller such that the steadystate error
vanishes. Both, the dynamical and
especially the static behaviour depend
strongly
on the choice of the controller. Therefore, in the
following the most important types of standard controllers will
be introduced.
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Up: Static properties of the
Previous: Transfer function G0(s) with
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Christian Schmid 20050509