Acne, Blemish Control

In engineering and mathematics, control theory deals with the behavior of dynamical systems. The desired output of a system is called the reference. more...

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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.

An example

Consider an automobile's cruise control, which is a device designed to maintain a constant vehicle speed. The output variable of the system is vehicle speed. The input variable is the engine's torque output, which is regulated by the throttle.

A simple way to implement cruise control is to lock the throttle position when the driver engages cruise control. However, on hilly terrain, the vehicle will slow down going uphill and accelerate going downhill. This type of controller is called an open-loop controller because there is no direct connection between the output of the system and its input.

In a closed-loop control system, a feedback control monitors the vehicle's speed and adjusts the throttle as necessary to maintain the desired speed. This feedback compensates for disturbances to the system, such as changes in slope of the ground or wind speed.

History

Although control systems of various types date back to antiquity, a more formal analysis of the field began with a dynamics analysis of the centrifugal governor, conducted by the physicist James Clerk Maxwell in 1868 entitled On Governors. This described and analyzed the phenomenon of "hunting," in which lags in the system can lead to overcompensation and unstable behavior. This generated a flurry of interest in the topic, during which Maxwell's classmate Edward John Routh generalized the results of Maxwell for the general class of linear systems. This result is called the Routh-Hurwitz Criterion.

A notable application of dynamic control was in the area of manned flight. The Wright Brothers made their first successful test flights on December 17, 1903 and were distinguished by their ability to control their flights for substantial periods (more so than the ability to produce lift from an airfoil, which was known). Control of the airplane was necessary for safe flight.

By World War II, control theory was an important part of fire-control systems, guidance systems, and electronics. The Space Race also depended on accurate spacecraft control. However, control theory also saw an increasing use in fields such as economics and sociology.

For a list of active and historical figures who have made a significant contribution to control theory, see People in systems and control.

Classical control theory: the closed-loop controller

To avoid the problems of the open-loop controller, control theory introduces feedback. A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inputs (e.g. voltage applied to an electric motor) have an effect on the process outputs (e.g. velocity or torque of the motor), which is measured with sensors and processed by the controller; the result (the control signal) is used as input to the process, closing the loop.

Read more at Wikipedia.org