Process step response based fractional PI^λD^μ controller parameters tuning for desired closed loop response

Abstract

In this paper, a tuning method of the fractional PI^λD^μ controllers for classical feedback control systems is proposed. The PI^λD^μ controller design strategy is drawn up such that the closed loop system is equivalent to a desired fractional order model whose transfer function is Bode's ideal function $G_d\left(s\right)=\frac{1}{1+{\left(s/{\omega }_u\right)}^m}$, a widely used function in the fractional order control domain because of its iso-damping property which is an important robustness feature. In this tuning technique, the values of the five parameters of the fractional PI^λD^μ controller are derived analytically using only the step response of a stable process without requirement of its model. The derived formulations of the tuning technique are presented. Illustrative examples are given to test the effectiveness and the usefulness of the proposed PI^λD^μ controller tuning approach.

Keywords:

• Bode's ideal function
• fractional PI^λD^μ controller
• iso-damping property
• robustness
• step response

Additional information

Notes on contributors

Nadir Fergani

Nadir Fergani was born in Annaba, Algeria in 1984. He has received the ‘Ingénieur d’Etat’ degree in electronics from Badji Mokhtar University, Annaba, Algeria, in 2007 and the Magister degree in control systems from Mentouri University, Constantine, Algeria, in 2010. In 2009, he joined the Signal Processing Laboratory as researcher of the Mentouri University, Constantine, Algeria where he is currently working towards his PhD degree. His current research interests are in the area of industrial process control and tuning of fractional order controllers.

Abdelfatah Charef

Abdelfatah Charef received the Diplôme des Etudes Supérieures (DES) from the University of Constantine, Algeria, in 1984, the master's and PhD degrees in electrical engineering from Drexel University, Philadelphia, Pennsylvania, USA, in 1987 and 1991, respectively. In September 1991, he joined the Department of Electronics of the University of Constantine, Algeria, where he is currently professor and director of the Signal Processing Laboratory. His current research interests are in the areas of Fractional Order Operators and Systems, Fractional Order Control, Fractional Order Signal Processing and Applications of Fractional Operators and Systems in Biomedical Signal Processing.