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Transfer function G_{0}(s) with delayed P behaviour
For this case from Eq. (7.15) the transfer function is

(7.23) 
This transfer function describes an open control loop with delayed
P behaviour. The variable is the
gain of this open
control loop. In this case it is composed of the
gain of the controller
and
of the plant
in multiplicative form

(7.24) 
With Eq. (7.18) one obtains for the steadystate error
of the closed control loop

(7.25) 
and for the step signal with
Eq. (7.19)

(7.26) 
It can be shown for a ramp input
signal according to Eq. (7.20) that the
double pole in Eq. (7.22) in the time
domain corresponds to
such that

(7.27) 
which is not finite. A similar situation results for a parabolic input signal using
Eq. (7.21).
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Christian Schmid 20050509