On dynamic and stability analysis of the nonlinear vehicle models using the concept of lyapunov stability
Loading...
Date
2015
Authors
Sadri, Sobhan
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The "on-road untripped rollover" is a dangerous accident, which kills thousands of
vehicle occupants every year. This type of rollover accident occurs in high-speed
emergency maneuvers without hitting any external objects. In fact, in this incident,
the vehicle is driven through the edges or beyond its yaw and roll stability limits.
Therefore, by analyzing the Lyapunov stability of accurate vehicle models, there will
be a chance to prevent this type of incidents. The problem is that accurate models
have complex dynamics and include nonlinear terms, which make the stability analysis
difficult. On the other hand, the available theoretical approaches for nonlinear
stability analysis are either not constructive or not effective.
The aim of this thesis is four-fold: a) to define a new measure of dynamics called
"modified Lyapunov exponents" to provide more insight into stability analysis of nonlinear
systems, b) to introduce the concept of Lyapunov exponents as a constructive
method for stability analysis of nonlinear vehicle models, c) to develop a proper nonlinear
vehicle roll model in sense of Lyapunov stability analysis, and d) to develop a
Scale Experimental Test Vehicle (SETV) with unique features as a vehicle test bed
for rollover experiments.
New modified Lyapunov exponents can measure the exponential convergent/divergent
rate of the perturbation vector in a specific direction driven by the dynamics in the
same direction. Their existence and invariant property are mathematically proven
and their indications are discussed.
The concept of Lyapunov exponents has been applied effectively to analyze the system
and structure stability of a nonlinear two degrees of freedom (2-DOF) bicycle vehicle
model and further to estimate its Lyapunov stability regions.
In the absence of a proper nonlinear vehicle model for Lyapunov stability analysis,
a new nonlinear 4-DOF vehicle roll model is developed that can predict the roll
motion of a conventional full vehicle model, however, it has simpler dynamics. The
Lyapunov stability of the model has been analyzed by Lyapunov linearization and
Lyapunov exponents methods. Moreover, the accuracy of the model in predicting the
roll behaviour of a real vehicle is justified by experiments on the SETV.
Description
Keywords
Vehicle Dynamics, Stability Analysis, Lyapunov Exponents