# Control Theory

Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs. The external input of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system.

The usual objective of a control theory is to calculate solutions for the proper corrective action from the controller that result in system stability, that is, the system will hold the set point and not oscillate around it.

The inputs and outputs of a continuous control system are generally related by differential equations. If these are linear with constant coefficients, a transfer function relating the input and output can be obtained by taking their Laplace transform. If the differential equations are nonlinear and have a known solution, it may be possible to linearize the nonlinear differential equations at that solution. If the resulting linear differential equations have constant coefficients one can take their Laplace transform to obtain a transfer function.

The transfer function is also known as the system function or network function. The transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant solution of the nonlinear differential equations describing the system.

Extensive use is usually made of a diagrammatic style known as the block diagram.

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