Īlthough a major application of mathematical control theory is in control systems engineering, which deals with the design of process control systems for industry, other applications range far beyond this. Control theory was further advanced by Edward Routh in 1874, Charles Sturm and in 1895, Adolf Hurwitz, who all contributed to the establishment of control stability criteria and from 1922 onwards, the development of PID control theory by Nicolas Minorsky. 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 equations describing the system.Ĭontrol theory dates from the 19th century, when the theoretical basis for the operation of governors was first described by James Clerk Maxwell. Įxtensive use is usually made of a diagrammatic style known as the block diagram. This is feedback control, which involves taking measurements using a sensor and making calculated adjustments to keep the measured variable within a set range by means of a 'final control element', such as a control valve.

This is the basis for the advanced type of automation that revolutionized manufacturing, aircraft, communications and other industries. Other aspects which are also studied are controllability and observability. 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. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). To do this, a controller with the requisite corrective behavior is required. 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 often with the aim to achieve a degree of optimality. For control theory in psychology and sociology, see control theory (sociology) and Perceptual control theory.Ĭontrol theory deals with the control of dynamical systems in engineered processes and machines. For control theory in linguistics, see control (linguistics). This article is about control theory in engineering.

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