## 5 Conclusions  
An explicit CDM and TVCM-VPF were proposed to improve the experimental accuracy and stability of STST. The effectiveness of the proposed method was validated by performing the STST on a three-story frame structure with TLD. The main conclusions are as follows:  
An explicit CDM for STST based on the CDM for dynamic RTST was proposed to improve the simulation accuracy of boundary conditions between the NS and ES. The proposed CDM provides explicit loading targets for the servo-hydraulic actuators in terms of displacement, velocity, and acceleration, and hence, an improved control accuracy of the boundary conditions is expected to be realized.  
The TVCM-VPF was proposed for the STST to achieve high stability and accuracy control of the desired displacement, velocity, and acceleration targets. Compared with the traditional PID control method, the proposed TVCM-VPF can achieve an improved control performance in terms of the stability and response rate owing to the contribution of the positive velocity feedback. This indicates that the TVCM-VPF can be effectively used for STSTs.  
Experiments on a three-story frame structure with a TLD were conducted to validate the effectiveness of the proposed methods for STST. Compared with the traditional PID control method, the response rate and control accuracy of the shaking table were significantly improved with the contribution of the TVCM-VPF. The STST results indicated that the accuracy of the acceleration and displacement waveform reproduction under TVCM were significantly improved compared with that of the PID control. To further validate the effectiveness of the proposed method, a comparison was performed between the STST based on the TVCM-VPF and the conventional full structure STT. The results showed that the displacement response results of the proposed STST are very close to those of the STT. This comparison reveals that STST based on TVCM-VPF performs well in terms of accuracy and is a reliable experimental strategy for evaluating the seismic performance of civil engineering structures.  
Consequently, the proposed method has broad application prospects in the performance evaluation of dynamic systems in the fields of structural engineering, offshore platform, bridge engineering, human-structure interaction system, and the vehicle-bridge vibration system, etc.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Earthquake** & **Response** & **Amplitude Deviation (\%)** & **Correlation Coefficient (\%)** \\ \hline \multirow{2}{*}{El Centro} & Displacement & 4.48 & 97.39 \\  & Acceleration & 11.38 & 66.21 \\ \hline \multirow{2}{*}{Taft} & Displacement & 12.17 & 92.03 \\  & Acceleration & 4.82 & 65.47 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Error comparison between shaking table substructure testing (STST) and the reference shaking table test (STT).  
**Author Contributions:** Conceptualization, G.X. and B.W.; Data curation, Y.B.; Methodology, G.X. and Z.W.; Project administration, G.X. and B.W.; Validation, Y.B. and G.Y.; Writing-original draft, G.X.; Writing-review and editing, G.X. and Z.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The National Natural Science Foundation of China (Grant Nos. 51778190, 51978213) and the National Key Research and Development Program of China (Grant No. 2017 YFC0703605, 2016 YFC0701106).  
**Conflicts of Interest:** The authors declare no conflict of interest.