System Error Transfer Function and Steady-State Error

Using block diagram reduction, it can be shown that the error transfer function for the single loop system is

Combining equations (1) and (2) gives the general form

The steady state error is found by using the final value theorem. Steady state errors for type "0" and type "1" systems for step, ramp, and parabolic inputs are calculated below.

Given these results, the results for type "2" and higher systems are easily deduced.

Type "0" System

The steady-state error of a type “0” system to step, ramp, and parabolic inputs may be

calculated as follows:

Step Input:

Ramp Input:

Parabolic Input:

Type "1" System

The steady-state error of a type “1” system to step, ramp, and parabolic inputs may be

calculated as follows:

Step Input:

Ramp Input:

Parabolic Input: