Vehicle Tip-over Prevention Using SDRE Controller

Abstract

Vehicle rollovers are known to produce the highest number of deaths amongst vehicle accidents. Rollover prevention systems currently available in commercial vehicles attempts to prevent any wheel lift-off the ground to avoid a subsequent rollover. In literature, attempts that were made to recover a vehicle from a tip-over point after a wheel lift-off has occurred are only a few. The present article proposes a State Dependent Riccati Equation (SDRE) based anti-rollover controller to recover a vehicle from tip-over point. SDRE method delivers a simple yet effective solution to the nonlinear optimal control problem. An Inverted Double Pendulum on a Cart Model (IDPC) acts as the base model in the controller. The tip-over point of the IDPC model is an unstable equilibrium point of the model and the gravity torque has a negligibly small effect in this vicinity. In the SDRE method, this unstable equilibrium point acts as a singularity point. A virtual rollover torque is used with the IDPC model instead of the gravity torque to overcome this problem. Essentially the controller makes use of a model that is more prone to rollover than the real model with gravity assistance. The controller is evaluated with IDPC model with gravity torque, as well as a 10 Degrees of Freedom (DOF) full vehicle model with a nonlinear tire model. A study is also conducted on the change in performance of the controller with weight value of roll state used in the performance index. Studies proved the controller to be simple yet effective in reinstating the vehicle model in all the near tip-over case studies conducted. The control input force was found to increase with increase in weight value of the roll state which resulted in a reduced reinstating time duration.