Numerical models and stability analysis of control-based methods for nonlinear vibration testing

Control-based methods have been proposed over the last two decades as robust means to perform nonlinear vibration testing. These approaches leverage feedback control to stabilize all equilibria and require limited information about the system under test to be effective. However, their control parameters are often tuned through trial and error and systematic tuning methods are lacking in the literature. The purpose of this work is to build accurate numerical models of these control-based methods to evaluate their performance and stability. Such models can clearly indicate the stability boundaries of different equilibria, and can provide valuable insight into potential destabilizing mechanisms. Governing differential equations are derived for CBC and PLL closed-loop systems. They are then solved with the harmonic balance method, and a stability analysis based on Hill’s method is also developed. The models are assessed with a Duffing oscillator, and the discrepancies between different filtering and control-based methods are highlighted.