1 Department of Mechanical Engineering, Technical University of Denmark2 Solid Mechanics, Department of Mechanical Engineering, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark5 IT Service, Administration, Technical University of Denmark6 Dynamical systems, Department of Mathematics, Technical University of Denmark
We investigate a non-invasive, locally stabilizing control scheme necessary for an experimental bifurcation analysis. Our test-rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators, and serves as a prototype for electromagnetic bearings and other machinery with build-in actuators. We propose a sequence of experiments that allows one to choose optimal control-gains, filter parameters and settings for a continuation method without a priori study of a model. Depending on the algorithm for estimating the Jacobian required by Newton's method we find two almost disjoint sets of suitable control parameters. Control-based continuation succeeds reliably in producing the full bifurcation diagram including both stable and unstable equilibrium states for an appropriately tuned controller.
Journal of Sound and Vibration, 2013, Vol 332, Issue 22