# Control of Automotive Semi-Active MR Suspensions for In-Wheel Electric Vehicles
## 3 Results and Discussion
### QoV
#### 3.1.2 Closed Loop  
The results in closed loop are presented for the normal \(Q\)\(V\), the modified \(Q\)\(V\) (in-wheel electric motor) and the modified \(Q\)\(V\) (in-wheel electric motor) considering the residual vertical force provided by the electric motor in Figures 16-18, respectively. For the case of the MQ\({}_{0}\)\(V\), in the step test (Figure 17a), the M1S is the unique controller that enhances the comfort (10%) which means that in comparison with an intermediate current value (\(1.25A\)) the M1S enhances the damping action during compression. By the case of the sprung mass test (Figure 17b), the best performance in comfort is giving by the FEB controller (15%), followed by the M1S. The rest of controllers decreases the performance. In the frequency domain, the SH controller gives a minimum improvement (12%) according to the IPSD (Figure 17d), and the pseudo-bode plot (Figure 17d), where it can be seen that the performance of the SH is similar to the \(1.25A\) baseline, which means that the baseline suspension is also a good option for improving comfort. According to the indexes discussed above, we can conclude that the SH enhances the comfort for the MQ\({}_{0}\)\(V\) in closed loop considering as reference a \(1.25A\) baseline suspension. By the side of the road holding, in the step test (Figure 17a), FEB controller gives the highest improvement (18%) followed by the M1S and GH controllers. For the unsprung mass test (Figure 17c), the best road holding performance (12%) is also given by the FEB controller, the rest of controllers, decreases the performance in comparison with the \(1.25A\) baseline. By the side of the frequency domain, the FEB controller provides the best improvement (15%) as well as the lowest gains in the bandwidths of interest, as it is shown in Figure 17i,e. The rest of the controllers gives almost the same performance than the \(1.25A\) baseline. According to the performance indexes, for the Mod\(QoV\), the best road holding improvement is given by the FEB controller in closed loop considering as reference a \(1.25A\) baseline suspension. The useful lifetime is improved by the FEB controller during the step, sprung and unsprung mass tests by \(15\%\), \(42\%\) and \(35\%\), respectively. The same occurs in the frequency domain, where the FEB enhances the useful lifetime in a \(22\%\) according to the IPSD, and minimizes the gains in the pseudo-bode plot. In the step and sprung mass test (Figure 17a,b) the FEB controller gives the biggest improvement followed by the M1S, while the rest of controllers decreases the performance. By the side of the unsprung mass test (Figure 17c), just the FEB controller is giving a useful lifetime improvement. The same occurs in the frequency domain, where the main improvement is giving by the FEB controller according to the Figure 17f,h and the rest of the controllers shows similar improvements in comparison with the \(1.25A\) baseline. That's why the FEB controller guarantees the useful lifetime improvement for the MQ\(oV\) in closed loop considering as reference a \(1.25A\) baseline suspension. Figure 15: Results from open loop simulations for the comparison in a nonlinear modified QoV model considering a \(1.25A\) baseline suspension and the residual vertical force. In the MQ_o_V_FV, comfort is improved in the step test (Figure 18a) by the SH controller in a 5% followed by the GH controller, the rest of the controllers gives negative improvements. Besides, in the sprung mass test (Figure 18b), the comfort is enhanced by the FEB controller by 15%. While the rest of controllers shows lower improvements than the baseline suspension. On the other hand, according to the IPSD (Figure 18a), the GH controller enhances the comfort by a 15% followed by the FEB controller. While in the pseudo-bode plot (Figure 18a), the lower gains are given by the SH controller followed by the GH controller. According to the information described above, it can be said that the SH controller gives the highest comfort improvement for the MQ_o_V_FV in closed loop.