For the mathematical analysis of control systems its possible to consider the controller as a simple computer. For example, a proportional controller may be thought of as a device which receives the error signal and puts out a signal proportional to it. Similarly, the final control element may be considered as a device which produces corrective action (related with output signal of the controller) on the process. In industry final control elements are operated electronically in most of the cases. However, here a pneumatic (needs air to operate) valve is chosen in order to understand the details.

…