## 4 Control Algorithm Evaluation
### Experimental Validation
With the passive suspension, the seat experiences a more pronounced hop, with a peak displacement as high as 0.05 m. In contrast, the controlled case exhibits a smoother curve, with vertical displacement suppressed to below 0.02 m. It is also noted that, due to the presence of friction and hysteresis damping, both cases exhibit a small steady-state error. For ride comfort assessment, Figure 6b illustrates the acceleration responses, revealing that the overall magnitude in the active case is smaller than in the passive case. The peak-to-peak acceleration value decreases from approximately 4 m/s\({}^{2}\) to 2.9 m/s\({}^{2}\) with the active control, representing a 27.5% improvement. Scenario 2. To further investigate the performance of the control algorithm, a medium-low frequency random excitation signal with a maximum amplitude of 0.02 m is applied to simulate a more typical operating condition. The random excitation is generated by superimposing several sets of random signals with different characteristic frequencies, with an amplitude range of \(\pm\)2 cm, and its main components are concentrated between 1 and 3 Hz, as shown in Figure 7. Its frequency-domain characteristics are similar to the vibration excitations typically borne by seat suspensions. Figure 8 compares the displacement responses across different scenarios. With the passive seat suspension, the system vibrations remain within a reasonable range; however, the peak displacement exceeds 2 cm at certain frequencies, which is larger than the excitation magnitude. This indicates that the passive seat suspension amplifies vibrations at specific frequencies, an undesirable characteristic for practical applications. In contrast, the original system displays an unstable response due to its low damping coefficient, with noticeable resonance between 7 and 10 s. During this period, the peak displacement rises above 6 cm, roughly three times the magnitude of the excitation. On the other hand, the seat with active  
Figure 6: System response in Scenario 1: (**a**) displacement and (**b**) acceleration. Figure 7: Random excitation signal in scenario 2.  
suspension exhibits the smallest vibration magnitude, with peak displacement suppressed to below 2 cm. These results highlight the effectiveness of the proposed control algorithm in isolating the seat from road roughness excitation. Figure 9 presents the acceleration response curves, which reflect the system riding comfort. In the original case, resonance causes the peak acceleration to reach as high as 9 m/s\({}^{2}\). The passive seat suspension helps stabilize the system, reducing the acceleration to around 3 m/s\({}^{2}\). However, the active seat suspension delivers the best performance, with acceleration fluctuations maintained within \(\pm\)2 m/s\({}^{2}\) throughout the entire process. Figure 10 offers a frequency-domain analysis of the three cases, showing that the active seat reduces acceleration transmissibility across a broad frequency range. The enlarged plot emphasizes that the active seat excels at mid-range frequencies (1-2 Hz), where transmissibility is reduced by more than 30%. In conclusion, the active seat significantly enhances riding comfort. Figure 8: Displacement response in scenario 2. Figure 9: Acceleration response in scenario 2. The profiles of suspension deformation and actuating force are shown in Figure 11 and Figure 12, respectively. Both the active and passive seats maintain suspension deformation within a relatively small range. However, the active seat generally exhibits slightly larger deformation compared to the passive seat, highlighting the inherent trade-off between ride comfort and suspension deformation. In contrast, the original case shows significant fluctuations due to resonance. As shown in Figure 12, the actuating force stays within \(\pm 300\) N thanks to the loose settings for the PFF.