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Chapter 10:
Proportional-Integral-Derivative Controllers
Control systems, in particular, feedback control systems, are important components in a number of instruments where stability and high precision are required for operation. A simple example of such a system might be a precision oven, where the temperature needs to be held to within a fraction of a degree over a long period of time. By sensing the temperature and controlling a heating or cooling element, the temperature can be maintained to very high precision. This is the basic principle behind a feedback controller. The temperature in the oven is set at a specific level, and as the temperature in the box moves from this set temperature, the heater will turn on or off so that there are very minimal temperature changes. A more complicated example might be an image stabilization system. The proportional-integral-derivative (PID) controller is a sophisticated type of controller that acts on the difference between the current state and the desired state, usually expressed as the set point. If the difference between the two states is large, the controller acts to restore the desired state. The effect of each of the three components of the controller on reducing the error is represented by a gain factor that is normally selected such that the system responds effectively to change and minimizes overshoot as the error is minimized. In this chapter we will be concentrating on both the digital and the analog circuit representations of the PID controller and some examples of where they are used in optical systems. In general, analog electronics allows us to work with faster controllers, and digital systems are easier to implement and change.
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