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