To improve the experimental accuracy and stability of shaking table substructure testing (STST), an explicit central difference method (CDM) and a three-variable control method (TVCM) with velocity positive feedback (VPF) are proposed in this study. First, the explicit CDM is presented for obtaining an improved control accuracy of the boundary conditions between the numerical and experimental substructures of STST. Compared with the traditional CDM, the proposed method can provide explicit control targets for displacement, velocity, and acceleration. Furthermore, a TVCM-VPF is proposed to improve the control stability and accuracy for loading the explicit control targets of displacement, velocity, and acceleration. The effectiveness of the proposed methods is validated by experiments on a three-story frame structure with a tuned liquid damper loaded on an old shaking table originally designed with the traditional displacement control mode. The experimental results show that the proposed explicit CDM works well, and the response rate and control accuracy of the shaking table are significantly improved with the contribution of the TVCM-VPF compared with those of the traditional proportional integral derivative (PID) controller. This indicates the advantage of the proposed TVCM-VPF over the traditional PID for STST. A comparison between the traditional shaking table test and STST shows that when the latter is based on the TVCM-VPF, it exhibits an excellent performance in terms of the stability and accuracy of displacement and an acceptable performance in terms of the acceleration accuracy.

中文翻译：

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基于带速度正反馈三变量控制方法的振动台子结构测试

为了提高振动台子结构测试（STST）的实验准确性和稳定性，本文提出了显式中心差分法（CDM）和带速度正反馈（VPF）的三变量控制法（TVCM）。首先，提出了显式CDM，以提高STST的数值和实验子结构之间的边界条件的控制精度。与传统的CDM相比，该方法可以为位移，速度和加速度提供明确的控制目标。此外，提出了TVCM-VPF以提高控制稳定性和准确性，以加载位移，速度和加速度等明确的控制目标。通过对三层框架结构进行试验，验证了所提方法的有效性，该框架结构的调谐液体阻尼器装在原来设计为传统位移控制模式的旧振动台上。实验结果表明，与传统的比例积分微分（PID）控制器相比，TVCM-VPF的贡献显着提高了所提出的显式CDM效果，显着提高了振动台的响应速度和控制精度。这表明所提出的TVCM-VPF优于STST的传统PID。传统摇床测试与STST的比较表明，当STST基于TVCM-VPF时，