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To date, various control strategies based on linear vehicle models have been researched and developed for improving lateral stability of car-trailer (CT) systems. Is a linear-model-based controller applicable to active safety systems for CT systems under emergency operating conditions, such as an evasive maneuver at high lateral accelerations? In order to answer the question, the applicability of an active trailer differential braking (ATDB) controller designed using a linear CT model is tested and evaluated, while the controller being applied to a CT system represented by a linear and a nonlinear CT model. The current research leads to the following insightful findings: the ATDB controller designed using the linear model can effectively improve the lateral stability of CT systems under regular evasive maneuvers at low lateral accelerations, but the controller is not applicable to CT active safety systems under emergency evasive maneuvers at high lateral accelerations.

This paper presents nonlinear bifurcation stability analysis of articulated vehicles with active trailer differential braking (ATDB) systems. ATDB systems have been proposed to improve stability of articulated vehicle systems to prevent unstable motion modes, e.g., jack-knifing, trailer sway and rollover. Generally, behaviors of a nonlinear dynamic system may change with varying parameters; a stable equilibrium can become unstable and a periodic oscillation may occur or a new equilibrium may appear making the previous equilibrium unstable once the parameters vary. The value of a parameter, at which these changes occur, is known as “bifurcation value” and the parameter is known as the “bifurcation parameter”. Conventionally, nonlinear bifurcation analysis approach is applied to examine the nonlinear dynamic characteristics of single-unit vehicles, e.g., cars, trucks, etc.

The phase-plane analysis technique has become a powerful tool for analyzing lateral stability of single-unit vehicles. Articulated vehicles, such as car-trailer combinations, consist of multiple vehicle units. Multi-unit vehicles exhibit unique dynamic features compared against single-unit vehicles. For example, a car-trailer may exhibit one of the three unstable motion modes, i.e., jack-knifing, trailer sway and rollover. Considering the distinguished configurations and dynamic features of articulated vehicles, it is questionable whether the phase-plane analysis method based on single-unit vehicles is applicable for analyzing the lateral stability of multi-unit vehicles. In order to address the problem, case studies are conducted to test the effectiveness of the phase-plane method for analyzing the lateral stability of a car-trailer combination, which is represented by a nonlinear vehicle model generated using the CarSim software package.