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Journal of Control Science and Engineering
Volume 2012 (2012), Article ID 269346, 9 pages
Research Article

Adaptive Control for Nonlinear Systems with Time-Varying Control Gain

1Programa de Ingeniería Ambiental, Facultad de Ingeniería y Arquitectura, Universidad Católica de Manizales, Carrena 23 No. 60-30, Manizales 170002, Colombia
2Departamento de Ingeniería Eléctrica, Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia, Sede Manizales, Electrónica y Computación, Percepción y Control Inteligente, Bloque Q, Campus La Nubia, Manizales 170003, Colombia

Received 21 November 2011; Accepted 11 April 2012

Academic Editor: Chengyu Cao

Copyright © 2012 Alejandro Rincon and Fabiola Angulo. 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.


We propose a scheme for nonlinear plants with time-varying control gain and time-varying plant coefficients, on the basis of a plant model consisting of a Brunovsky-type model with polynomials as approximators. We develop an adaptive robust control scheme for this plant, under the following assumptions: (i) the plant terms involve time-varying but bounded coefficients, being its upper bound unknown; (ii) the control gain is unknown, not necessarily bounded, and only its signum is known. To achieve robustness, we use a combination of robustifying control inputs and dead zone-type update laws. We apply this methodology to the speed control of a permanent magnet synchronous motor (PMSM), and we achieve proper tracking results.