Impedance matching for dynamic substructuring

This paper presents a new strategy for dynamic substructuring in which an actuator/shaker is not viewed as a tracking device, but rather as a dynamic system whose impedance is to match that of a virtual substructure. The strategy also decouples control design from the physical substructure. In this paper, such control design is approached from an optimization viewpoint. The main contributions are (a) single and multi-objective optimal impedance matching design of dynamic substructuring controllers using linear matrix inequalities, (b) experimental validation, particularly using a lightly damped physical substructure (which poses significant stability challenges using conventional approaches), (c) use of an electromagnetic actuator as an active mass driver to represent virtual substructures, (d) use of not only linear single and multi-degree of freedom but also nonlinear virtual substructures, and (e) two ways of applying earthquake excitation to the substructured system—by means of a shake table at the base or using an active mass driver at the top. Controllers designed using this approach are easy to implement and result in stable and accurate dynamic substructuring. Source code for control design using the impedance matching approach is included as online supplemental material with this paper.