Sunday , June 24 2018

Determination of the Switching Times of the Bang-bang Control for a Linear Stepping Motor by Lyapunov Functions

Kamel Ben SAAD, Ahlem MBAREK, Mohamed BENREJEB
Unité de recherche LARA automatique, Ecole Nationale d’Ingénieurs de Tunis
BP. 37 le Belvédère, 1002, Tunis, Tunisia

Abstract: The linear tubular switched reluctance stepping motor is widely used in applications requiring high-precision linear positioning operations. But, the position evolution of this kind of stepping motors is oscillatory in the case of an open-loop control. In order to damp the position response of such motor, the bang-bang control is adopted. This classical control is simple to implement in practice. However, its successful application is dependent on the suitable determination of the switching instants for which there are no systematic methods allowing their determination. In this paper, a study allowing the determination of the switching instants of the bang-bang control is presented. This study is based on a stability analysis performed by Lyapunov’s direct method which is suitable for the studied nonlinear system. The validity of the proposed method is proven by numerical simulations and in practice by the use of a test bench.

Keywords: Linear Tubular Switched Reluctance Stepping Motor, overshoot, Lyapunov fuction, Bang-Bang control

Kamel Ben Saad was born in 1976 in Tunis, Tunisia. He graduated in 2000 from “Ecole Nationale d’Ingénieurs de Tunis” (ENIT). He also received his master degree from ENIT in 2001 and his PhD degree in Electrical Engineering from “Ecole Centrale de Lille” and ENIT in 2005. He is currently Assistant Professor at the ENIT. His research interests are in the area of machines, classical and intelligent control.

Mbarek Ahlem was born in 1980 in Nabeul, Tunisia. She graduated in 2005 from Ecole Nationale d’Ingénieurs de Monastir. She received her master degree in Electrical Engineering from “Ecole Nationale d’Ingénieurs de Tunis” (ENIT) in 2007. She is currently a PhD student in ENIT. Her research interests are in the area of stepping motors control.

Mohamed Benrejeb was born in Tunisia in 1950. He obtained the Diploma of “Ingénieur IDN” in 1973, The Master degree of Automatic Control in 1974, the PhD in Automatic Control of the University of Lille in 1976 and the DSc of the same University in 1980. Full Professor at “Ecole Nationale d’Ingénieurs de Tunis” since 1985 and at “Ecole Centrale de Lille” since 2003. His research interests are in the area of analysis and synthesis of complex systems based on classical and non conventional approaches.

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CITE THIS PAPER AS:
Kamel Ben SAAD, Ahlem MBAREK, Mohamed BENREJEB, Determination of the Switching Times of the Bang-bang Control for a Linear Stepping Motor by Lyapunov Functions, Studies in Informatics and Control, ISSN 1220-1766, vol. 17 (4), pp. 393-406, 2008.