## 3 Simulation Studies
### Time Domain Performance Evaluation  
#### 3.3.1 Random Road Profile  
In this section the effectiveness of the proposed strategies in improving ride comfort is evaluated when the QvM is subject a random road profile at different vehicle speeds. The road profile used in this study is of a class E (very poor) according to ISO 8606 standard, which has a road roughness of \(\Phi(\Omega_{0})=256\times 10^{-6}\) m\({}^{3}\). For the sake of brevity, only the time responses in terms of the seat acceleration and seat suspension travel, as well as the PSD of the seat acceleration at a vehicle speed of 60 km/h is presented. The results are presented in Figures 4-6. From Figure 4 it canbe seen that the proposed controllers are more effective in reducing the seat acceleration when compared with the passive system. Controllers A3, A4, and A5, which use both feedforward preview information together with feedback signals, provide the best performance, while the PID active seat suspension slightly reduces the seat acceleration compared with the passive system as shown in Figure 4f. As expected, the superior vibration attenuation of the proposed control strategies results in increased seat suspension travel compared with the passive alternative. This is illustrated in Figure 5 in which controller A5 generates the highest seat suspension travel.  
Figure 6 shows that the PSD of the active seat suspension combined with any of the proposed control strategies (A1 to A5) has lower PSD compared to the passive system over a wide frequency range, especially over the range of (4-8 Hz). Once again, the controllers A3, A4, and A5 deliver the lowest PSD when compared to other strategies. Although the PID active seat suspension provides an approximately comparable PSD to those of the proposed controllers over a frequency range less than (10 Hz), and it has a higher PSD than that of the passive system outside this frequency range, as shown in Figure 6f.  
Figure 7a-c compare the simulated SEAT factors, the frequency-weighted RMS seat acceleration and the maximum seat suspension travel of the passive and active seat suspensions at a range of  
Figure 4: Simulated seat acceleration of the passive and active seat suspensions at a vehicle speed of 60 km/h. (**a**) A1; (**b**) A2; (**c**) A3; (**d**) A4; (**e**) A5; (**f**) PID.  
Figure 3: Simulated frequency responses of the passive and active seat suspensions.  
vehicle speeds. Taking into account the random nature of the road input the simulations were repeated 30 times for each vehicle speed over a time interval of 20 s and then an average was taken. It can be seen that all the proposed control strategies provide improved vibration attenuation, as well as significantly lower frequency-weighted RMS seat acceleration than both the passive and the PID active seat suspensions, regardless of the vehicle speed. Once again the controllers A5, A3, and A4 provide the best improvement SEAT factor, isolating at least 45% of the transmitted vibration at all vehicle speeds compared with the passive system. The PID active system isolates only 23% of this vibration and also results in a larger seat suspension displacement compared to either controllers A3 or A4, as shown in Figure 7c.  
Figure 5: Simulated seat suspension travel of the passive and active seat suspensions at a vehicle speed of 60 km/h. (**a**) A1; (**b**) A2; (**c**) A3; (**d**) A4; (**e**) A5; (**f**) PID.  
Figure 6: PSD of the seat acceleration for passive and active seat suspensions at a vehicle speed of 60 km/h. (**a**) A1; (**b**) A2; (**c**) A3; (**d**) A4; (**e**) A5; (**f**) PID.