Formulation of equivalent relay controls for nonlinear systems

Abstract

This work is devoted to the problem of determining the moments of switching in limited relay controls for nonlinear systems, which provide achievement of system states, close to the states, obtained under the influence of arbitrary controls limited in the same range. It is shown that the number of the moments of switching in limited relay control is specified by an approximation order of the stated in this work functions h_i(t), which depend on transitional functions and a matrix of coefficients during the system operating. Expressions for calculation of values of the switching moments in case of linear approximation of function h_i(t) are shown. For the general case of polynomial approximation of functions h_i(t), values of the switching moments of relay control can be evaluated by resolving of the system of equations, given in this work. It is defined that the evaluated moments of switching of limited relay control depend on initial reference control of arbitrary form, limited in the same margins only. The example of determination of switching moments of relay control for the speed-up task of direct current electric motor with independent excitation is given in the work.