Widely used in earthquake engineering, Hybrid testing is promoted in various domains such as wind engineering, coastal structures and fluid-structure interaction. It also begins to be applied to fire engineering (Hybrid Fire Testing or HFT) for coupling fire tests and numerical simulations. However, HFT is still in its infancy. Yet, some tests have been performed and some algorithms have been developed. Recently, Mergny et al. [ 1 ] proposed a framework based on linear control system theory for a displacement control procedure. It uses proportional integral (PI) controller and allows performing HFT with non-linear substructures. The method was validated numerically but no analysis was provided about stability. This paper aims to describe the effects on stability of the main sources of errors in the case of HFT using PI control, namely delays, experimental errors and estimation of the stiffness of the physical substructure that is essential for most of the methodologies that have been developed so far. The research shows first through the equations of a single degree of freedom (SDOF) system that the estimation of the stiffness is a potential source of instability and affects directly the design of the PI controller. A simplified model for MDOF system was developed. Then, the research highlights that the effect of the experimental errors can involve a modification of the apparent mechanical response of the specimen and causes instability. However, this effect can be greatly limited. Finally, the delay is not a source of instability. A virtual hybrid test is performed in a steel frame and shows that the simplified model is a satisfying approximation and that described effects of the estimation of the stiffness established for a SDOF system can be observed for a complex system.

中文翻译：

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使用 PI 控制进行混合火灾测试的稳定性

混合测试广泛应用于地震工程，在风工程、海岸结构和流固耦合等各个领域得到推广。它还开始应用于消防工程（混合火灾测试或 HFT），以将火灾测试和数值模拟相结合。然而，高频交易仍处于起步阶段。然而，已经进行了一些测试并开发了一些算法。最近，Mergny 等人。[1] 提出了一个基于线性控制系统理论的位移控制程序框架。它使用比例积分 (PI) 控制器并允许使用非线性子结构执行 HFT。该方法经过数值验证，但未提供稳定性分析。本文旨在描述在使用 PI 控制的 HFT 情况下，主要误差源对稳定性的影响，即延迟、物理子结构刚度的实验误差和估计，这对于迄今为止开发的大多数方法至关重要。该研究首先通过单自由度 (SDOF) 系统的方程表明，刚度的估计是潜在的不稳定源，并直接影响 PI 控制器的设计。为 MDOF 系统开发了一个简化模型。然后，研究强调，实验误差的影响可能涉及修改试样的表观机械响应并导致不稳定。但是，这种影响可能会受到很大限制。最后，延迟不是不稳定的根源。