Optimal Control Allocation Of Semi-active Suspension For Vehicle Rollover Prevention

Vehicle rollover is a critical public safety issue with high fatality.The statistics of National Highway Traffic Safety Administration(NHTSA)show that approximately 32% of all deaths from passenger vehicle crashes are related to rollover accidents in 2015.Since 2004,vehicle rollover resistance has been part of NHTSA's New Car Assessment Program(NCAP)with standard dynamic tests to evaluate the ability of a vehicle to avoid rollovers,and vehicle rollover prevention is important for vehicle dynamics and active vehicle safety.Vehicle rollover prevention contains two main stages: rollover detection and rollover mitigation control.For rollover detection,a real-time,accurate and predictive rollover index attracts more and more attention.However,most of the existing indices do not consider complete rollover dynamics and lead to limited work range and accuracy.For rollover control,detailed dynamic characteristics of actuators including the transient and saturation characteristics of suspension dampers are neglected in most integrated rollover control,meanwhile,the optimal control allocation of semi-active suspension for vehicle rollover are not studied widely.This paper concentrates on vehicle rollover prevention integrating semi-active suspension and differential braking and mainly addresses roll center identification,rollover detection and mitigation.The main contributions and conclusions are as follows:1)Roll center identification and vertical tyre load estimationConsidering the measurability of roll angle,roll rate and roll acceleration,three algorithms are proposed for roll center identification,respectively.In detail,the recursive least square with the disturbance observer algorithm(RLSDA)is utilized when all roll signals are obtained.When roll angle and roll rate are measurable,an adaptive sliding mode observer(ASMO)is proposed.The extended Kalman filter(EKF)is developed when only roll angel is available.Meanwhile,an adaptive robust observer is designed for vertical tyre load estimation,in which the linear matrix inequation(LMI)technique is used for a rapid calculating of observer gains.Simulation results demonstrate that the both the RLSDA and ASMO can estimated roll center accurately while the EKF reaches a 94% accuracy.Besides,the maximum estimation error for load transfer ratio is below 0.1 in Fishhook and J-turn tests.2)Contour line of load transfer ratio based rollover predictionThe contour line of load transfer ratio(CL-LTR)is proposed via the roll dynamics phase plane analysis,and its analytical solution of one-degree-of-freedom vehicle roll model and extension for full vehicle are derived,which describes LTR threshold precisely in roll phase plane.Moreover,the CL-LTR-based vehicle rollover index(CLRI)is proposed with benefits of providing an accurate prediction of vehicle rollover threat and is evaluated via vehicle dynamics study.The results demonstrate that The CLRI provides a novel approach to evaluate vehicle rollover risks,describing LTR change rate precisely and bringing an accurate prediction of vehicle rollover threat,which benefits vehicle rollover prevention.3)Optimal control allocation for MRV controlled semi-active suspensionThe hierarchic control and control allocation methodologies are employed to design the coordinating rollover control: firstly,the model predictive control(MPC)and sliding mode control(SMC)are utilized to calculated the upper control moment for rollover and yaw stability,respectively;then,an optimal objective is proposed for reducing the dynamic tyre load and then an optimal allocation algorithm of damper forces with consideration of the saturation of suspension dampers is designed via the Lagrangian multiplier method;finally,the damping force tracking control is developed for improving the transient performance of dampers via ITAE-based control.Comparison between the proposed optimal control allocation with a fuzzy control illustrates that the critical velocity for rollover stability is increased by 25% with the optimal control allocation when vehicle rollover is controlled by semi-active suspension alone.Furthermore,when rollover is controlled by coordinated semi-active suspension and differential braking,the optimal semi-active suspension control can improve the controlled optimal objective by 75% on average compared to the fuzzy semi-active suspension control,showing significant benefits in optimizing load transfer ratio and enhancing vehicle rollover stability.