High-Order Filtered PID Controller Tuning Based on Magnitude Optimum

Damir Vrančić,Mikuláš Huba

doi:10.3390/math9121340

Damir Vrančić, Mikuláš Huba

Open Access

https://doi.org/10.3390/math9121340

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Abstract

The paper presents a tuning method for PID controllers with higher-order derivatives and higher-order controller filters (HO-PID), where the controller and filter orders can be arbitrarily chosen by the user. The controller and filter parameters are tuned according to the magnitude optimum criteria and the specified noise gain of the controller. The advantages of the proposed approach are twofold. First, all parameters can be obtained from the process transfer function or from the measured input and output time responses of the process as the steady-state changes. Second, the a priori defined controller noise gain limits the amount of HO-PID output noise. Therefore, the method can be successfully applied in practice. The work shows that the HO-PID controllers can significantly improve the control performance of various process models compared to the standard PID controllers. Of course, the increased efficiency is limited by the selected noise gain. The proposed tuning method is illustrated on several process models and compared with two other tuning methods for higher-order controllers.

Highlights

The PID controllers are widespread in many industries and are frequently included in embedded solutions [1,2,3,4]
While the first-order process can be efficiently controlled by the PI controller and the second-order process by the PID controller, the control efficiency for higher-order processes can be improved by increasing the controller order beyond the PID control
The HO-PID controller parameters will be derived according to the magnitude optimum multiple integration (MOMI) tuning method, which is based on the magnitude

Summary

Introduction

The PID controllers are widespread in many industries and are frequently included in embedded solutions [1,2,3,4]. Tuning methods for even higher-order controllers (m > 3) were developed for the integrating process model with a time delay (IPTD) [25,26,27]. This paper presents the PIDm n controller and filter tuning method, which is based on the parametric or the non-parametric process description. It means that the process can be given by the general transfer function (of the arbitrary order and time delay) or by the process input and output time-responses during the steady-state change of the process.

HO-PID Controller Tuning

HO-PID Controller with Specified HF Noise Amplification

Robustness

Comparison with Other Tuning Methods

Conclusions