Equivalent Force Control Method For Real-time Substructure Testing

Modern structures become larger and more complex than before. For these structures, experimental tests with the whole structural models would be difficult and expensive. A possible and economic way for this would be performing substructure tests with large or full scale if unknown or nonlinear properties of the structures are concentrated on part of them. Real-time loading is required for the tests of structures those include highly velocity- and/or acceleration-dependant components. Real-time substructure testing (RSTing) was proposed to solve these problems by performing real-time tests on key elements of the structure with a full or large scale and simulating the others with numerical model. For the tests of modern structures with multi-degree-of-freedom (MDOF), an integration method with unconditional stability is highly desirable. Implicit methods are normally unconditionally stable, while they need time-consuming numerical iteration to solve the nonlinear equations of motion in RST. In stead of numerical iteration, equivalent force control method (EFCM) uses force feedback control strategy to solve the equations. With the EFCM, the implicit integration methods are successfully applied for RST. Therefore, The RST with EFCM shows great potentials on disclosing the dynamic behavior of modern structures.This paper investigates several key issues concerning the performance of the EFCM for RSTs of modern structures, and evaluates the seismic performance of an offshore platform and masonry-infilled frame structure with the EFCM. The main research work and conclusions are as following:1. The effectiveness of the EFCM is verified by RSTs of linear elastic structures. The EFCM is introduced, the proportional-derivative (PD) equivalent force controller is designed, and the pseudo-dynamic tests and RSTs with spring specimen are performed. It is shown that the equivalent force responses subjected to step equivalent force commands have zero steady-state error for linear elastic structures, and the feedback control loop is stable since all parameters in the system are positive. It is concluded from pseudo-dynamic and RSTs that the EFCM may exhibit excellent performance in terms of stability and accuracy if the equivalent force controller is properly designed.2. The overshooting problem which may arise for MDOF structures due to the relatively quick response feedback from the numerical substructure in the closed-loop EFC is investigated, and the EFCM is applied to evaluate the seismic performance of an offshore platform. The overshooting of equivalent force response is analyzed and this problem may be resolved by reducing either the EFC gains or the increment size of the equivalent force command. The effectiveness of the proposed methods is verified by numerical simulations. It is shown from the RSTs of offshore platform with the EFCM that the overshooting problem is successfully resolved by reducing the EFC gains and the linear interpolation of the equivalent force commands, and accurate results are obtained by the EFCM. Experimental results also show that the displacement responses of the offshore platform can be effectively controlled with the magnetorheological (MR) fluid dampers, while the acceleration responses can only affected slightly.3. The determination of the force-displacement conversion factor (a key component of EFC) for nonlinear structures using EFCM with a PD equivalent force controller is investigated. The method for choosing the force-displacement conversion factor is proposed either for specimens with neglect able inertia and damping force or for specimens with considerable inertia and damping force, and its effectiveness is validated through numerical simulations. The analysis conducted here shows that the force-displacement conversion factor is largely governed by the properties of the numerical substructure and the numerical scheme when a small integration time interval is used, such as (ωSΔt ) 24. Otherwise, the factor has to be determined with the secant stiffness of the specimen and of the numerical substructure if a PD controller is used for EFC.4. The EFCM with a proportional-integral (PI) equivalent force controller is investigated. It is demonstrated in this paper that with the use of a 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 is derived with the Routh stability criterion. The steady-state error is analyzed based on Laplace's Terminal-Value Theorem. Methods for designing and tuning a PI controller for RST using EFC are presented, and the effectiveness of the EFCM is verified with numerical simulations and actual tests of structures with spring and damper specimen, respectively. Analytical results show that with the use of initial stiffness matrix to construct the conversion matrix, the stable limit is K I≈2ξAωA (1 + KP), and the equivalent force responses subjected to step commands have zero steady-state error. The simulation results also show 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. is also demonstrated through numerical simulation.5. The seismic performance of a masonry-infilled frame structure is numerically investigated. The total approach and dynamic substructure approach, both with combined force-displacement control and considerable specimen mass, RST with the EFCM are introduced. The equivalent force interpolation function and the restoring force correction method for the specimen are proposed. Numerical simulation results show that the EFCM with the second-order polynomial interpolation and the linear restoring force correction can exhibit excellent accuracy. Numerical results also show that the stability of the EFCM is better than the central difference method.