## 6 Comparison with Existing Methods  
To comprehensively investigate the KF-ADC strategy proposed in this study, several other promising delay compensation methods were employed to provide the reference for evaluating the proposed compensator strategy. These are the widely used proportional integral (PI) control with a phase lead compensator ([PERSON], [PERSON] et al. [32]), the model-based controller ([PERSON], [PERSON] [19], the adaptive model reference controller (aMRC, [PERSON] and [PERSON] [42]), and the tracking error-based adaptive delay compensation method (TE-AC, [PERSON] and [PERSON] [43]). The simulation results provided in [PERSON] and Spencer [42] and [PERSON] and Mercan [43] are cited here.  
The evaluation criteria for vRTHS employing nominal parameters with different partitioning configurations under the El Centro earthquake are shown in Figure 13. It can be seen in the figure that the nine criteria provided by PI are generally the largest, indicating that the traditional control method may not be very effective to deal with variant time delay in RTHS. With the exception of the tracking criteria of \(J_{2}\) and \(J_{3}\), the simulation results generated by aMRC are better than that by MBC, implying that the time delay in RTHS is varying, and constant delay compensation is not sufficient. The aMRC exhibits better performance compared to TE-AC, which is mainly caused by the large number of parameters that should be adjusted in TE-AC.  
Furthermore, it can be seen in Figure 13 that the proposed delay compensation scheme is competitive compared with the promising aMRC strategy. With the exception of the calculated time delay of the proposed method is a little larger than that of the aMFC, the other eight evaluation criteria provided by the proposed method are generally smaller, especially for \(J_{2}\) and \(J_{3}\). The reason is that the low-pass filter and the reference model in the aMRC strategy should be determined empirically,  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Earthquake Record**} & \multirow{2}{*}{**Case**} & \multicolumn{8}{c}{**Evaluation Criteria**} \\  & & \(J_{1}\) & \(J_{2}\) & \(J_{3}\) & \(J_{4}\) & \(J_{5}\) & \(J_{6}\) & \(J_{7}\) & \(J_{8}\) & \(J_{9}\) \\ \hline \multirow{4}{*}{El Centro} & Case 1 & 0.42 & 1.50 & 2.16 & 4.90 & 3.80 & 4.35 & 4.37 & 2.87 & 2.87 \\  & Case 2 & 0.20 & 1.23 & 1.76 & 3.40 & 2.30 & 2.93 & 2.94 & 1.71 & 1.71 \\  & Case 3 & 0.27 & 0.97 & 1.57 & 5.23 & 3.86 & 5.15 & 5.15 & 3.57 & 3.62 \\  & Case 4 & 0.30 & 1.19 & 1.80 & 6.59 & 3.97 & 6.20 & 6.22 & 3.39 & 3.38 \\  & Case 1 & 0.29 & 1.40 & 1.41 & 3.11 & 2.17 & 2.77 & 2.78 & 1.67 & 1.66 \\  & Case 2 & 0.27 & 1.26 & 1.30 & 3.99 & 2.59 & 3.75 & 3.75 & 2.20 & 2.21 \\  & Case 3 & 0.33 & 1.41 & 1.63 & 3.77 & 2.72 & 3.77 & 3.76 & 2.49 & 2.48 \\  & Case 4 & 0.32 & 1.33 & 1.43 & 5.13 & 2.98 & 5.00 & 5.00 & 2.87 & 2.87 \\  & Case 1 & 0.19 & 1.58 & 1.75 & 3.71 & 3.19 & 3.16 & 3.17 & 2.61 & 2.60 \\ \multirow{4}{*}{Mogan Hill} & Case 2 & 0.19 & 1.48 & 1.36 & 3.55 & 2.64 & 3.05 & 3.06 & 2.02 & 2.03 \\  & Case 3 & 0.25 & 1.50 & 1.52 & 4.42 & 2.81 & 4.18 & 4.19 & 2.23 & 2.21 \\ \multirow{4}{*}{Kobe} & Case 4 & 0.16 & 1.15 & 1.42 & 5.19 & 4.49 & 4.86 & 4.87 & 4.13 & 4.11 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Mean of evaluation criteria for perturbed cases.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Earthquake Record**} & \multirow{2}{*}{**Case**} & \multicolumn{8}{c}{**Evaluation Criteria**} \\  & & \(J_{1}\) & \(J_{2}\) & \(J_{3}\) & \(J_{4}\) & \(J_{5}\) & \(J_{6}\) & \(J_{7}\) & \(J_{8}\) & \(J_{9}\) \\ \hline \multirow{4}{*}{El Centro} & Case 1 & 0.31 & 0.39 & 0.66 & 1.53 & 0.95 & 1.57 & 1.58 & 1.02 & 1.03 \\  & Case 2 & 0.22 & 0.26 & 0.49 & 0.79 & 0.45 & 0.88 & 0.88 & 0.54 & 0.53 \\  & Case 3 & 0.27 & 0.31 & 0.58 & 1.69 & 1.29 & 1.80 & 1.80 & 1.35 & 1.36 \\  & Casewhich are extremely important. In summary, the proposed method is effective and practical for use in RTHS.