This paper reports the first application of nonlinear substructuring control (NLSC) to shake table experiments in which the table dynamics is significantly affected by the specimen. Substructuring experiments using a shake table require simultaneous control of acceleration and displacement of the table because it functions as both an actuation system and a part of the substructure in the experiments. NLSC was developed as an enhanced version of linear substructuring control (LSC), the basic method for the control of dynamically substructured system. This paper first describes the formulation of substructures for shake table experiments using a multiple-degree-of-freedom structure and NLSC design for the substructures. The stability analysis of NLSC, which has three controllers, becomes much more complicated, more frequently showing conditional stability than is observed in conventional experiments. To assess various conditionally stable systems, this paper proposes an equivalent approach that can systematically count encirclements of the critical point in Nyquist plots. In the stability analysis using the proposed approach, NLSC is more robust against parameter variations in the substructures than LSC. In addition, the error feedback controller in both LSC and NLSC enhances the robustness against the variations. This study numerically and experimentally examined control performances for shake table substructuring experiments involving nonlinear characteristics. In the examinations, NLSC achieved the expected displacement and acceleration control with stability and reasonable accuracy, whereas LSC could not. The error feedback controller design of NLSC was found to be essential for performing shake table substructuring experiments with severe nonlinear characteristics.

中文翻译：

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振动台子结构实验中加速度和位移同时控制的非线性子结构控制

本文报告了非线性子结构控制 (NLSC) 在振动台实验中的首次应用，其中振动台的动力学受到试样的显着影响。使用振动台的子结构实验需要同时控制振动台的加速度和位移，因为它在实验中既作为驱动系统又作为子结构的一部分。NLSC 是作为线性子结构控制 (LSC) 的增强版本而开发的，它是动态子结构系统控制的基本方法。本文首先描述了使用多自由度结构和子结构的 NLSC 设计的振动台实验子结构的公式化。具有三个控制器的 NLSC 的稳定性分析变得更加复杂，比在常规实验中观察到的更频繁地显示条件稳定性。为了评估各种条件稳定系统，本文提出了一种等效方法，可以系统地计算奈奎斯特图中临界点的包围圈数。在使用所提出方法的稳定性分析中，NLSC 比 LSC 更能抵抗子结构中的参数变化。此外，LSC 和 NLSC 中的误差反馈控制器增强了对变化的鲁棒性。本研究通过数值和实验检验了涉及非线性特性的振动台子结构实验的控制性能。在考试中，NLSC 实现了预期的位移和加速度控制，稳定且精度合理，而 LSC 则不能。