Effect of handling characteristics on minimum time cornering with torque vectoring

ABSTRACT In this paper, the effect of both passive and actively-modified vehicle handling characteristics on minimum time manoeuvring for vehicles with 4-wheel torque vectoring (TV) capability is studied. First, a baseline optimal TV strategy is sought, independent of any causal control law. An optimal control problem (OCP) is initially formulated considering 4 independent wheel torque inputs, together with the steering angle rate, as the control variables. Using this formulation, the performance benefit using TV against an electric drive train with a fixed torque distribution, is demonstrated. The sensitivity of TV-controlled manoeuvre time to the passive understeer gradient of the vehicle is then studied. A second formulation of the OCP is introduced where a closed-loop TV controller is incorporated into the system dynamics of the OCP. This formulation allows the effect of actively modifying a vehicle's handling characteristic via TV on its minimum time cornering performance of the vehicle to be assessed. In particular, the effect of the target understeer gradient as the key tuning parameter of the literature-standard steady-state linear single-track model yaw rate reference is analysed.

[1]  Kaoru Sawase,et al.  Effect of the Right-and-left Torque Vectoring System in Various Types of Drivetrain , 2007 .

[2]  Dongpu Cao,et al.  Evaluation of optimal yaw rate reference for electric vehicle torque vectoring , 2016 .

[3]  Dongpu Cao,et al.  Optimal yaw-rate target for electric vehicle torque vectoring system , 2016 .

[4]  Damien Brayshaw.  Use of numerical optimisation to determine on-limit handling behaviour of race cars , 2004 .

[5]  Aditya A. Paranjape,et al.  Aggressive Turn-Around Manoeuvres with an Agile Fixed-Wing UAV , 2016 .

[6]  D. J. Purdy,et al.  Quasi-steady-state linearisation of the racing vehicle acceleration envelope: a limited slip differential example , 2014 .

[7]  Davide Tavernini,et al.  Minimum time cornering: the effect of road surface and car transmission layout , 2013 .

[8]  Jo Yung Wong,et al.  Theory of ground vehicles , 1978 .

[9]  David J. N. Limebeer,et al.  Optimal control for a Formula One car with variable parameters , 2014 .

[10]  Anil V. Rao,et al.  An efficient overloaded method for computing derivatives of mathematical functions in MATLAB , 2013, TOMS.

[11]  M. Massaro,et al.  Neuromuscular-Steering Dynamics: Motorcycle Riders vs. Car Drivers , 2012 .

[12]  A. T. van Zanten,et al.  Bosch ESP Systems: 5 Years of Experience , 2000 .

[13]  D. Casanova,et al.  Minimum Time Manoeuvring: The Significance of Yaw Inertia , 2000 .

[14]  Johan Andreasson,et al.  Global force potential of over-actuated vehicles , 2010 .

[15]  Naohiro Yuhara,et al.  Advanced Steering System Adaptable to Lateral Control Task and Driver's Intention , 2001 .

[16]  Efstathios Velenis,et al.  Optimality Properties and Driver Input Parameterization for Trail-braking Cornering , 2008, Eur. J. Control.

[17]  Anil V. Rao,et al.  GPOPS-II , 2014, ACM Trans. Math. Softw..

[18]  Patrick Gruber,et al.  Wheel Torque Distribution Criteria for Electric Vehicles With Torque-Vectoring Differentials , 2014, IEEE Transactions on Vehicular Technology.

[19]  Dongpu Cao,et al.  The impact of hybrid and electric powertrains on vehicle dynamics, control systems and energy regeneration , 2012 .

[20]  Aleksander B. Hac,et al.  Exploring the Trade-Off of Handling Stability and Responsiveness with Advanced Control Systems , 2007 .

[21]  Shinichiro Horiuchi.  Evaluation of chassis control method through optimisation-based controllability region computation , 2012 .

[22]  D. J. Purdy,et al.  The Control Authority of Passive and Active Torque Vectoring Differentials for Motorsport Applications , 2013 .

[23]  Yasuji Shibahata,et al.  Comparison of Three Active Chassis Control Methods for Stabilizing Yaw Moments , 1994 .

[24]  David Crolla,et al.  A review of yaw rate and sideslip controllers for passenger vehicles , 2007 .

[25]  Shinichiro Horiuchi.  Evaluation of chassis control algorithms using controllability region analysis , 2016 .

[26]  Mara Tanelli,et al.  Minimum-time manoeuvring in electric vehicles with four wheel-individual-motors , 2014 .

[27]  Anil V. Rao,et al.  A Source Transformation via Operator Overloading Method for the Automatic Differentiation of Mathematical Functions in MATLAB , 2016, ACM Trans. Math. Softw..

[28]  David J. N. Limebeer,et al.  Optimal Control of a Formula One Car on a Three-Dimensional Track—Part 2: Optimal Control , 2015 .

[29]  John T. Betts,et al.  Practical Methods for Optimal Control and Estimation Using Nonlinear Programming , 2009 .

[30]  Christian Hoffmann,et al.  Torque vectoring for an electric vehicle using an LPV drive controller and a torque and slip limiter , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[31]  Yvonne Schuhmacher,et al.  Race Car Vehicle Dynamics , 2016 .

[32]  D. Casanova,et al.  On minimum time vehicle manoeuvring: the theoretical optimal lap , 2000 .

[33]  Efstathios Velenis,et al.  Optimal control of motorsport differentials , 2015 .

[34]  Emilio Frazzoli,et al.  Steady-state drifting stabilization of RWD vehicles , 2011 .

[35]  Hans B. Pacejka,et al.  Tyre Modelling for Use in Vehicle Dynamics Studies , 1987 .

[36]  Sören Hohmann,et al.  Potential of Vehicle Dynamics via Single Wheel Drive for Installation Space Optimized Electric Vehicles , 2012 .

[37]  Roberto Lot,et al.  A General Method for the Evaluation of Vehicle Manoeuvrability with Special Emphasis on Motorcycles , 1999 .

[38]  Efstathios Velenis,et al.  Rear wheel torque vectoring model predictive control with velocity regulation for electric vehicles , 2015 .

[39]  Kazuhiko Shimada,et al.  IMPROVEMENT OF VEHICLE MANEUVERABILITY BY DIRECT YAW MOMENT CONTROL. , 1992 .

[40]  Aldo Sorniotti,et al.  The Application of Control and Wheel Torque Allocation Techniques to Driving Modes for Fully Electric Vehicles , 2014 .

[41]  Aldo Sorniotti,et al.  Direct yaw moment control actuated through electric drivetrains and friction brakes: Theoretical design and experimental assessment , 2015 .