Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 341405, 14 pages
Research Article

Robust Sliding Mode Control for Tokamaks

1Department of Automatic Control and Systems Engineering, EUITI de Bilbao, University of the Basque Country (UPV/EHU), Rafael Moreno, 3, 48013 Bizkaia, Spain
2Laboratorio Nacional de Fusión, EURATOM/CIEMAT, 28040 Madrid, Spain

Received 29 May 2012; Accepted 1 August 2012

Academic Editor: Jun-Juh Yan

Copyright © 2012 I. Garrido et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nuclear fusion has arisen as an alternative energy to avoid carbon dioxide emissions, being the tokamak a promising nuclear fusion reactor that uses a magnetic field to confine plasma in the shape of a torus. However, different kinds of magnetohydrodynamic instabilities may affect tokamak plasma equilibrium, causing severe reduction of particle confinement and leading to plasma disruptions. In this sense, numerous efforts and resources have been devoted to seeking solutions for the different plasma control problems so as to avoid energy confinement time decrements in these devices. In particular, since the growth rate of the vertical instability increases with the internal inductance, lowering the internal inductance is a fundamental issue to address for the elongated plasmas employed within the advanced tokamaks currently under development. In this sense, this paper introduces a lumped parameter numerical model of the tokamak in order to design a novel robust sliding mode controller for the internal inductance using the transformer primary coil as actuator.