Filtered dynamic inversion for vibration control of structures with uncertainty

This paper presents a controller for uncertain structures that are minimum phase and potentially subject to unknown-and-unmeasured disturbances. The controller combines dynamic inversion with a low-pass filter to yield a single-parameter high-gain-stabilizing controller. Filtered dynamic inversion requires limited model information, is independent of system order, requires only output feedback, and makes the average power of the command following error arbitrarily small despite the presence of unknown disturbances. The controller is applied to structures modeled by finite-dimensional vector second-order systems with unknown and arbitrarily large order. We also present an adaptive filtereddynamic- inversion controller, which uses a high-gain adaptive law to increase the controller parameter until the desired performance is achieved. Finally, the controller is extended to vector second-order nonlinear systems, in which case full-state feedback may be required. Examples are given to demonstrate the application and performance of the controller.