Calculation of offset from the closed-loop transfer function

Calculation of Offset from the Closed-Loop Transfer Function 

Referring to Fig. 7.36, for a proportional controller Gc(j) = Kc (equation 7.62). Assume for simplicity that the time constants of G,(j) (the final control element) and H(j) (the measuring element) are negligible compared with that of G2(j) (the 

Offset is defined as the difference between the desired and actual response of the output as t - (Section 7.2.3), i.e. in this case  

Thus the offset is reduced as the controller gain Kc is increased. 

Load Change with PI Control From equation 7.63  

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