Control theory: Difference between revisions

Revision as of 13:01, 17 January 2023

Revision as of 18:04, 25 January 2023

Line 5:

'''Control theory''' is a field of mathematics that deals with the [[control system|control]] of [[dynamical system]]s in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control [[Stability theory|stability]]; often with the aim to achieve a degree of [[Optimal control|optimality]].

To do this, a '''controller''' with the requisite corrective behavior is required. This controller monitors the controlled [[process variable]] (PV), and compares it with the reference or [[Setpoint (control system)|set point]] (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are [[controllability]] and [[observability]]. Control theory is used in [[control system engineering]] to design automation that have revolutionized manufacturing, aircraft, communications and other industries, and created new fields such as [[robotics]].

Extensive use is usually made of a diagrammatic style known as the [[block diagram]]. In it the [[transfer function]], also known as the system function or network function, is a mathematical model of the relation between the input and output based on the [[differential equation]]s describing the system.