A new method for experimental tuning of proportional integral controllers for non minimum phase systems based on the step response

In this paper we present a new method for tuning Proportional Integral (PI) controllers, for non-minimum phase systems, from experimental data obtained through an open-loop step test on the process to be controlled. As a novelty compared to previous works, the proposed approach allows the user to freely select the robustness as the desired Ms value, and the trade-off between performance and measurement noise amplification. Furthermore, the proposed method outperforms all previous step-response-based methods in the literature in terms of accuracy. The tuning procedure requires first measuring the process gain, the value and time of the minimum of the inverse oscillation, and the times taken to reach the zero value and 35.3% and 85.3% of the final output and then applying a set of tuning equations. The tuning equations approximate the controller that minimises the Integral of Absolute Error (IAE) of the disturbance response and are very accurate for a wide range of non-oscillatory stable inverse-response systems. The user can select the desired robustness (through the required maximum of the Sensitivity function Ms), unlike usual methods that allow the user only to choose between two or three predefined robustness levels. The PI controller that minimises 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 the user to find the desired trade-off between performance and actuator activity due to sensor measurement noise. The tuning procedure is shown to be more accurate, flexible, and less conservative than previous methods. A free JavaScript web application has been developed to implement the tuning procedure.