Velocity plus displacement equivalent force control for real-time substructure testing

This paper employs a velocity plus displacement (V+D)-based equivalent force control (EFC) method to solve the velocity/displacement difference equation in a real-time substructure test. This method uses type 2 feedback control loops to replace mathematical iteration to solve the nonlinear dynamic equation. A spectral radius analysis of the amplification matrix shows that the type 2 EFC-explicit, Newmark-β method has beneficial numerical characteristics for this method. Its stability limit of Ω = 2 remains unchanged regardless of the system damping because the velocity is achieved with very high accuracy during simulation. In contrast, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation are shown to decrease with an increase in system damping. In fact, the EFC-average acceleration method is shown to change from unconditionally stable to conditionally stable. We also show that if an over-damped system with a damping ratio of 1.05 is considered, the stability limit is reduced to Ω =1.45. Finally, the results from an experiment with a single-degree-of-freedom structure installed with a magneto-rheological (MR) damper are presented. The results demonstrate that the proposed method is able to follow both displacement and velocity commands with moderate accuracy, resulting in improved test performance and accuracy for structures that are sensitive to both velocity and displacement inputs. Although the findings of the study are promising, additional test data and several further improvements will be required to draw general conclusions.