Преобразование нелинейных систем управления к эквивалентным линейным в канонической форме Бруновского

Abstract

The authors developed a specialized program for the universal package of simulation MatLab that automates the conversion of a wide class of nonlinear control systems to the equivalent linear form in the canonical Brunovsky form using involutive distributions of geometric control theory in the space of "input - state". This article provides an example of an application program to obtain the equivalent linear mathematical model of the motion of diesel trains, which consists of ten ordinary nonlinear differential equations with four control circuits and describes the drive with two parallel running traction asynchronous motors. Thus the synthesized linear model in Brunovsky form has four cells and controllability index equal to four. The resulting linear motion model of a diesel train can be used to find the optimal controls and to study the slipping and skidding processes.