Static acceleration error constant

Fig: 1 Response of a type 2 unity-feedback system to a parabolic input.

 

The steady-state error of the system with a unit-parabolic input (acceleration input), which is defined by

The steady-state error is then

Note that the acceleration error, the steady-state error due to a parabolic input, is an error in position.

The values of K_a are obtained as follows:

Note that both type 0 and type 1 systems are incapable of following a parabolic input in the steady state. The type 2 system with unity feedback can follow a parabolic input with a finite error signal. Figure 1 shows an example of the response of a type 2 system with unity feedback to a parabolic input. The type 3 or higher system with unity feedback follows a parabolic input with zero error at steady state.