A control system is an interconnection of components forming a system configuration that will provide a desired system response. The basis for analysis of a system is the foundation provided by linear system theory . Many type of controllers are available in the industry, the main two types are: on/off and linear control system. Linear control systems use linear negative feedback to produce a control signal mathematically based on other variables, with a view to maintain the controlled process within an acceptable operating range. The output from a linear control system into the controlled process may be in the form of a directly variable signal . The main devices which are used in linear control system are: proportional controller and proportional with (integral or derivative action) controller or a sum of integral and derivative controller (PID). 1.1 Proportional (P) control
A proportional control system is a type of linear feedback control system which is more complex than an on-off control system, but simpler than a proportional-integral-derivative (PID) control system . In the proportional control algorithm, the controller output is proportional to the error signal, which is the difference between the set point and the process variable. In other words, the output of a proportional controller is the multiplication product of the error signal and the proportional gain.  P controller can be mathematically expressed as:
y: Output of the proportional controller
Kp: Proportional gain
e(t): Instantaneous process error at time (t).
Where: SP is set point and PV is process variable.
1.2 Proportional-Integral (PI) Control
PI controllers are often employed in practice where its combination of P and I controller and are connected in parallel. This type of controller is used to eliminate offset and it shows a maximum overshoot and settling time similar to the P controller but no steady-state...