Control theory

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

In a control system a controller manipulates the inputs to a system. In the control systems one or more output variables of a system need to follow a certain reference over time. By manipulating the input, the controller wants to obtain the desired effect on the output of the system. If we were to take a system without a controller it would simply have an input and an output. As there is no way to track the output relative to the input then the system is practically useless. If we add a controller, by feeding the output through the controller back to the input the output can be manipulated to meet the desired criteria. For example, if a kettle did not have a controller and it were switched on it would continue to boil the water indefinitely. By adding a controller, the boiling water (reference) is fed back to the input through the controller. The controller then tells the input to turn off the power as the water is already boiling. The system without the controller is called the open-loop system. When you add a controller in a feedback loop you create a closed-loop system. Open-loop systems are rarely ever consider stable as they cannot be controlled. Closed-loop systems incorporate a controller or series of controllers which, depending on the current output, configure the input such that the output will have the desired response.