Regenerative Braking and Yaw Dynamics Optimal Control in Hybrid Vehicles

In hybrid vehicles, regenerative braking is used in order to recover energy when vehiclebrakes. Energy is recovered by converting the vehicle kinetic energy into electric energy tobe stored in electricity buffers, i.e., batteries or capacitors. The recovered energy can then beused for powering the vehicle and thus reduce the fuel consumption. In particular, in order togenerate a braking force, the wheels can be connected to the electric motor, thus providingmotion energy to the generator and charging the electric buffer. When regenerative brakingis applied, the connection of the wheels to the generator results in a load torque (i.e., a braketorque), slowing the vehicle down, and at the same time enables energy recovery.In this paper, we consider hybrid drivelines where the electric motor is connected to therear axle, i.e., the regenerative braking takes place by braking the rear wheels, and focus onthe implications of the regenerative braking on the vehicle dynamics.The scenario considered in this paper (i.e., regenerative braking at the rear axle) is challengingfrom both the brake force delivery and distribution and the vehicle stabilizationperspectives [1]. In fact, we first observe that the maximum force the regenerative brakingcan deliver is limited and, in general, less than the friction braking. In particular, a brakingforce request from the driver might not be delivered entirely through regenerative brakingand a combination of friction and regenerative braking might be necessary. Secondly, werecall that an “optimum” brake proportioning between front and rear axles exists, such thatthe braking performance is maximized and the vehicle stability is preserved (see [2] for adetailed explanation). Clearly, maximizing the braking at one axle might conflict with a brakeforce distribution determined according to some “optimum” brake proportioning. Moreover,preserving the vehicle stability and comfort on slippery surfaces while maximizing the energyrecovering is a significant challenge as well. In particular, on low friction surfaces, the braketorque from regenerative braking might be large enough to lock-up the rear wheel. This wouldinduce an oversteering behavior and might even lead to instability, i.e., vehicle spinning [1].Even though instability does not occur, the driver might perceive a reduction of comfort asconsequence of braking at the rear wheels. In particular, on low friction surfaces, where thevehicle can easily operate at the limit of tire force capabilities, a sudden reduction of lateralforce might be experienced as consequence of braking.In this paper, we consider testing scenarios where the driver demands a braking force whilethe vehicle is performing a cornering manoeuvres on slippery surfaces, i.e., snow or ice. Thecontrol objective is to maximize the energy recovery (i.e., the regenerative braking), while (i)delivering the requested braking force by introducing front and rear friction braking as well,if necessary, (ii) preserving the vehicle stability and (iii) limit the lateral force reduction. Weshow how this problem can be effectively formulated as a Model Predictive Control (MPC)problem. In particular, we design a cost function in order to achieve our control objectives.Every time step, based on measurements of the demanded brake force, the vehicle yaw turningrate and longitudinal and lateral velocities, we repeatedly solve an optimization problem inorder to find the braking policy minimizing the cost function while fulfilling design and systemconstraints. As shown in [3], such control approach can be high computational demandingand even prevent real-time implementation. In order to implement our MPC algorithms inreal-time, we resort to the low complexity MPC formulation used in [4], [5], [6] to solveautonomous path following problems.REFERENCES[1] M. Hancock and F. Assadian. Impact of regenerative braking on vehicle stability. IET The Institution of Engineeringand Technology, Hybrid Vehicle Conference, 2006.[2] T. Gillespie. Fundamentals of Vehicle Dynamics, chapter 3, pages 60–67. Society of Automotive Engineers (SAE),1992.[3] F. Borrelli, P. Falcone, T. Keviczky, J. Asgari, and D. Hrovat. MPC-based approach to active steering for autonomousvehicle systems. Int. J. Vehicle Autonomous Systems, 3(2/3/4):265–291, 2005.[4] P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat. Predictive active steering control for autonomous vehiclesystems. IEEE Trans. on Control System Technology, 15(3), 2007.[5] P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat. Linear time varying model predictive control and itsapplication to active steering systems: Stability analisys and experimental validation. International Journal of Robustand Nonlinear Control., 18:862–875, 2008.[6] P. Falcone. Nonlinear Model Predictive Control for Autonomous Vehicles. PhD thesis, Universit`a del Sannio,Dipartimento di Ingegneria, Piazza Roma 21, 82100, Benevento, Italy, June 2007