On the Derivative Backoff Problem in PID Controllers

Abstract

The Proportional-Integral-Derivative (PID) is by far the most common controller in process industries. In practice, a problem with PID controllers may arise when the controlled process variable (PV) saturates. At this point, the error, i.e., the difference between the set point (SP) and PV becomes constant, and so the derivative control action becomes zero or backs off. This leads to a sudden increase in the total controller output and as a result the process variable moves above its limit showing larger overshoot and settling time. To solve this problem, it is proposed to modify the PID controller action when the PV saturates. The modification is simply to multiply the derivative part by a suitable gain, transfer it to the integral part, and then the derivative part is set to zero. When the process output later becomes unsaturated, the derivative action is activated again. This technique is shown to reduce the overshoot, settling time, integral of absolute error (IAE), and works well in the presence of measurement noise. Although the optimal value of the gain depends on the size of disturbance which is not usually known, a fixed value of 2 is shown to be reasonable for most levels of disturbance.