Cruise Control Units

Control theory is an interdisciplinary branch of engineering and mathematics, that deals with the behavior of dynamical systems. The desired output of a system is called the reference. more...

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When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system.

Overview

Control theory is

theory, that deals with influencing the behavior of dynamical systems; interdisciplinary subfield of science which originated in engineering and mathematics, and evolved into use by the social sciences, like psychology, sociology and criminology.;

An example

Consider an automobile's cruise control, which is a device designed to maintain a constant vehicle speed; the desired or reference speed, provided by the driver. The system in this case is the vehicle. The system output is the vehicle speed, and the control variable is the engine's throttle position which influences engine torque output.

A simple way to implement cruise control is to lock the throttle position when the driver engages cruise control. However, on hilly terrain, the vehicle will slow down going uphill and accelerate going downhill. In fact, any parameter different than what was assumed at design time will translate into a proportional error in the output velocity, including exact mass of the vehicle, wind resistance, and tire pressure. This type of controller is called an open-loop controller because there is no direct connection between the output of the system (the engine torque) and the actual conditions encountered; that is to say, the system does not and can not compensate for unexpected forces.

In a closed-loop control system, a sensor monitors the output (the vehicle's speed) and feeds the data to a computer which continuously adjusts the control input (the throttle) as necessary to keep the control error to a minimum (to maintain the desired speed). Feedback on how the system is actually performing allows the controller (vehicle's on board computer) to dynamically compensate for disturbances to the system, such as changes in slope of the ground or wind speed. An ideal feedback control system cancels out all errors, effectively mitigating the effects of any forces that may or may not arise during operation and producing a response in the system that perfectly matches the user's wishes.

History

Although control systems of various types date back to antiquity, a more formal analysis of the field began with a dynamics analysis of the centrifugal governor, conducted by the physicist James Clerk Maxwell in 1868 entitled On Governors. This described and analyzed the phenomenon of "hunting", in which lags in the system can lead to overcompensation and unstable behavior. This generated a flurry of interest in the topic, during which Maxwell's classmate Edward John Routh generalized the results of Maxwell for the general class of linear systems. Independently, Adolf Hurwitz analyzed system stability using differential equations in 1877. This result is called the Routh-Hurwitz theorem.

Read more at Wikipedia.org