Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 842896, 20 pages
doi:10.1155/2010/842896
Research Article

Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems

Renato de Aguiar Teixeira Mendes,1 Edvaldo Assunção,1 Marcelo C. M. Teixeira,1 and Cristiano Q. Andrea2

1Department of Electrical Engineering, Universidade Estadual Paulista (UNESP), Campus of Ilha Solteira, 15385-000 Ilha Solteira, Brazil
2Academic Department of Electronics, Federal Technological University of Paraná (UTFPR), 80230910 Curitiba, PR, Brazil

Received 1 December 2009; Revised 29 June 2010; Accepted 9 December 2010

Academic Editor: Fernando Lobo Pereira

Copyright © 2010 Renato de Aguiar Teixeira Mendes 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.

Abstract

The problem of signal tracking in discrete linear time invariant systems, in the presence of a disturbance signal in the plant, is solved using a new zero-variation methodology. A discrete-time dynamic output feedback controller is designed in order to minimize the ℋ ∞ norm between the exogen input and the output signal of the system, such that the effect of the disturbance is attenuated. Then, the zeros modification is used to minimize the ℋ ∞ norm from the reference input signal to the error signal. The error is taken as the difference between the reference and the output signal. The proposed design is formulated in linear matrix inequalities (LMIs) framework, such that the optimal solution of the stated problem is obtained. The method can be applied to plants with delay. The control of a delayed system illustrates the effectiveness of the proposed method.