PID controller

A proportional–integral–derivative controller (PID controller) is a control loop feedback mechanism (controller) commonly used in industrial control systems. A PID controller continuously calculates an error value ${\displaystyle e(t)}$ as the difference between a desired setpoint and a measured process variable and applies a correction based on proportional, integral, and derivative terms (sometimes denoted P, I, and D respectively) which give their name to the controller type.

A PID controller continuously calculates an error value ${\displaystyle e(t)}$ as the difference between a desired setpoint and a measured process variable and applies a correction based on proportional, integral, and derivative terms. The controller attempts to minimize the error over time by adjustment of a control variable ${\displaystyle u(t)}$, such as the position of a control valve, a damper, or the power supplied to a heating element, to a new value determined by a weighted sum:

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