Control Theory

Control theory is an interdisciplinary subfield of science, which originated from the branch of engineering and mathematics that deals with the behavior of dynamical systems, and later evolved into use by the social sciences like psychology, sociology and criminology. The process of designing a system to control behavior of a dynamic system is called “control philosophy”. Control systems are not about anything specific, rather it’s all about information flow and feedbacks. It is all about massive chains of feedbacks that run inside machines, humans, societies and systems all around. In a way it connects the researcher to “Unified Systems Theory”.    

Control theory is the field of applied mathematics that is relevant to the control of certain physical processes and systems. Although control theory has deep connections with classical areas of mathematics, such as the calculation of variations and the theory of differential equations, it did not become a field in its own right until the late 1950’s and early 1960’s when there were problems arising in engineering and economics. These problems were recognized as variants of problems in differential equations and in the calculus of variations, though they were not covered by existing theories. After that special modifications of classical techniques and theories were devised to solve individual problems.

 Model identification and robustness

 A control theory system must always have some robustness property. A robust controller is such that its properties do not change much given condition that it is applied to a system slightly different from the mathematical one used for its synthesis. This specification is important: no real physical system truly behaves like the series of differential equations used to represent it mathematically. Typically a simpler mathematical model is chosen in order to simplify calculations; otherwise the true system dynamics can be so complicated that a complete model is impossible.

System identification

The process of determining the equations that govern the model’s dynamics is called system identification.

Systems classifications

Systems classifications include nonlinear systems control, nonlinear systems control and decentralized systems. When the system is controlled by multiple controllers, the problem is one of decentralized control. Decentralization is helpful in many ways, for instance, it helps control systems operate over a larger geographical area.

Main control strategies

Some of the control theory strategies include adaptive control which uses on- line identification of the process parameters or modification of controller gains. Hierarchical control system is arranged using a set of devices and governing software is arranged in a hierarchical tree. Intelligent control, optimal control, robust control and stochastic control are the other types.

Questions:

• What is Control Theory?
• What are the 3 major classifications of the systems?