PID position control

A PID controller continuously calculates an error value

as the difference between a desired setpointand a measured process variable and applies a correction based on proportional, integral, and derivativeterms. The controller attempts to minimize the error over time by adjustment of a control variable

, 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:

where

, , and , all non-negative, denote the coefficients for the proportional, integral, andderivative terms, respectively (sometimes denoted P, I, and D). In this model:

• • 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.