Control Theory

What is Control Theory?

Control theory is a branch of Applied Mathematics dealing with the use of feedback to 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, namely man-made systems and biological systems.

A simple example of a man-made system is cruise control for 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 the controller in the system.
More information on cruise control.

Control theory is thus closely linked to engineering and technology, which has been its traditional sphere of influence, dating back several centuries. For example, in the 18th century the invention of the regulator for 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, however, 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 many technological 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 in biology. Indeed many aspects of the human body illustrate the role of control in a biological system. For example, our sense of balance depends 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 is visual feedback that enables you to remain balanced.

Feedback control also enables the human body to maintain its temperature within a narrow range. More generally, the homeostasis of 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.