Nonlinear substructuring control for parameter changes in multi-degree-of-freedom systems

Nonlinear substructuring control (NLSC) was developed to render linear substructuring control (LSC), particularly used in dynamically substructured system (DSS), more robust against nonlinearities. This NLSC was examined both numerically and experimentally via substructure tests of nonlinear single-degree-of-freedom (SDOF) systems demonstrating a base-isolated structure. This study examines the application of NLSC to nonlinear multi-degree-of-freedom (MDOF) systems. To begin, NLSC for nonlinear MDOF systems is discussed, and its stability with respect to a pure time delay, which is a critical element in many substructure tests, is analysed by applying the Nyquist criterion. Next, its controller design and stability analysis are numerically and experimentally examined via substructure tests. In the examination, a nonlinear 4DOF system subjected to a ground motion is selected as an emulated system for substructure tests. Based on this emulated system, three types of substructure tests are numerically simulated; the first simulation examines the ground floor as the physical substructure, the second one examines the ground and first floors, and the third one examines only the first floor. Finally, by using a test rig consisting of an actuator and a rubber bearing, a series of substructure experiments targeting the ground floor as the physical substructure was implemented. In both examinations, the design of the NLSC controller has established its efficiency in substructure tests of nonlinear MDOF systems. A stability analysis with respect to pure time delays has been also found useful for predicting instability conditions of substructure tests with nonlinear MDOF systems.