## 4 Experiments
### Experimental Results  
The content of the experiment mainly comprises the following three parts: (1) the FFC parameter, which is optimized through DDPG under the condition of a proper FBC parameter; (2) the FBC parameter is optimized in a reasonable FFC parameter; (3) FFC and FBC parameters optimizing simultaneously. Figure 9 shows the experimental results of FFC parameter self-learning by the DDPG algorithm when the FBC proportional gain is fixed at 1.8. Figure 9a-e are the learning curves of the 0/20/40/80/100 th episode, where the horizontal axis is the number of steps, the red line is the value of the FFC parameter, and the blue line is the corresponding value of the action reward. Figure 9f reflects the convergence of the FFC parameter in the whole self-learning process. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Components** & **Symbol** & **Parameter** & **Value** \\ \hline Payload & \(m\) & Mass & 1750 kg \\ \hline Helical spring & \(k\) & Stiffness & 300,000 N/m \\ \(c\) & Damping & 490 Ns/m \\ \hline Voice-coil motor & \(K_{T}\) & Force constant & 80 N/A \\  & \(R_{M}\) & Resistant & 34.5 \(\Omega\) \\  & \(L_{M}\) & Inductance & 28 mh \\  & & Moving distance & 28 mm \\  & & Frequency range & \(\leq\)200 Hz \\ \hline Geophone & \(f_{g}\) & Natural frequency & 4.5 Hz \\  & \(G_{g}\) & sensitivity & 100.4 V/m/s \\  & \(R_{d}\) & Internal resistant & 2450 \(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of components in AVRS. Figure 9: The experimental results of FFC single parameter self-learning in DDPG: (**a**–**e**) are the learning curves of the 0/20/40/80/100 th episode, respectively; (**f**) are the curves of the whole self-learning process. Figure 10 shows that there is an approximate normal envelope distribution relationship between the FFC parameter and the state reward value. When the parameter is located between \([-15,\,-5]\), the active vibration reduction performance becomes better with the increase in the FFC parameter. When it is bigger than \(-4\), the control performance gradually deteriorates. When the parameter is at the limit value of \(-15\) or \(5\), the system state value is negative, indicating that the system is in a state of vibration amplification or instability. The parameter range of the maximum state reward value is \([-5,\,-4]\), as marked in the red circle, which is consistent with the region corresponding to the parameter convergence value in Figure 9f, indicating that the DDPG algorithm can track the optimal value range of single-parameter FFC during self-learning. As shown in Figure 11, the FFC proportional control parameter is fixed to \(-4.5\), and the DDPG optimization learning is carried out when the initial value of the FBC proportional parameter is \(0\). Figure 11a-e are also the learning curves of the \(0/20/40/80/100\)th episode. Figure 11f reflects the convergence range of the FBC parameter at \([2,\,3]\). Figure 11: The experimental results of FBC single parameter self-learning in DDPG: (**a–e**) are the learning curves of the \(0/20/40/80/100\)th episode, respectively; (**f**) are the curves of the whole self-learning process. Figure 10: Scatter diagram of state reward and feed-forward proportional parameter. The experimental learning curve in Figure 12 can be divided into three regions: the stable region, the transition region, and the unstable region. It is observed that when the FBC parameter is less than 2.5, the system is in the stable region, and with the increase in the FBC parameter, the control performance of the system improves gradually. In the transition region of [2.5; 6], it is found that there is a similar hysteresis characteristic between the system state reward and the FBC proportional parameter. Therefore, when the FBC parameter increases monotonously from 2.5 to 4.5, the system performance deteriorates.