# Analytical Investigation of Vertical Force Control in In-Wheel Motors for Enhanced Ride Comfort
## 3 Results and Discussion
### Frequency-Weighted Acceleration
The black dashed lines represent the maximum continuous force limit of 3570 N, while the black dotted lines represent the maximum peak force limit of 8240 N, according to the parameters in Figure 14 (The yellow line in Figures 15-17 is the reference force, zero newtons). Moreover, the root mean square (RMS) of the vertical acceleration of the sprung mass, corresponding to various proportional gains and types of road profiles, is shown in Tables 6-8. Tables 6-8 demonstrate that increasing the proportional gains reduces the RMS of the vertical acceleration of the sprung mass, or the frequency-weighted acceleration. Conversely, Figures 15-17 illustrate that higher proportional gains lead to an increase in the front wheel driving forces of the IWM. Considering the time response of the front wheel driving forces for the road profile classes A to B in Figure 15, with \(K_{p}=300\), the blue line indicates that most of the driving forces are within the continuous force limit, and the peak forces are within the peak force limit. Thus, \(K_{p}=300\) is suitable for this case, resulting in an improvement of up to 7.58% in frequency-weighted acceleration compared to the open-loop system. Similarly, for the road profile classes B to C in Figure 16, with \(K_{p}=150\), the blue line shows that most of the driving forces are within the continuous force limit, and the peak forces are within the peak force limit. Therefore, \(K_{p}=150\) is appropriate for this case, resulting in an improvement of up to 3.96% in frequency-weighted acceleration compared to the open-loop system. Figure 16: Time response of the front wheel force for the road profile classes B to C.  
Figure 15: Time response of the front wheel force for the road profile classes A to B.  
Additionally, considering the time response of the front wheel driving forces for the road profile classes C to D in Figure 17, with \(K_{p}=75\), the blue line indicates that most of the driving forces are within the continuous force limit, and the peak forces are within the peak force limit. Thus, \(K_{p}=75\) is suitable for this situation, resulting in an improvement of up to 2.01% in frequency-weighted acceleration compared to the open-loop system. In summary, the closed-loop systems with the proportional ride-blending controller for the IWM effectively reduce the frequency-weighted acceleration, as per ISO 2631, and the RMS of the vertical acceleration of the sprung mass. The results demonstrate that increasing the proportional gain decreases both the frequency-weighted acceleration and the RMS of the vertical acceleration of the sprung mass. However, due to the torque limitations of the IWMs, excessively high proportional gains may prevent the motors from generating sufficient torque and force to reduce the vertical acceleration effectively. Table 9 summarizes the suitable proportional gains for each type of road profile and shows the corresponding percentage reduction in frequency-weighted acceleration. To achieve optimal reduction, an adaptive proportional gain controller based on the values in Table 9 may be implemented to maximize the decrease in frequency-weighted acceleration.