Robust stabilization of flexible mechanical systems under noise uncertainties and time-varying parameter perturbations

This article presents a new time domain approach to treat the active stabilization (active vibration control) problem of flexible mechanical systems under (1) mode truncation, (2) nonlinear/linear time-varying parameter perturbations, (3) noise (input noise and measurement noise), and (4) noise uncertainties. In the proposed approach, the residual model is viewed as an additive perturbation to the controlled dynamics. A new robust stability condition is derived for the flexible mechanical system that is controlled by a linear-quadratic-Gaussian (LQG)-based controller and subject to mode truncation, noise uncertainties, and nonlinear/linear time-varying parameter perturbations. The proposed new condition gives an insight into the relationship between the stability margins of the controlled and residual mode subsystems, spillover effect, and additive time-varying parameter perturbations. Finally, two examples are given to confirm the presented approach.