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Mathematical Problems in Engineering
Volume 2012, Article ID 735245, 25 pages
http://dx.doi.org/10.1155/2012/735245
Research Article

An Optimal Robust Pole Placement with Fixed Transparent Controller Structure on the Basis of Nonnegativity of Even Spectral Polynomials

1Faculty of Electrical Engineering and Computer Science (FERI), University of Maribor, 2000 Maribor, Slovenia
2Margento B.V., Telstone 8, 1043 BV Amsterdam, The Netherlands

Received 29 May 2012; Accepted 17 October 2012

Academic Editor: Jun-Juh Yan

Copyright © 2012 Andrej Sarjaš 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

This paper presents the synthesis of an optimal robust controller with the use of pole placement technique. The presented method includes solving a polynomial equation on the basis of the chosen fixed characteristic polynomial and introduced parametric solutions with a known parametric structure of the controller. Robustness criteria in an unstructured uncertainty description with metrics of norm are for a more reliable and effective formulation of objective functions for optimization presented in the form of a spectral polynomial with positivity conditions. The method enables robust low-order controller design by using plant simplification with partial-fraction decomposition, where the simplification remainder is added to the performance weight. The controller structure is assembled of well-known parts such as disturbance rejection, and reference tracking. The approach also allows the possibility of multiobjective optimization of robust criteria, application of mixed sensitivity problem, and other closed-loop limitation criteria, where the common criteria function can be composed from different unrelated criteria. Optimization and controller design are performed with iterative evolution algorithm.