中文摘要：

该文采用等效力控制（EFC）来求解在实时子结构试验中的速度差分方程，采用反馈控制取代数学迭代来求解非线性动力方程。谱半径分析表明，由于准确地模拟了速度响应，结合显式Newmark-β算法的等效力控制方法的稳定界限与系统的阻尼系数无关，在不同阻尼比下稳定界限保持为0=-2，具有良好的数值特性。而直接预测速度的中心差分法和采用线性插值模拟速度的平均加速度等效力控制方法，其稳定界限随着系统阻尼比的增大而降低，对于过阻尼结构（阻尼比大于1），原本无条件稳定的平均加速度等效力控制方法变为条件稳定：对于阻尼比为1．05的动力系统，其稳定界限为Ω=-1．45。最后，采用该文方法对安装磁流变（MR）阻尼器的单自由度结构的地震响应进行数值分析，结果表明该文方法能正确跟踪结构速度和位移命令，因而对于速度相关型结构体系，具有良好的适用性和精确性。

英文摘要：

This paper employs the equivalent force control （EFC） method to solve the velocity difference equation in a real-time substructure test, and uses a feedback control loop to replace the mathematical iteration to solve the nonlinear dynamic equation. Spectral radius analysis of the amplification matrix shows that the EFC combined with the explicit Newmark-β method has good numerical characteristics. Its stability limit of Ω=2 remains unchanged regardless of the system damping, because the velocity is perfectly achieved during simulation Compared with the proposed method, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation decrease with the increase of system damping. The unconditionally stable EFC-average acceleration method even comes to be conditionally stable. If an over-damped system with a damping ratio of 1.05 is considered, the stability limit is D=-1.45. Finally, numerical simulation of single degree of freedom structure installed with magneto-rheological （MR） damperdemonstrates that the proposed method is able to track both displacement and velocity commands accurately, thus having good applicability and accuracy for velocity-sensitive structures.