Optimal tuning of PID controllers with derivative filter for stable processes using three points from the step response

Abstract

This paper proposes a novel approach for tuning Proportional Integral Derivative (PID) controllers, utilizing experimental data obtained from an open-loop step input. We propose to use the measurements of the times taken to reach 5%, 35.3% and 85.3% of the final output, as well as the process static gain, to tune the controller. The tuning equations are applicable for a wide range of stable and over damped systems. Starting from an approximate model with three real poles and time delay (obtained from the measurements), the tuning equations approximate the controller that minimizes the Integral of Absolute Error (IAE) of the disturbance response. The designer can freely decide the Sensitivity Margin (M_s) to fix a desired robustness, as a difference with respect to other known methods where the user chooses among few predefined robustness values. The user can also select freely the derivative filter parameter, N, to find the required compromise between speed response and measurement noise amplification. For N=0 a PI controller is chosen. As N increases, a faster PID controller is selected, with higher noise amplification. We have also developed a web-based application and an Android application, downloadable for free, that implement the tuning equations as well as the whole required procedure.

Keywords: Derivative filter; PID tuning; Proportional Integral Derivative; Sensitivity margin; Step response.