Regenerative Braking and Yaw Dynamics Optimal Control in Hybrid Vehicles
Paper i proceeding, 2009
In hybrid vehicles, regenerative braking is used in order to recover energy when vehicle
brakes. Energy is recovered by converting the vehicle kinetic energy into electric energy to
be stored in electricity buffers, i.e., batteries or capacitors. The recovered energy can then be
used for powering the vehicle and thus reduce the fuel consumption. In particular, in order to
generate a braking force, the wheels can be connected to the electric motor, thus providing
motion energy to the generator and charging the electric buffer. When regenerative braking
is applied, the connection of the wheels to the generator results in a load torque (i.e., a brake
torque), 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 the
rear axle, i.e., the regenerative braking takes place by braking the rear wheels, and focus on
the implications of the regenerative braking on the vehicle dynamics.
The scenario considered in this paper (i.e., regenerative braking at the rear axle) is challenging
from both the brake force delivery and distribution and the vehicle stabilization
perspectives . In fact, we first observe that the maximum force the regenerative braking
can deliver is limited and, in general, less than the friction braking. In particular, a braking
force request from the driver might not be delivered entirely through regenerative braking
and a combination of friction and regenerative braking might be necessary. Secondly, we
recall that an “optimum” brake proportioning between front and rear axles exists, such that
the braking performance is maximized and the vehicle stability is preserved (see  for a
detailed explanation). Clearly, maximizing the braking at one axle might conflict with a brake
force distribution determined according to some “optimum” brake proportioning. Moreover,
preserving the vehicle stability and comfort on slippery surfaces while maximizing the energy
recovering is a significant challenge as well. In particular, on low friction surfaces, the brake
torque from regenerative braking might be large enough to lock-up the rear wheel. This would
induce an oversteering behavior and might even lead to instability, i.e., vehicle spinning .
Even though instability does not occur, the driver might perceive a reduction of comfort as
consequence of braking at the rear wheels. In particular, on low friction surfaces, where the
vehicle can easily operate at the limit of tire force capabilities, a sudden reduction of lateral
force might be experienced as consequence of braking.
In this paper, we consider testing scenarios where the driver demands a braking force while
the vehicle is performing a cornering manoeuvres on slippery surfaces, i.e., snow or ice. The
control 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. We
show 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 turning
rate and longitudinal and lateral velocities, we repeatedly solve an optimization problem in
order to find the braking policy minimizing the cost function while fulfilling design and system
constraints. As shown in , such control approach can be high computational demanding
and even prevent real-time implementation. In order to implement our MPC algorithms in
real-time, we resort to the low complexity MPC formulation used in , ,  to solve
autonomous path following problems.
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 T. Gillespie. Fundamentals of Vehicle Dynamics, chapter 3, pages 60–67. Society of Automotive Engineers (SAE),
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systems. IEEE Trans. on Control System Technology, 15(3), 2007.
 P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, and D. Hrovat. Linear time varying model predictive control and its
application to active steering systems: Stability analisys and experimental validation. International Journal of Robust
and Nonlinear Control., 18:862–875, 2008.
 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.
Vehicle Stability Control
Hybrid Electric Vehicles