What is Control theory?
[[File:Boulton and Watt centrifugal governor-MJ.jpg|thumb|[[Centrifugal governor]] of a Watt steam engine, of 1788.]] '''Control theory''' is an [[interdisciplinary]] branch of [[engineering]] and [[mathematics]]. It deals with the behavior of [[Systems engineering|systems]]. The desired [[output]] of a system is called the ''reference''. In that context, a system can be influenced by certain input values. Depending on the input values, the system may change its state or its behavior. Common questions control theory asks: * Is a system in a stable state? * How sensitive is the system to changed of input parameters? * Are all variables within a given range? * Is it possible to reach a predefined target state? * If the target state can be reached, what must the input variables be set to, so that the target state is reached? One of the first modern people to talk about control theory was [[James Clerk Maxwell]]. In his work On Governors, of 1868, he looked at the dynamic properties of centrifugal governors, as they were used by [[Steam engine|steam engines]].<ref>{{Cite journal|last=Maxwell|first=James Clerk|date=1868-01-01|title=I. On governors|url=https://royalsocietypublishing.org/doi/10.1098/rspl.1867.0055|journal=Proceedings of the Royal Society of London|volume=16|pages=270–283|doi=10.1098/rspl.1867.0055|s2cid=51751195}}</ref> Such governors were already used to regulate the speed of [[Windmill|windmills]]. ==Mathematical model== A system is a model used to describe the behaviour of something in the real world that takes inputs and produces outputs. For example, a car is a system in that the driver chooses how hard to press on the gas pedal (the input) and the car drives along the road at a certain speed (the output). In the case of a car, the input to the gas pedal does not fully determine the speed of the car. The weight in the car, the incline of the road, the traction of the tires, the current speed of the car, and other factors can all change the output received for a particular input. Control th