Robust constrained control for vibration suppression of mismatched systems

摘要

Almost all undesirable vibrations in technical systems are caused by unknown or uncertain excitations. In cases where these vibrations need to be actively attenuated it is very often not possible to equip the system for that purpose with enough actuators. Also, in general, necessary control actions via these actuators cannot be employed over a desired range because of their boundedness. We propose a control scheme that allows for these control deficiencies no matter how small the bounds of the controllers are and how many actuators are implemented. The scheme is based on Lyapunov stability theory; it relates to robustness vis-à-vis unknown but bounded excitations. In addition to the controller design via Lyapunov theory, a stability analysis is carried out to compute the ball of ultimate boundedness for a certain class of Lyapunov functions. To demonstrate the effectiveness of the control we consider a mechanical system with 2 degrees of freedom where the masses are elastically coupled. The unknown excitation acts on one of these masses. Two controllers are compared particularly with respect to attenuation of vibrations.