Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2012, Article ID 735245, 25 pages doi:10.1155/2012/735245 Research Article An H ∞ Optimal Robust Pole Placement with Fixed Transparent Controller Structure on the Basis of Nonnegativity of Even Spectral Polynomials Andrej Sarja ˇ s, 1 Rajko Sveˇ cko, 1 and Amor Chowdhury 2 1 Faculty of Electrical Engineering and Computer Science (FERI), University of Maribor, 2000 Maribor, Slovenia 2 Margento B.V., Telstone 8, 1043 BV Amsterdam, The Netherlands Correspondence should be addressed to Andrej Sarjaˇ s, andrej.sarjas@uni-mb.si Received 29 May 2012; Accepted 17 October 2012 Academic Editor: Jun-Juh Yan Copyright q 2012 Andrej Sarjaˇ s 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. 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 H ∞ 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. 1. Introduction Synthesis of closed-loop control system is based on a mathematical model of the plant, which should enable reliable prediction of input/output response, so that it can be used in controller synthesis. Uncertainty of the plant and external disturbance are the central issues of robust closed-loop control. Modern robust control approaches are mostly presented as a set of optimization problems, where the solution and the optimization procedure depend