A fast model predictive control allocation of distributed drive electric vehicles for tire slip energy saving with stability constraints

Abstract This paper proposes a fast model predictive control allocation (MPCA) approach to minimize the tire slip power loss on contact patches for distributed drive electric vehicles (DDEV). In this strategy, two assumptions are set up from a practical focus: (1) the vehicle acceleration and yaw rate are measurable by global position system (GPS)/ inertial navigation system (INS) and inertial measurement unit (IMU), respectively; (2) the longitudinal velocity, road adhesion factor, and vehicle yaw rate are arranged to be “already known” by advanced estimators. For the strategy design, a CarSim-embedded driver model and a linear quadratic regulator (LQR) based direct yaw moment controller, are respectively applied to calculate the desired longitudinal traction and yaw moment as a virtual input first. Then, a MPCA method is proposed to reasonably distribute the virtual input among four in-wheel motors in order to optimize the tire slip power loss and vehicle stability performance. To accurately characterize tire slip power loss in MPCA, a tire slip estimator is established for tire slip information acquirement. Moreover, addressing on the heavily computational challenge in MPCA, a modified continuation/generalized minimal residual (C/GMRES) algorithm is employed. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the barrier functions are applied for transforming the inequality constraints to equivalent cost. According to Pontryagin’s minimum principle (PMP) conditions, the existence and uniqueness for solution of the modified C/GMRES algorithm are strictly proved. Subsequently, a Karush–Kuhn–Tucker​ (KKT) condition based approach is developed to fast gain the optimally initial solution in C/GMRES algorithm for extending application. Finally, numerical simulation validations are implemented and demonstrate that the proposed MPCA can ensure the compatibility between the tire slip power loss reduction and vehicle stability in a computationally efficient way.

[1]  Yanjun Huang,et al.  Lane Keeping Control of Autonomous Vehicles With Prescribed Performance Considering the Rollover Prevention and Input Saturation , 2020, IEEE Transactions on Intelligent Transportation Systems.

[2]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[3]  Hiroshi Fujimoto,et al.  Driving torque control method for electric vehicle with in‐wheel motors , 2012 .

[4]  Xudong Zhang,et al.  A Real-Time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles , 2020, IEEE Transactions on Vehicular Technology.

[5]  Wei Zheng,et al.  Karush-Kuhn-Tuckert based global optimization algorithm design for solving stability torque allocation of distributed drive electric vehicles , 2017, J. Frankl. Inst..

[6]  Yoshio Kano,et al.  A study on tyre force distribution controls for full drive-by-wire electric vehicle , 2014 .

[7]  Fei Li,et al.  Fuzzy Observer-Based Prescribed Performance Control of Vehicle Roll Behavior via Controllable Damper , 2019, IEEE Access.

[8]  Hong Chen,et al.  Nonlinear MPC-based slip control for electric vehicles with vehicle safety constraints , 2016 .

[9]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[10]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[11]  Tor Arne Johansen,et al.  Control allocation - A survey , 2013, Autom..

[12]  Eugene L. Allgower,et al.  Numerical continuation methods - an introduction , 1990, Springer series in computational mathematics.

[13]  Jing Na,et al.  MME-EKF-Based Path-Tracking Control of Autonomous Vehicles Considering Input Saturation , 2019, IEEE Transactions on Vehicular Technology.

[14]  Cristiano Maria Verrelli,et al.  Automatic motor speed reference generators for cruise and lateral control of electric vehicles with in-wheel motors , 2018 .

[15]  Masaki Yamamoto,et al.  Efficient direct yaw moment control: tyre slip power loss minimisation for four-independent wheel drive vehicle , 2018 .

[16]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[17]  Rongrong Wang,et al.  A novel global sensitivity analysis on the observation accuracy of the coupled vehicle model , 2018, Vehicle System Dynamics.

[18]  Rajesh Rajamani,et al.  Vehicle dynamics and control , 2005 .

[19]  Weiwen Deng,et al.  Model predictive control allocation for stability improvement of four-wheel drive electric vehicles in critical driving condition , 2015 .

[20]  Jian Chen,et al.  Lateral stability integrated with energy efficiency control for electric vehicles , 2019, Mechanical Systems and Signal Processing.

[21]  Hong Chen,et al.  Vehicle dynamic state estimation: state of the art schemes and perspectives , 2018, IEEE/CAA Journal of Automatica Sinica.

[22]  Yechen Qin,et al.  Lane keeping of autonomous vehicles based on differential steering with adaptive multivariable super-twisting control , 2018, Mechanical Systems and Signal Processing.

[23]  Knut Graichen,et al.  Nonlinear model predictive torque control and setpoint computation of induction machines for high performance applications , 2020 .

[24]  Ming Yue,et al.  Stability Control for FWID-EVs With Supervision Mechanism in Critical Cornering Situations , 2018, IEEE Transactions on Vehicular Technology.

[25]  Yanjun Huang,et al.  Stability control of electric vehicles with in-wheel motors by considering tire slip energy , 2019, Mechanical Systems and Signal Processing.

[26]  Kanghyun Nam,et al.  Torque Vectoring Algorithm of Electronic-Four-Wheel Drive Vehicles for Enhancement of Cornering Performance , 2020, IEEE Transactions on Vehicular Technology.

[27]  Masaki Yamamoto,et al.  Direct yaw moment control and power consumption of in-wheel motor vehicle in steady-state turning , 2017 .

[28]  Dietmar Göhlich,et al.  Improvement in the vehicle stability of distributed-drive electric vehicles based on integrated model-matching control , 2018 .

[29]  Yan Chen,et al.  Design and Experimental Evaluations on Energy Efficient Control Allocation Methods for Overactuated Electric Vehicles: Longitudinal Motion Case , 2014, IEEE/ASME Transactions on Mechatronics.

[30]  Y. Hori,et al.  Four-wheel driving-force distribution method based on driving stiffness and slip ratio estimation for electric vehicle with in-wheel motors , 2012, 2012 IEEE Vehicle Power and Propulsion Conference.

[31]  Y. Zou,et al.  Usage pattern analysis of Beijing private electric vehicles based on real-world data , 2019, Energy.

[32]  Tao Zhang,et al.  A Computationally Efficient Path-Following Control Strategy of Autonomous Electric Vehicles With Yaw Motion Stabilization , 2020, IEEE Transactions on Transportation Electrification.

[33]  Patrick Gruber,et al.  Yaw Rate and Sideslip Angle Control Through Single Input Single Output Direct Yaw Moment Control , 2020, IEEE Transactions on Control Systems Technology.

[34]  Tao Zhang,et al.  An Integrated Longitudinal and Lateral Vehicle Following Control System With Radar and Vehicle-to-Vehicle Communication , 2019, IEEE Transactions on Vehicular Technology.

[35]  Toshiyuki Ohtsuka,et al.  A continuation/GMRES method for fast computation of nonlinear receding horizon control , 2004, Autom..

[36]  Bin Li,et al.  An optimal torque distribution control strategy for four-independent wheel drive electric vehicles , 2015 .

[37]  Aldo Sorniotti,et al.  Energy-Efficient Torque-Vectoring Control of Electric Vehicles With Multiple Drivetrains , 2018, IEEE Transactions on Vehicular Technology.