This paper proposes an electronic stability control and shows MIL and HIL simulations performed for evaluation. Two designs are presented, one based on two-degrees-of-freedom linear model that includes side-slip and yaw motion and other based on three-degrees-of-freedom linear model that includes roll motion. Model-in-the-loop and Hardware-in-the-loop simulations were performed to test ESC on vehicle represented by a nonlinear model that considers lateral, yaw and roll motions and an intelligent driver model to generate the steering wheel command as driver reaction to vehicle motion in respect with desired path. It's found from simulations for double lane change maneuver that the proposed controller is effective in reducing of sideslipping, rolling and yaw rate errors, keeping the steering stable in scenarios where the driver loses control of the vehicle, even in presence of disturbances in vehicle response in relation with response predicted by linear model used for control design. Keywords Electronic stability control • Linear quadratic regulator • Hardware-in-the-loop • Vehicle steering dynamic List of symbols a Length from front axis to center of mass b Length from rear axis to center of mass l Vehicle total length from rear axis to front axis t f Front track width t r Rear track width h s Height of center of mass above rolling center h Height of center of mass m s Sprung mass I zz Yawing inertial moment I xx Rolling inertial moment I xz Inertial product related to yawing and rolling c f Front rolling damping coefficient c r Rear rolling damping coefficient k f Front rolling stiffness coefficient k r Rear rolling stiffness coefficient f ∕ Front steer-by-roll coefficient M u Extra yaw moment given as control signal I s Steering coefficient u Vehicle longitudinal speed v Vehicle lateral speed Yaw angle Roll angle f Steering angle of front wheels r Steering angle of rear wheels D Front steer angle due to the driver's steering wheel command F yi Lateral force generated by tire i Camber angle i Tire slip angle of wheel i Vehicle side-slip angle g Gravity acceleration C i Cornering stiffness of wheel i C i Camber stiffness K Camber gradient r ∕ Rear steer-by-roll coefficient Tire-road friction coefficient

This paper presents an upper-level vehicular stability controller based on parameterized MPC strategy. The proposed system computes the additional moment applied on the vehicle's yaw axis to improve the lateral stability. In the MPC formulation, the optimization problem is defined as a quadratic programming derived from a linear time-invariant model of vehicle dynamics. The control system is implemented based on a model that considers the rolling movement and on a simpler model that does not consider it, in order to evaluate the effects of using a more representative linear model for more accurate prediction or a simplified model for faster calculation. Constraints are imposed on the optimization problem to deal with the limits in the corrective yaw moment. A parameterized MPC approach is designed to reduce the number of optimization variables, and hence, reducing the computation time required for real-time implementation. Model-in-the-loop simulations are proposed to evaluate the effectiveness of the MPC strategy to avoid steering instability. Simulations are performed for profiling the calculation time, tuning the parameters, and testing algorithm running in an ARM-Cortex A8 on real-time control. Simulation results show that the proposed control strategy is effective in preventing destabilization and demonstrates that even with a longer computation time, the resulting MPC scheme meets the control requirements successfully, even under the presence of model disturbances.INDEX TERMS Electronic stability control, model predictive control, vehicle lateral stability.

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