## 5 Conclusions and Future Developments  
The evaluation of two different lateral stability controllers for automotive vehicles has been performed, comparing the two solutions with a benchmark ESP solution already used in car models actually in the market. Both Linear Quadratic Regulator and Sliding Mode Control aim at the direct regulation of the vehicle's yaw rate and side-slip angle to achieve stability improvements with respect to the conventional solution, based solely on yaw rate tracking. In this work, the tracking and stability capabilities of LQR and SMC strategies are investigated. The controllers share the same algorithm for the control objective definitions, so the output comparability is ensured by the same reference modeling approach. However, the proposed solutions differ from the optimal control effort calculations aspect. In its most common configuration, the LQR controller can apply a yaw moment to the car body with a differential braking technique to stabilize the trajectory. The SMC controller is developed respecting important features to ensure flexibility and portability of the strategy with respect to quite different powertrain architectures. The best performance of this controller can be obtained by considering independent electric hub motors for 4 WD vehicles, which guarantee a higher applicable yaw momentum thanks to the easiness of 4-quadrant torque control, enabling the exploiting of traction forces. In addition, the 2-dimension sliding surface formulation enables the option to apply even steer angle corrections. The assessment is performed in a co-simulation environment exploiting an RT driving simulator hardware system, which allows a driver to perform different reference maneuvers, piloting the vehicle through steer and pedal interface devices. The maneuvers are inspired by standard cornering tests to assess achievement in terms of lateral stability using a Human-in-the-Loop approach. This means that a control rig composed of the vehicle, environment, and driver is required. Evaluating the stability performances in this kind of test is very challenging since there is a significant interaction between these elements. Therefore, the results are a combination of inner car handling dynamics and driver road-holding capabilities. To highlight the outputs, more difficult operative situations have been simulated with respect to the boundary conditions specified by the ISO regulations. Figure 12: Evaluation of the trajectory and longitudinal speed in case of Non-controlled vehicle (Passive), Commercial-controlled vehicle (Active), SMC, and LQR controlled, in a _Lane Change_ maneuver of 150 km/h and a lateral displacement of about 3 m.  
Performance achievements related to standardized vehicle speed and steer command are quite negligible since the vehicle operates in a steady-state mode. Instead, bringing the vehicle near to unstable conditions allows us to make more evident the effects of the controllers, which aims at leading the vehicle back to a linear behavior. The executed cornering maneuvers could show some gaps between each other in terms of steering amplitude and rate, as well as speed tracking. This is due to the inability of any human driver to ensure the perfect repeatability of the tests. However, to mitigate this aspect, multiple tests are conducted, comparing the most similar ones. The simulation campaign consists of a preliminary _off-line test phase_, in which controllers are tuned. _Ramp Steer_ was fundamental for the definition of the effort constraints, adopted as saturation limits for brake pressures and wheel torques. Instead, _Step Steer_ tests with low lateral acceleration were useful for the tuning of parameters related to control objective definitions (e.g., tire cornering stiffness). The _on-line test phase_ refers to standard cornering maneuvers in HiL configuration. Results highlight as both proposed control strategies enable improved performances with respect to Non-controlled and Commercial-controlled vehicle scenarios.