# Enhancement of Yaw Moment Control for Drivers with Excessive Steering in Emergency Lane Changes
## 5 Simulations
### Case III: The Acting-Alone Enhanced Yaw Moment Control  
By applying the same parameter values as in Case I and Case II, we demonstrate in this case the performance of the vehicle under the acting-alone enhanced yaw moment control (56) (i.e., \(\delta_{sat}=0\) and \(\delta_{f}=\delta_{d}\)), which is the traditional DYM approach to managing the instability effect of excessive driver steering. Figure 9a,b depicts the responses of the vehicle speed \(V_{0}\), wheel speeds \(\omega_{j}\), the front-wheel steering angle \(\delta_{f}\), and the steering angle limit \(\widetilde{\delta}_{\text{lim}}\). Compared with the results of Case I and Case II, the vehicle speed \(V_{0}\) is the lowest after the control process. Figure 9c,d shows the responses of the yaw moment \(M_{z}\) and the distributed wheel control torques \(T_{j}\), respectively. In comparison to the results of Case II, the acting-alone yaw moment control appears to generate considerable yaw moment and wheel torques in the periods of [0.5, 1.8] and [2.1, 3.5] in seconds to suppress the instability effect caused by the excessive driver steering \(\left|\delta_{f}\right|>\widetilde{\delta}_{\text{lim}}\) as shown in Figure 9b. Although the vehicle state \((\beta,\gamma)\) shown in Figure 9e,f remains close to the reference state \((\beta_{ref},\gamma_{ref})\), there is some obvious overshoot and deviation in the response of yaw rate \(\gamma\). Figure 9g shows the resulting acceleration \((a_{x},a_{y})\) with the lateral acceleration \(a_{y}\) close to the safety limit \(\widetilde{a}_{y,\text{lim}}=0.68\text{ g}\) in the periods of [1, 1.7] and [2.8, 3.5] in seconds, and Figure 9h-1 displays the responses of the combined wheel slip magnitudes \(\left\|\mathbf{S}_{j}\right\|\) and the wheel slips \(\mathbf{S}_{j}=\left[s_{Lj},s_{Sj}\right]^{T}\) of the four wheels in that order. We observe that the two front wheels experience significant coexistence of longitudinal and lateral wheel slips (i.e., \(\left\|\mathbf{S}_{j}\right\|\), \(j=1,2\)) in the periods of [1, 1.7] and [2.8, 3.5] in seconds. During these periods, the friction forces of the two front wheels are operating within the friction saturation region, and therefore the control system has a limited capacity to address additional stabilization challenges. The deviation of the yaw rate from its safety reference in Figure 9f and the two front wheels operating in the friction saturation region in Figure 9h are the drawbacks when the acting-alone yaw moment control is employed to counter the driver's excessive steering. In Case III, we specifically evaluated the effectiveness of using DYM alone during emergency lane changes. This serves as a baseline for comparison with our proposed control system. As expected, the standalone DYM effectively regulates the vehicle state close to the reference state, as shown in Figure 9e,f. However, it struggles to maintain cornering within the tire/road friction saturation zone due to excessive driver input, as depicted in Figure 9h-1. Our proposed control system, demonstrated in Cases I and II, shows significant improvements.