Control Valve : Let us assume that the control valve for this system follows a first order dynamics, hence

(IV.23)

The following figure is a representation of closed loop control configuration of liquid level in a tank.

Fig. IV.8: Schematic of closed loop control configuration of liquid level in a storage tank

IV.2.2 Effect of P controller on a process

Without losing the generality, let us assume for the following derivation. Let us concentrate on servo problem only. Regulatory problem can be solved in an analogous manner. We shall find closed loop response of first order and second order processes under the influence of a P controller.