EXPLICIT EQUIVALENT FORCE CONTROL METHOD BASED ON VELOCITY

This paper employs the equivalent force control (EFC) method to solve the velocity difference equation in a real-time substructure test, and uses a feedback control loop to replace the mathematical iteration to solve the nonlinear dynamic equation. Spectral radius analysis of the amplification matrix shows that the EFC combined with the explicit Newmark-β method has good numerical characteristics. Its stability limit of Ω=2 remains unchanged regardless of the system damping, because the velocity is perfectly achieved during simulation. Compared with the proposed method, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation decrease with the increase of system damping. The unconditionally stable EFC-average acceleration method even comes to be conditionally stable. If an over-damped system with a damping ratio of 1.05 is considered, the stability limit is Ω=1.45. Finally, numerical simulation of single degree of freedom structure installed with magneto-rheological (MR) damper demonstrates that the proposed method is able to track both displacement and velocity commands accurately, thus having good applicability and accuracy for velocity-sensitive structures.