## 5 Control Effectiveness under Multi-Type Hazard Excitation
### Control Effectiveness Analysis  
According to the numerical results of the structure with the TRID/ARID system, the control effectiveness is shown in Table 3. As shown in the swing angle time history, the structures with the ARID system have a smaller peak angle and a more stable response. It can also be seen in Table 3 that the control effectiveness of the ARID system is better in all cases. The ARID system shows a better robustness than the TRID system.  
The control effectiveness analysis results of the five conditions [44] are shown in Table 4. As can be seen from the experimental and numerical results, it can be concluded that there is a very good agreement between the experimental and numerical results. The ARID system delivers a better control performance.  
In the free vibration condition, the swing angle decreases very quickly. The swing angle response of the structures is totally controlled. The control effectiveness is apparent. In the forced vibration condition, the ARID system controls the swing angle within a small range and remains stable. The ARID system can absorb energy to reduce the influences of excitations on the structures. In the sweep excitation condition, the swing angle is also controlled within a small range. Furthermore, the swing angle exhibits a slight change as the excitation frequency changes. The structural response is stable. The ARID system can deliver a superior control performance in the whole frequency range. In the earthquake and sea wave excitation conditions, the swing angle is also controlled within a small range and the structural response is stable. When the excitation frequency changes rapidly, the swing  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Experiment**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Control Effectiveness**} & \multicolumn{2}{c}{**Peak Swing Angle (\({}^{\circ}\))**} \\ \hline
**Case** & **Peak Reduction Rate (_Peak_)** & **Peak Reduction Rate (RMS)** & **with ARID Control** & **without Control** \\ \hline Free vibration & - & 88\% & 47.76 & 47.37 \\ Forced vibration & 97\% & 97\% & 1.67 & 53.44 \\ Sweep excitation & 90\% & 90\% & 2.29 & 22.06 \\ Earthquake excitation & 85\% & 96\% & 2.20 & 14.24 \\ Sea wave excitation & 94\% & 97\% & 1.67 & 28.65 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Control effectiveness comparison of the ARID system.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Control Effectiveness**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Peak Reduction Rate (_Peak_)**} & **RMS Reduction Rate (RMS)** \\ \hline
**Case** & **TRID** & **ARID** & **TRID** & **ARID** \\ \hline Free vibration & - & - & 50\% & 82\% \\ Forced vibration & 31\% & 88\% & 28\% & 90\% \\ Sweep excitation & 25\% & 52\% & 73\% & 80\% \\ Earthquake excitation & 45\% & 75\% & 59\% & 93\% \\ Sea wave excitation & 73\% & 87\% & 77\% & 94\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Control effectiveness comparison of the ARID system with the TRID system.  
angle may change rapidly, but the change is tiny compared with that of the structure without control. The ARID system acts as a filter and consumes excitation energy to reduce the structural response.  
The control performance of the ARID system is excellent. It can significantly reduce the maximum swing angle of the suspended structure. The experimental results show that it can reduce more than 90% of the swing angle response in most working conditions. Furthermore, the swing angle can be controlled within a very small range and it can satisfy most of the structural stability demand. It can be concluded that the ARID system has a better robustness.