# Optimal Control Method of Semi-Active Suspension System and Processor-in-the-Loop Verification
## 4 Discussion  
The test results for the highest bump for the passive system and the SASS are in Figure 21. Considering the passive system's response (Figure 21a), the sprung mass displacement was completed in about 3.5 cycles. For the same bump, the sprung mass displacement of SASS in Figure 21b was damped in about 1 cycle. A similar result was observed for the sprung mass acceleration between the passive system and the SASS. In the passive system (Figure 21a), the body oscillations took 2.5 s after the application of the bump input, while it took only 1 s for the SASS (Figure 21b). In addition, the unsprung mass oscillations of the passive system took longer to reach equilibrium compared to the SASS. In the passive system, the tire oscillations took 2 s after applying the bump input, while in the SASS, it took only 0.6 s.  
The test results for the medium bump comparing the passive system and the SASS are shown in Figure 22. Regarding the passive system's response (Figure 22a), the sprung mass displacement was completed within approximately 1.5 cycles. Furthermore, the SASS (Figure 22b) ensured a damped sprung mass displacement in just a 0.75 cycle for the same  
Figure 23: Test lowest bump (**a**) passive system (**b**) SASS. bump. A similar trend was observed in terms of the sprung mass acceleration between the passive system and the SASS. In the case of the passive system (Figure 22a), it took 1 s for the body oscillations to settle after the application of the bump input, whereas the SASS accomplished this within 0.7 s (Figure 22b). Additionally, the unsprung mass oscillations of the passive system required more time to reach equilibrium compared to those of the SASS. The tire oscillations in the passive system took 0.5 s to stabilize following the bump input, whereas the SASS achieved this in 0.4 s.  
The comparative test results for the lowest bump between the passive system and the SASS are presented in Figure 23. When examining the response of the passive system (Figure 23a), it can be detected that the sprung mass displacement was completed within approximately 1.5 cycles. In contrast, the SASS (Figure 23b) achieved a damped sprung mass displacement for the same bump in just 0.5 cycles. The periods of the parameters obtained from the lowest bump were nearly equal to the medium bump results, while their amplitudes were reduced. A similar case occurred when considering the sprung mass acceleration in the passive system and the SASS. In the passive system (Figure 23a), it took 1 s for the body oscillations to settle following the application of the bump input, while the SASS accomplished this within 0.5 s (Figure 23b). Furthermore, compared to the SASS, the passive system required more time for the unsprung mass oscillations to reach equilibrium. The tire oscillations in the passive system took 0.4 s, while the SASS achieved this in 0.35 s.  
The RMS values of three critical parameters for both the passive and the SASS were calculated by using the data from the test results obtained with the oscilloscope. These values were obtained for all three different bumps and can be seen in Table 4. The sprung mass displacement was improved by 59.10% for the highest bump, 19.96% for the medium bump, and 16.8% for the lowest bump with SASS. The improvement rates for the sprung mass acceleration in the SASS were 63.45% for the highest bump, 31.39% for the medium bump, and 18.35% for the lowest bump. Finally, the suspension deflection in the SASS was enhanced with improvement rates of 52.78% for the highest bump, 16.07% for the medium bump, and 15.76% for the lowest bump. Considering the aforementioned results, the best improvement was achieved in sprung mass acceleration for all the bumps. This means that ride comfort was notably enhanced with the proposed controller. This is the result of determining the weight coefficient larger than the other terms for the sprung mass acceleration in the objective function. Furthermore, suspension deflection was improved for all of the bumps.