Sun, T., Lee, E., and He, Y., "Non-Linear Bifurcation Stability Analysis for Articulated Vehicles with Active Trailer Differential Braking Systems," SAE Int. J. Mater. Manf. 9(3):688-698, 2016, doi:10.4271/2016-01-0433.
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. Little attention has been paid to investigate the feasibility and effectiveness of the bifurcation analysis method for nonlinear stability analysis of articulated vehicles under varied operating conditions, e.g., varied forward speed and trailer payload. This motivates the research to examine stability boundaries of equilibrium and limit cycles in the parameter space and to predict qualitative changes in system’s behaviour (bifurcations) occurring at their equilibrium points. To this end, a nonlinear yaw-roll model with 6 degrees of freedom (DOF) is generated to simulate the nonlinear dynamics of articulated vehicles. The nonlinear yaw-roll model is also used to design an ATDB controller based on a fuzzy logic control technique. The bifurcation analysis based on the phase-plane method is conducted to evaluate the yaw and roll stability of the articulated vehicle. Built upon the conventional bifurcation analysis for single-unit vehicles, an innovative bifurcation analysis technique is developed in order to effectively assess the nonlinear stability of articulated vehicles. The applicability and effectiveness of the newly developed technique is examined and demonstrated.