IV.2.3 Offset in the output due to a P controller
The ultimate closed loop response at 
under P controller never reaches its desired setpoint. There always remains a discrepancy between the final value of response and the setpoint. This discrepancy is called the offset . Following derivation gives an account of the offset shown by first order and second order processes.
The final values of the processes on unit step change in setpoint are
 |
(IV.28) |
 |
(IV.29) |
Hence,
 |
(IV.30) |
On choosing 
, a zero offset can theoretically be obtained. However, such a higher value of Kc is neither practical nor possible. Note that, processes having integrator term 
in their transfer functions do not exhibit offsets.
The following figures show the offsets exhibited by a first and second order processes. In both the cases, offset is 