(a) First order process	(b) second order process

Fig. IV.9: Offsets exhibited by first order and second order processes

Note that both natural period of oscillation and damping factor decreased in closed loop response;more the value of controller gain less are the values of natural period of oscillation and damping factor. As a result the closed loop response becomes more oscillatory than its open loop counterpart.

IV.2.4 Effect of integral control action on a process

We shall find closed loop response of first order process under the influence of an “integral only” controller.

(IV.31)

It indicates that the order of the dynamics for the closed loop response is increased when integral control action is used. As a result, the response becomes sluggish.

Following derivation gives an account of the offset shown by first order closed loop process with a PI controller. The final value of the process on unit step change in setpoint is

(IV.32)