Novel multi-degree-of-freedom force–displacement mixed control framework for low loading rate substructure hybrid testing

In substructure hybrid tests, imposing realistic multi-degree-of-freedom (MDOF) displacement and force boundary conditions on a specimen involves controlling several actuators to emulate the MDOF boundary conditions of the experimental substructure. This setup presents significant challenges for decoupling control in MDOF systems. Due to the typically high stiffness of the specimen in the axial direction, force control is preferred over displacement control, which has limited accuracy in this direction. Typically, force control in the axial direction is combined with simultaneous displacement control in the softer direction, forming an MDOF force-displacement mixed control scheme. This scheme transforms force control into displacement control in the inner loop in the axial direction to ensure safe loading. The scheme involves addressing two major challenges: the nonlinear force–displacement transformation and the nonlinear coordinate transformation from the local actuator space (LAS) to the global Cartesian coordinate (GCC) system. To address these challenges, the Modified Newton–Raphson iteration integrated with proportional integral plus feed-forward (MNR-PIFF) and incremental kinematic transformation integrated with proportional integral plus feed-forward (IKT-PIFF) methods are proposed. Based on these methods, a novel MDOF force–displacement mixed control (NMFDC) framework is developed for substructure hybrid testing. A 6-DOF cyclic test simulation using the NMFDC framework was conducted to demonstrate its superiority. Furthermore, a 6-DOF cyclic test and substructure hybrid test at low loading rates were performed to validate the NMFDC framework because of the loading equipment limit. Experimental results and numerical simulations indicate that the NMFDC framework achieves swifter response with lower error levels. For applications in fast and real-time hybrid testing, dynamic loading equipment need to be used, the PIFF controller in the NMFDC framework should be replaced by adaptive time delay compensation in future developments.