The process output is represented by

(V.1)

The control objective is to maintain at the desired setpoint . Hence the eq (V.1) can be rewritten as

(V.2)

The eq. (V.2) can be rearranged in the following manner:

or

.....................................................(V.3)

The eq. (V.3) can be schematically represented by Fig V.3(b).

For the sake of simplicity, measuring element and final control element were not considered as parts of the feedforward control configuration as shown in Fig V.3(b). In a more generalized case, when such elements are added in the controller configuration, the resulting control structure takes the form of Fig V.3(c). A generalized form of controller equation can be written as

.......................................................................................................(V.4)

And

(V.5)

In case of regulatory problem (disturbance rejection) i.e. when , the controller should be able to reject the effect of disturbance and ensure no deviation in the output, i.e. . In other words,

................................................................................................................(V.6)

or

.........................................................................................................................(V.7)

In case of servo problem (setpoint tracking), i.e. when , the controller should be able to ensure that output tracks the setpoint, i.e. . In other words,

.......................................................................................................................(V.8)

or

....................................................................................(V.9)