Control theory deals with the study or behavior of dynamical systems that takes inputs. Reference is the term used for external inputs given to a system. A controller is used to manipulate the inputs that are given to a system in the case when one or more output variables are required to follow a particular reference for certain time so as to obtain the required effect on the system's output.

In a continuous control system, the inputs and the outputs are usually related by differential equations in some or other manner. In the case when these differential equations are linear along with constant coefficients as well, then we can obtain a transfer function that will relate the input and output simply by finding the Laplace transform.

In the case when these differential equations are not linear and also if their solution is known, then there is a possibility that we can linearize the non linear differential equation at that known solution. And then if the resulting linear equation has constant coefficients, we can find its Laplace transform in order to obtain the transfer function.

**The extensive use is usually made of a kind of diagram commonly known as the block diagram of a feedback control system.**Basically the definition of control theory has two parts:

**1)** It deals with influencing the behavior of dynamical systems.

**2)** It is a subfield of science, originated in engineering and mathematics in interdisciplinary manner and is also evolved in use by social sciences as in psychology, criminology, sociology and financial system as well.It is being considered having four functions that are measure, compare compute and correct which are completed by five main elements which are detector, transducer, transmitter, controller and final control element. The detector, transducer and transmitter are contained in one unit in practicality as they together complete the measuring function.

The controller completes the compare and compute functions which are implemented electronically by proportional control, PID controller, PI controller or programmable logic controller. The final control element completes the correct function. This element is responsible for changing an input and output in a control system that further affects the controlled variable.