## 4 Control Algorithm Evaluation
### Experimental Validation  
To further evaluate the performance of the proposed controller in a practical setting, a 6-DOF vibration platform is used to simulate the cabin floor, as shown in Figure 5. The lower base of the seat suspension is mounted on top of the platform, and two sandbags are used to emulate the driver. The active seat suspension is controlled by an NI CompactRIO 9074, equipped with NI 9205 and NI 9264 modules, operating at a control frequency of 200 Hz. Two displacement sensors (optoNCDT 1302-100, Micro Epsilon, Ortenburg, Germany) are employed to measure the vertical displacement of the seat and the suspension \begin{table}
\begin{tabular}{c c c c} \hline
**Symbol** & **Value** & **Unit** & **Description** \\ \hline \(m_{d}\) & 75 & kg & Mass of driver \\ \(m_{s}\) & 15 & kg & Mass of seat \\ \(k_{d}\) & 90,000 & N\(\cdot\)m\({}^{-1}\) & Stiffness of driver \\ \(k_{s}\) & 4500 & N\(\cdot\)m\({}^{-1}\) & Stiffness of seat suspension \\ \(c_{d}\) & 2500 & N\(\cdot\)s\(\cdot\)m\({}^{-1}\) & Damping coefficient of driver \\ \(c_{s}\) & 426 & N\(\cdot\)s\(\cdot\)m\({}^{-1}\) & Damping coefficient of active suspension \\ \(c_{p}\) & 600 & N\(\cdot\)s\(\cdot\)m\({}^{-1}\) & Damping coefficient of passive suspension \\ \(F_{c}\) & 36 & N & Coulomb friction \\ \(k_{a}\) & 200 & N/A & Equivalent control gain of the actuator \\ \hline \(n\) & 2 & N/A & \\ \(\eta\) & 30,861 & N/A & Shape and amplitude coefficients of the \\ \(\lambda\) & 19,973 & N/A & hysteresis loop \\ \(\gamma\) & 203 & N/A & \\ \hline \end{tabular}
\end{table} 
Table 1: Nominal parameter values of the 2-DOF driver-seat model. Figure 4: Simulation acceleration transmissibility. deformation. The vertical velocity is calculated by taking the time derivative of the displacement signal. Comparative experiments, including passive, original, and controlled cases, are conducted. The passive experiment is performed using a passive seat suspension, which consists of a spring and damper system designed for heavy-duty vehicles. Two scenarios are designed to evaluate the performance of the proposed controller. Considering the limit of the actuator, the PPF of the control algorithm in the experiments is set to be relatively loose: \(\varphi_{1}(t)=(0.2-0.1)e^{-3.5t}+0.1\). The control gains are selected as \(k_{1}=5\), \(k_{2}=5\). In order to verify the robustness of the control algorithm, perturbed system parameters are applied. The total weight of the sandbags is about 60 kg, which is 15 kg less than the nominal value. Moreover, due to suspension deformation and the nonlinear spring and damper, the actual stiffness and damping coefficients of the seat suspension are time-variant and unknown. To better illustrate the performance of the proposed control strategy, the unadjusted, passive, and active cases are tested in the experiment:  
1. Original case: The shock absorbers remain untuned, preserving their factory-original state (approximate 370 N\(\cdot\)s\(\cdot\)m\({}^{-1}\)). The motor and gear reduction are not installed. 2. Passive case: The damping coefficient has been optimally adjusted based on the nominal model (Table 1), reaching approximately 600 N\(\cdot\)s\(\cdot\)m\({}^{-1}\). 3. Active case: The damping coefficient has been appropriately reduced to meet the requirements of active control, with a value of approximately 400 N\(\cdot\)s/m. Scenario 1. In this scenario, the driver-seat system is subject to a bump excitation. The profile of the excitation can be described using the following equation:  
\[z_{v}= \begin{cases}\dfrac{h_{b}}{2}\bigg{(}1-\cos\bigg{(}\dfrac{2\pi t}{t_{w}} \bigg{)}\bigg{)}&0\leq t\leq t_{w}\\ 0&\text{elsewhere}\end{cases} , \tag{53}\]  
where \(h_{b}=0.035\) m and \(t_{w}=0.625\) s are the height and length of the bump, respectively. The comparison between the controlled and original systems is presented in Figure 6.  
Figure 5: Experimental setup. Figure 6a shows the displacement responses for both the active and passive cases.