STABILITY ANALYSIS OF PIECEWISE DEFINITE NONLINEAR AMBIGUOUS SYSTEM BY DIRECT LYAPUNOV METHOD

Piecewise definite nonlinear ambiguous system including a couple of nonlinear elements where one of them possesses odd symmetric piecewise definite ambiguous hysteresis characteristic and other – piecewise linear odd symmetric relay characteristic is considered. The stability analysis questions using relay control system of separately excited DC generator with two excitation windings that ensures the reference pulse current series reproducing are investigated. To achieve a goal the direct Lyapunov method and Dini derivatives mathematical tool that suggests sufficient conditions of continuous differentiability requirement fulfillment which is made to the Lyapunov function are implemented. The Lyapunov function that allows judging about an asymptotic stability of the system is derived. The simulation results of the transients in DC generator armature circuit and the graphs of obtained Lyapunov function and its complete time derivative indicating the second Lyapunov theorem execution are given.

Authors: B. V. Bruslinovskiy, N. A. Dobroskok, V. S. Lavrinovskiy, R. I. Galiullin, O. V. Mokhova

Direction: Electrical Engineering

Keywords: Separately excited DC generator, hysteresis, relay control system, direct Lyapunov method, Dini derivatives

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