Structured singular value control With general two-degree-of-freedom feedback loop factorisation for single-input single-output systems

Abstract

General two-degree-of-freedom feedback loop factorisation for single-input single-output systems applied to oscillating plants with time delay, periodic changes of the controlled plant parameters and astatism using the D-K iteration and algebraic approach is described in this paper. The algebraic approach combines the structured singular value, algebraic theory and algorithm of global optimisation solving remaining issues in structured singular value framework. The algorithm for global optimisation can be alternated with direct search methods such as Nelder-Mead simplex method giving solutions for problems with one local extreme for final tune-up optimisation. As a global optimisation method, Differential Migration is used proving to be reliable in solving this type of problems. The D-K iteration is used as a reference method representing standard procedure for deriving optimal controller in the structured singular value theory. The results obtained from the D-K iteration are compared with the algebraic approach.