Higher life forms maintain their body temperature to within half a degree.
Space telescopes maintain a pointing accuracy within about a millionth of a degree.
Computer hard disk drive read heads maintain an accuracy within about a micron.
Control is a common concept that underlies all dynamic systems, both natural and artificial. More specifically, feedback control is the basic mechanism by which systems, whether mechanical, electrical, or biological, maintain their equilibrium or homeostasis. In other words, the process of causing a system variable to conform to some desired reference value.
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In open-loop control, the system does not measure the output and there is no compensation of that output to make it conform to the desired output. I like to call this "good-luck-anticipating-the-system-exactly-and-getting-it-to-work control".
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In closed-loop control, the system uses feedback, which is the process of measuring a control variable and returning the output to influence the value of the variable. This is essentially how we design devices to automatically regulate themselves with great accuracy.
As you might expect, before we can even talk about controlling physical systems, we must find ways to model them mathematically. Fortunately, systems modelling is a large field and there are many ways to efficiently represent systems for both analytical and computational purposes.
Systems
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Currently, there are two main approaches to control theory: classical control and modern control. To really understand the reasons for such a division, one should be vaguely familiar with the history of automatic control, which briefly outlines the field's development from the water clocks and float regulators of the ancient Greeks and Arabs to the modern nonlinear systems currently used in aircraft controls and robotics.
Classical control, developing as it did for feedback amplifier design, was naturally couched in the frequency domain and the s-plane. Relying on transform methods, it is primarily applicable to linear time-invariant (LTI) systems, though some extensions were made to nonlinear systems. Classical control design makes extensive use of trial-and-error and qualitative graphical techniques, as well as a great deal of experience and intuition to balance all the factors that contribute to the system's overall behaviour.
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Unfortunately, classical control theory is difficult to apply to multi-input/multi-output (MIMO) and multi-loop systems, which led to the development of modern control.
Modern control is fundamentally a time domain approach based on linear algebra. Because the system's dynamical interconnections are described by vectors and matrices, modern control techniques can easily be extended to MIMO systems simply by increasing their dimensions. Fortunately, much of the intuition of classical control techniques can be incorporated into modern control design.
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Despite the "classical" and "modern" labels of these two areas, they both deal with continuous time systems only. This weakness, of course, had to be addressed since even 30 years ago it was clear that the computerization of control would revolutionize controller design and therefore discrete time techniques had to be developed. So we also have:
Digital control, which uses both classical and modern control techniques to implement control systems digitally in either hardware or software. Digital control systems naturally have their own quirks in addition to their tremendous advantages, which is why digital control is considered to be a separate area.
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Control theory is generally applied to controller design. Keep in mind that this is only the very tip of the iceberg; control is an astoundingly rich field that touches upon virtually every aspect of science and engineering. It's almost a kind of meta-science and is definitely paradigmatic of what creative engineering design is all about.
Thanks: eipi10
REFERENCES:
Franklin, G.F., J.D. Powell, A. Emami-Naeini. Feedback Control of Dynamic Systems, 3rd ed. Addison-Wesley, 1994.
First chapter of Lewis, F.L. Applied Optimal Control and Estimation. Prentice-Hall, 1992. http://www.theorem.net/lewis1.html
ECE311S/410F/411S lecture notes, University of Toronto