Robust feedback models with structured uncertainties for human–structure interaction

Structural engineering developments have implemented new design techniques that allow the construction of large structures with lighter and high-strength elements. Structures such as grandstands, slabs and pedestrian bridges may be prone to excessive vibrations due to human activities. Traditional dynamic modeling approaches to represent the human–structure interaction (HSI) are often used to predict the dynamic behavior of the coupled system based on deterministic mass–spring–damper (MSD) mechanical components. However, these models cannot precisely represent variabilities and uncertainties in human and structural systems. In this study, three HSI robust models are developed and experimentally validated on a test structure. First, a traditional MSD coupled model is proposed where the human subsystem includes structured uncertainties in its biomechanical parameters. Then, two models are developed and synthesized from robust control theory using H∞ and μ-synthesis, implementing structured uncertainties in the frequency and damping ratio of the plant to capture the intra- and inter-variability in the biomechanical parameters. The results demonstrate that the developed robust HSI models provide effective and reliable approaches to predict the range of probable responses of the coupled human–structure system for different occupants.