What is Control?

Broadly speaking, control theory studies how to make systems behave in certain ways (i.e., "control" them) by supplying proper "inputs" to them. For example, suppose that the system under consideration is the electrical power grid. The objective is to deliver a certain amount of power by supplying input energy via various sources. Control theory is used to answer questions such as:

• How exactly should this power be put onto the grid so that the output of the grid behaves in a certain way?
• How quickly do the power levels at the destinations reach their desired values?
• If there are failures in the grid, how should the input to the grid be modified so that the system does not become unstable and lead to blackouts?

As another example, consider a wind turbine. In order to operate the turbine efficiently, it is required to rotate at a certain speed -- if it rotates too quickly, the mechanical structure can be damaged, and if it rotates too slowly, it may not produce as much power as it should. The rate of rotation of the turbine can be controlled by varying the angles of the turbine blades based on the current wind speed. In this case, control theory can be used to answer the question: What is the most efficient strategy for varying the blade angles in order to obtain a certain rate of rotation?

Similar questions can be posed for almost any application, whether it be in engineering, biology, economics, or the social sciences; the role of control theory is to provide answers to these questions using rigorous mathematical analysis and tools.