Hopf-curve-based torque distribution strategy for avoiding limit cycle vibration in hybrid braking system model

Limit cycle vibration affects ride comfort and safety of electric vehicle. In the present study, a Hopf curve was proposed for development of brake torque distribution strategy to circumvent limit cycle vibration. The stability and bifurcation conditions were evaluated based on brake-driveline coupling model of the hybrid braking system. The limit cycle vibration was predicted through the boundary between stable and unstable equilibrium regions. The findings showed that the limit cycle vibration was circumvented by tuning the hydraulic braking force based on the Hopf curve. The insufficient braking torque caused by the decrease in hydraulic braking force was compensated by the driven motor. The findings of the present study provide information on the passive suppression of limit cycle vibration in hybrid braking system to improve the comfort of electric vehicles.