Mathematical Equivalence Between Dynamic Substructuring and Feedback Control Theory

Abstract

This paper presents a reformulation of dynamic substructuring for vibrating structural systems as a feedback control problem. Frequency based substructuring (FBS) using admittance coupling of two substructures is shown to be mathematically equivalent to a feedback control system with the primary substructure acting as the controller and the secondary substructure acting as the plant. This formulation can be used to perform time-domain simulations of dynamic substructuring problems using MATLAB’s Simulink environment, whereby the primary substructure can be modeled by three possible approaches: (1) Laplace domain transfer functions, (2) state-space models, or (3) finite impulse response functions. The secondary substructure can be represented by a variety of Simulink blocks including nonlinear elements. By inserting an actuator transfer system between the two substructures, this formulation also provides the basis for real-time hybrid substructuring (RTHS) for coupling numerical and physical substructures as a cyber-physical system similar to hardware-in-the-loop testing. In typical RTHS the numerical substructure acts as the controller and the actuator with physical substructure acts as the plant. This feedback control formulation will lead to further advancements for both dynamic substructuring and RTHS by adapting methods from classical and modern feedback control theory.