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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

mathematical problems in engineering

An<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mi>ℋ</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:mrow></mml:math>Optimal Robust Pole Placement with Fixed Transparent Controller Structure on the Basis of Nonnegativity of Even Spectral Polynomials

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