Equivalent Force Control Method for Real-time Testing of Nonlinear Structures

The equivalent force control (EFC) method replaces numerical iteration with a feedback control strategy to solve the nonlinear equations of motion using an implicit integration method for real-time substructure tests (RSTs). The method, however, requires the conversion of the equivalent forces to structural displacements using a conversion matrix. It is demonstrated in this article that with the use of a proportional-integral (PI) controller for the EFC, one has the convenience of choosing the initial stiffness matrix of a structure to construct the conversion matrix regardless of the properties and degree of nonlinearity of the system. The stability condition of the EFC using a PI controller has been derived with the Routh stability criterion. Methods for designing and tuning a PI controller for RST using EFC have been presented and excellent system performance has been obtained from numerical simulations and actual tests. The simulation results showed that the EFC method using a PI controller and the initial stiffness matrix to construct the conversion matrix can deliver excellent performance even for structural systems that develop a severe strain-softening behavior. Its superiority over iteration method proposed by Jung et al. [2007] Jung, R. Y., Shing, P. B., Stauffer, E. and Thoen, B. 2007. Performance of a real-time pseudo dynamic test system considering nonlinear structural response. Earthquake Engineering and Structural Dynamics, 36: 1785–1809.  [Google Scholar] was demonstrated through numerical simulation. This provides an efficient means to test nonlinear multiple-degrees-of-freedom structures.