Where, is the constant of proportion. Linearization of the model around its nominal operating point , expressing it in its deviation form and converting it in Laplace domain yields the following open loop transfer function:

(IV.19)

Incidentally, in this example . Needless to mention, this is a trivial case and should not be generalized.

Measuring device : Differential Pressure (DP) cell is a measuring device that measures differential pressure (ΔP) between two ends. output of DP cell maps a second order behavior with the differential pressure. In this example, DP cell measures the height of liquid level in the tank by comparing pressure exerted by liquid at one end with that of atmospheric pressure at the other. The pressure exerted by the liquid on the DP cell is linearly proportional to height of the liquid. Hence,

(IV.20)

where measured value of the height of the liquid, actual height of the liquid, constants.

Controller : As is the setpoint, the error can be expressed as

(IV.21)

Let us assume that we use a PI controller, the control action can be expressed as

(IV.22)