Multidimensional boundary control for real-time hybrid simulation: A complexity-driven taxonomy

By coupling physical with numerical substructures in real time, RTHS provides a comprehensive approach to full-scale structural experimentation. However, its practical implementation is constrained by time-delay errors, algorithmic stability challenges, and boundary coordination issues. While recent research has focused on algorithm-specific improvements—such as numerical integration and delay compensation—there remains a lack of standardized metrics to quantify system complexity. Existing hardware-based classification schemes inadequately capture the fundamental relationships between testing objectives and control parameters, thereby limiting the scalability and benchmarking of RTHS systems for complex structural applications. This study introduces a novel three-tiered classification framework (L1–L3) based on boundary control dimensionality, moving beyond traditional hardware-centric paradigms. By explicitly addressing interactions at external boundaries (experimental substructure–environment) and internal boundaries (experimental–numerical interfaces), the framework enables the establishment of quantitative correlations between system complexity and dynamic performance. Analysis of representative case studies and benchmark problems demonstrates significant variation in complexity levels, control strategies, and evaluation metrics across RTHS configurations, supporting the development of a unified and scalable framework applicable from single-DOF validation to multi-DOF collaborative control systems.