Transfer function G₀(s) with delayed P behaviour

For this case from Eq. (7.15) the transfer function is

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

With Eq. (7.18) one obtains for the steady-state error of the closed control loop

and for the step signal with Eq. (7.19)

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

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