# A Review of Low-Frequency Active Vibration Control of Seat Suspension Systems
## 2 Seating Systems with Active Suspension
### Simulation
The results proved that the fuzzy PID controller in that study was the best for the low-frequency vibration control of the seating system. Figure 21: Block diagram of the proportional-integral-derivative (PID) control system [PERSON] et al. (2019). A feed-forward adaptive controller (Figure 23) combined with the FXLMS algorithm and a feedback controller combined with the H-infinity algorithm was proposed by [PERSON] and [PERSON] (2004) [70] to reduce the small-amplitude vibration of a vehicle seating system. The researchers compared three different control methods and found that the FXLMS feed-forward adaptive controller alone could reduce the vibration amplitude of 4.8 dB at 10 Hz when it was turned on compared with the situation when the controller was turned off. The feedback controller with the H-infinity algorithm could reduce the vibration amplitude of 3.6 dB. Finally, the hybrid controller combined with the two control methods successfully reduced the vibration amplitude of 11 dB. The possible reason for this may have been that although the feed-forward adaptive FXLMS algorithm has the advantage of taking less computational time and easy implementation, it relies on the measurable reference signal. Once an unpredictable change of the vibration source occurs, this change greatly affects the convergence speed of the adaptive feed-forward controller algorithm. However, the feedback controller based on the H-infinity algorithm has good and robust performance. Therefore, the hybrid controller combining the advantages of the two algorithms should have the best and most robust performance for seat vibration control. A feedback controller based on the H-infinity algorithm was proposed by [PERSON] et al. (2011) [71] to reduce the vibration transmissibility of a seating system. A 3-DOF mass-spring biological model (Figure 24) was introduced to simulate the human body to improve the accuracy of the controller. Unlike the traditional H-infinity algorithm controller, the controller in this paper was optimized with a targeted frequency range by using the generalized Kalman-Yakubovich-Popov (KYP) lemma, which is mainly controlled in the sensitive frequency range of human body (4-8 Hz). According to the ISO 2631 standard, the D-class road profile roughness was simulated as the road surface excitation for the active suspension system. The simulation results showed that the system could significantly reduce vibration in the targeted range (4-8 Hz). Figure 23: Schematic of the hybrid controller [70]. Figure 22: Fuzzy logic controller block [69]. [PERSON] et al. (2012) [72] proposed an integrated control strategy that combines the driver body biodynamic model and the quarter car model to include active seat suspension and active vehicle suspension vibration controls to enhance ride comfort (Figure 25). In the controller design, the state feedback H-infinity controller of model simplification provides good robustness, considering friction as a feedback signal. According to the experiment results, the system can largely reduce the driver's head acceleration. It was shown that integrated active seat suspension and vehicle suspension controls could improve comfort compared with other separate controls. The different control system design details are summarized in Table 2.  
Figure 24: Three-DOF biodynamic model [71]. Figure 25: The model of the integral control strategy [72]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Author** & **Method** & **Target Frequency** & **Vibration Control Performance Criterion** & **Model** & **Performance** & **Fros and Cons** \\ \hline [PERSON] et al. (2018) & PID control & 7.51 Hz & Displacement (m) & 5-DOF & The peaks of vibration amplitude