Investigation of road train divergent stability loss when moving along a program trajectory
DOI:
https://doi.org/10.15587/2312-8372.2018.150924Keywords:
characteristic equation, first Lyapunov method, parameter continuation method, bifurcation set, divergent stability lossAbstract
The object of research is transport driven multilink wheel systems. In the development of the realized possibility of controlled movement of a semi-trailer truck along a program trajectory, the possibility of constructing a bifurcation set by a velocity parameter is considered. The velocity value is calculated for each discrete value of the calculated real trajectory. The trajectory can be specified in an explicit, implicit, parametric form or by the law of variation of the curvature radius. The study of this parameter is one of the most problematic places for analyzing the stability of the movement of a road train.
Changes in this parameter at certain values, called bifurcation, lead to changes in the qualitative structure of the solutions of the system of differential equations and, as a result, divergent stability of the road train. For such an investigation of the phenomenon, the method of continuation by parameter and the first Lyapunov method are applied.
During the research, many bifurcation velocity values are obtained. This is due to the fact that the proposed approach has a number of features, in particular, an iteration is performed for all control parameters of the program trajectory, and for each such value, the velocity has been iterated until its bifurcation value is reached.
At each iteration, the roots of the characteristic equation are checked for the presence of at least one root with a positive real part, which corresponds to the bifurcation value of the parameter of the velocity of a road train according to Lyapunov. Due to this, it is possible to obtain this set by an exclusively analytical method using computer calculations, without resorting to the use of graphic-analytical methods.
Obtaining these bifurcation sets can practically be used both to limit the velocity of a road train and to warn of its excess. Compared with similar known methods, this provides such advantages as a significant acceleration of the construction of this set and, as a result, its use in real time.References
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Copyright (c) 2018 Vasyl Popivshchyi, Anatoliy Bezverkhyi, Dmitry Tatievskyi
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