Control-Based Continuation of a Hybrid Numerical/Physical Substructured System

Abstract

Control-based continuation is a relatively new technique for tracking the orbits and bifurcations in a physical experiment under parameter variations. It leverages ideas from the dynamical systems community, particularly from numerical continuation, and combines them with feedback control. A related idea is that of hybrid testing, whereby a physical system is substructured into two parts: one physical and one numerical. The two substructures are connected in real-time via actuators and sensors to form a closed system. This methodology enables the testing of large-scale structures without needing to build everything. In this paper, we will present initial results from combining these two methodologies and we show how the nonlinear dynamics and bifurcations of a particular coupled system can be explored systematically even though a model for the full system is not available. The principal benefit of combining these two methods is that parameter studies become much more straightforward—the numerical model contains numerous parameters that can be adjusted programmatically allowing for an extensive investigation of the full system.