A DAE Solver for Coordination of Force-Controlled Hybrid Testing

Abstract

Hybrid testing couples numerical simulation with physical experiments by enforcing compatibility and equilibrium at the interface between numerical and physical substructures. This paper presents a force-controlled hybrid-testing formulation for stiff physical substructures coupled to nonlinear numerical substructures. Displacement compatibility is imposed directly on the numerical equations of motion to form a differential-algebraic equation. The interface force is obtained using Baumgarte-stabilized Lagrange multipliers. Physical-substructure velocity and acceleration, which are not measured in pseudo-dynamic testing, are estimated from displacement feedback using cubic regression. A linear illustrative system is used to assess convergence, stability, numerical damping, and period distortion for explicit time-integration schemes. The formulation is then demonstrated experimentally by coupling a stiff axially loaded steel-bar physical substructure to a nonlinear two-degree-of-freedom numerical substructure with a Duffing-type spring. The hybrid test remains stable, reproduces the dominant simulated dynamics, and maintains displacement compatibility despite noisy camera-based displacement feedback. These results show that Baumgarte-stabilized constraint dynamics provide a practical strategy for force-controlled hybrid testing of stiff physical substructures.