Stability in Hybrid Fire Testing using PI control

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.