A nonlinear adaptive backstepping approach applied to a three phase PWM AC–DC converter feeding induction heating A. Hadri-Hamida a, * , A. Allag b , M.Y. Hammoudi b , S.M. Mimoune b , S. Zerouali b , M.Y. Ayad c , M. Becherif c , E. Miliani c , A. Miraoui c a Laboratory of Electrotechnics of Constantine, University of Mentouri, 25000 Constantine, Algeria b MSE Laboratory, Department of Electrical Engineering, University of Biskra, BP 145, 07000 Biskra, Algeria c GESC Department, University of Technologies Belfort-Montbe ´liard, Belfort, Cedex 90010, France Received 24 May 2006; received in revised form 10 February 2008; accepted 10 February 2008 Available online 26 February 2008 Abstract This paper presents a new control strategy for a three phase PWM converter, which consists of applying an adaptive nonlinear control. The input–output feedback linearization approach is based on the exact cancellation of the nonlinearity, for this reason, this technique is not efficient, because system parameters can vary. First a nonlinear system modelling is derived with state variables of the input current and the output voltage by using power balance of the input and output, the nonlinear adaptive backstepping control can compensate the nonlinearities in the nominal system and the uncertainties. Simulation results are obtained using Matlab/Simulink. These results show how the adaptive backstepping law updates the system parameters and provide an efficient control design both for tracking and regulation in order to improve the power factor. Ó 2008 Elsevier B.V. All rights reserved. PACS: 05.45.a; 02.30.Yy; 07.50.Ek; 07.05.Dz Keywords: Adaptive nonlinear control; AC–DC converter; PWM converter; Induction heating 1. Introduction In the past few years remarkable progress has been made in development of high power density DC/DC converters using resonant link schemes which utilize high speed devices such as fast recovery transistors and GTOs. These new converters not only have high power density but also possess very low switching losses since switching of the devices are made at zero-voltage instants and thus enable the total system to operate at 1007-5704/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2008.02.005 * Corresponding author. Tel./fax: +213 33 74 27 33. E-mail address: am_hadri@yahoo.fr (A. Hadri-Hamida). Available online at www.sciencedirect.com Communications in Nonlinear Science and Numerical Simulation 14 (2009) 1515–1525 www.elsevier.com/locate/cnsns