An \(\mathcal H_{\infty}\) optimal robust pole placement with fixed transparent controller structure on the basis of nonnegativity of even spectral polynomials (Q1955136)

Summary: We present 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 \(\mathcal H_{\infty}\) 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.