DESIRABLE ATTRACTORS OF THE STATE’S REPRESENTATIVE POINT AS A PATTERNS FOR A MAGNETOLEVITATION TRAIN’S MECHANICAL SUBSYSTEM’S LONGITUDINAL MOTION CONSTRUCTING

Abstract

The quality of a magnetically levitated train’s mechanical subsystem’s motion is one of the main criteria that determine the consumer properties of the transport complex, which includes such a train. The practical implementation of this quality is limited: on the one hand, by the need to meet the requirements of the transportation process, and, on the other, by the inadmissibility of spending excessive generalized resources on it. To avoid this collision, for each typical operational and emergency mode, a rational pattern of desired dynamics must be formed a priori, which its in-kind imple- mentation must follow as accurately as possible. The aim of the study was to identify the specified pattern and, using it, create a methodology for constructing the desired longitudinal motions of the train's mechanical subsystem. An attractor, that fully and synthetically reflects all of a dynamic system's properties, can be successfully used as a representative carrier of any of its possible movements. If the system is controllable, the synthesis of such movements becomes possible based on the properties of the attractor. Due to the limited dynamic sufficiency of the subsystem, the desired reference phase trajectory may remain unat- tainable. For this, in particular, reason it is advisable to designate each of the aforementioned patterns not as a separate phase trajectory, but as their family, which forms a «tube» of reference motions. The process of motion synthesis is interpreted as two-stage: forced transfer of the representing point from its initial position to the attractor; further motion along it. At both of these stages, the subsystem, under the influence of the imposed control, must, within a given time, transition from the initial phase state to the required final state. Therefore, at both stages, the specified control should be rationally constructed according to terminal principles. Motion patterns, as well as transitions to them, should be rationally constructed according to the methodology developed by one of the study's authors. The relations, that implement the synthesized methodology, were accepted as the algorithmic basis of the software complex which carry out the construction of the desired longitudinal motions of the subsystem. The constructions were carried out for the parameters of a train, which is composed of Japanese MLU-002 magnetic levitation cars. The illustrative results correspond to movements in the modes of starting, acceleration, service and emergency braking. The analysis of the obtained results indicates that, using the developed methodology, the construction of a magnetically levitated train’s mechanical subsystem’s desired motions, based on it's state’s representative point’s corresponding attractors, can be successfully implemented in cases that correspond to all operating modes.