Control Theory

What is Control Theory?

Control theory is a branch of Applied Mathematics dealing with the use ofÌýfeedbackÌýto influence the behaviour of a system in order to achieve a desired goal. One can distinguish two classes of systems for which control theory plays an indispensable role, namelyÌýman-made systemsÌý²¹²Ô»åÌýbiological systems.

A simple example of a man-made system isÌýcruise controlÌýfor a car. The actual speed is recorded by the speedometer and is "fed-back" and compared to the speed setting on the cruise control, which causes the engine to accelerate if the speed is too low. The cruise control device is referred to as theÌýcontrollerÌýin the system.
More information on cruise control.

Control theory is thus closely linked toÌý±ð²Ô²µ¾±²Ô±ð±ð°ù¾±²Ô²µÌýandÌý³Ù±ð³¦³ó²Ô´Ç±ô´Ç²µ²â, which has been its traditional sphere of influence, dating back several centuries. For example, in the 18th century the invention of theÌýregulatorÌýfor a steam engine, a type of control mechanism, had a significant impact on industrial development in Europe. The development of the mathematical theory of control,Ìýhowever, began much later and has taken place mainly during the past 60 years.

In the second half of the 20th century, control theory played a major role in manyÌýtechnological advances, for example:

  • Control of spacecraft
  • CANADARM, the Space Shuttle's robotic arm
  • Robot technology
  • Antilock braking systems
  • Smart fluid technology

More information on man-made systems.

On the other hand, it is being increasingly recognized that control theory plays an important role inÌýbiology. Indeed many aspects of the human body illustrate the role of control in a biological system. For example, our sense of balanceÌýdepends on feedback. Most people can remain balanced while standing on one foot. If you close your eyes in this situation, however, you will quickly start wobbling. This simple experiment shows that it isÌývisual feedbackÌýthat enables you to remain balanced.

Feedback control also enables the human body toÌýmaintain its temperatureÌýwithin a narrow range. More generally, theÌýhomeostasisÌýof a living organism, i.e. the state of balance between its interdependent elements, is maintained through the use of feedback control.
More information on niological systems.