Equivalent force control method for generalized real-time substructure testing with implicit integration

This paper presents a new method, called the equivalent force control method, for solving the nonlinear equations of motion in a real-time substructure test using an implicit time integration algorithm. The method replaces the numerical iteration in implicit integration with a force-feedback control loop, while displacement control is retained to control the motion of an actuator. The method is formulated in such a way that it represents a unified approach that also encompasses the effective force test method. The accuracy and effectiveness of the method have been demonstrated with numerical simulations of real-time substructure tests with physical substructures represented by spring and damper elements, respectively. The method has also been validated with actual tests in which a Magnetorheological damper was used as the physical substructure.