A new method for experimental tuning of PI controllers based on the step response. (September 2022) - Sanchis, Roberto; Peñarrocha-Alós, Ignacio
Abstract: In this paper we present a new method for tuning Proportional Integral (PI) controllers from experimental data obtained through an open loop step test over the process to be controlled. The tuning procedure requires first the measurement of the process gain, and the times taken to reach the 5%, 35.3% and 85.3% of the final output and then applying a set of tuning equations. The tuning equations approximate the controller that minimizes the Integral of Absolute Error (IAE) of the disturbance response for a model with three real poles and time delay and are very accurate for a wide range of non oscillatory stable systems. The user can select the desired robustness (through the required maximum of the Sensitivity function ( M s )), as a difference with usual methods that allow only to choose among two or three predefined robustness. The PI controller that minimizes the disturbance IAE is defined by default, but the user can also select a detuning factor to define slower controllers with the same robustness, allowing to find the desired compromise between performance and actuator activity due to sensor measurement noise. An application for Android, that can be downloaded for free, and a web based application, have been developed to implement the tuning procedure. Highlights: A new method for tuning PI controllers from the step response data is presented. A set of equations allow to compute Kp and Ti as a function of simple measurements taken in the step response. The desired robustness can be selected in terms of Ms, and the PI that minimizes the disturbance IAE is obtained. It also allows to find the desired compromise between performance and noise amplification (maintaining robustness). An application (for Android or web) has been developed, that implements the tuning procedure. The tuning procedure requires the measurement of the process gain, and the times taken to reach the 5%, 35.3% and 85.3% of the final output of the step response. The tuning equations are accurate for a wide range of processes, with different values of L τ being lag dominant or delay dominant.