Offset is a sustained error that cannot be eliminated by proportional control alone The basic equation of proportional control is as follows:

CO (t) = Kp e(t) + CO (0)

Where CO(t) is the controller output, CO(0) is the zero error controller output. when PV equals SP, then error is zero: e(t) = 0 if e(t) is zero, then CO equals the CO(0) if CO is steady at CO(0), then the PV settles to some steady value. The steady value is known by performing experiment on the system. And value CO(0) is adjusted so that PV settles in the range of set point. If a process disturbance occurs, CO(0) value will not change and it will cause permanent change in error and this is offset error in proportional control