###### Abstract  
This study concerns the comparative investigation of two advanced lateral stability automotive controllers with respect to a commercial solution. The research aims to improve the stability performances achieved by a combined tracking of yaw rate and side-slip angle through the application of optimal efforts. The proposed solutions are based on Linear Quadratic Regulation and Sliding Mode Control, respectively. Both rely on the same approach for the control objective definition but differ from the action perspective. This solution involves the adoption of a differential braking actuation technique to deliver a desired yaw moment to the car body to track controlled states. Indeed, a sliding controller can also traction torques of hub-motor configurations as well as steering corrections, achieving vehicle stability and a driving response in accordance with the pilot's intentions. Calibration and validation of the controllers are performed through a Hardware-in-the-Loop simulation rig, along with a real-time static simulator, performing different close-loop maneuvers to assess achievements in terms of lateral stability. Results show that both solutions ensure higher handling performances if compared to Non-controlled or Commercial-controlled vehicle scenarios. automotive; lateral stability; sliding mode control; torque vectoring; steer-by-wire; mechatronic; driving simulator; Hardware-in-the-Loop +
Footnote †: journal: Applied  
In this work, the authors intend to propose two different lateral stability solutions to achieve higher lateral stability performances. The first control strategy is developed and implemented in a Rear Wheel Drive (RWD) electric vehicle using an innovative Brake-By-Wire (BBW) architecture developed by Meccanica 42 S.r.l. [13]. This ESP is based on a tracking **Linear Quadratic Regulator (LQR)** able to find the optimal control gains to make the car follow the reference yaw rate and side slip angle. Compared to the State-of-Art (SoA) [14; 15; 16; 17], which acts leading the side-slip angle and the yaw rate under a saturation limit, in this case, a continuous regulation on their values is assured by implementing not only the actual but also the reference yaw rate and side-slip angle values. Thus, by exploiting the brake actuators' capabilities, it is possible to nullify the errors between the car and the dynamic reference model. In this way, the onset of instability is prevented, and a delay between the upper controller and the pressure controllers is not led. The output defined by the stability control is the total yaw moment that the car has to have to follow the ideal behavior. This total yaw moment is ensured by a developed logic that splits the moment into the four brake units. It is based on the moment sign, defining which side of the car to actuate. Then, according to the wheel adhesion condition, a percentage of braking torque is delivered to the wheel on that side. In addition, an algorithm that redistributes the control efforts as the wheel reaches its braking pressure limit is implemented to guarantee the yaw moment required by the control. The second one was previously developed for IWM-driven Electric Vehicles (EVs) equipped with BW systems [18; 19; 20] and is based on **Sliding Mode Control (SMC)** methodology. This particular vehicle layout has been the subject of numerous studies [21; 22; 23; 24]. In the available SoA, we can find many papers proposing a coordinated control between steering and differential torque allocation to achieve higher stability performances [25; 26; 27; 28; 29; 30; 31]. The proposed solution provides combined actions between the Steer-by-Wire (SBW) system and torque allocation to ensure the tracking of side-slip angle \(\beta\) and yaw rate \(r\). Optimal control signals, i.e., adjusting yaw moment and correcting steering angle, are calculated through a Lyapunov candidate, which leads the derivatives of the controlled state to converge to 0 asymptotically.