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 as the difference between a desired set point 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 as the difference between a desired set point 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:

• P accounts for present values of the error. For example, if the error is large and positive, the control output will also be large and positive.
• I accounts for past values of the error. For example, if the current output is not sufficiently strong, the integral of the error will accumulate over time, and the controller will respond by applying a stronger action.
• D accounts for possible future trends of the error, based on its current rate of change.