Transfer function G₀(s) with delayed I₂ behaviour

The transfer function for this particular case is

and it describes a system with delayed behaviour. For the steady-state error of the closed loop system it follows in the case of a stable loop for a step and ramp input signal

and for a parabolic input signal

From these results, especially from Eqs. (7.26), (7.30) and (7.33) and from Table 7.1 it follows, that the steady-state error

Table 7.1: Steady-state 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 steady-state error is much smaller the smaller the value of the static control factor

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 steady-state 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.