Mode localization by state feedback control quasi-perturbation of a multi-degree-of-freedom system

Abstract

This thesis describes attempts to produce mode localization in a multi-degree-of-freedom experimental test system through state feedback control of the system. Mode localization is a phenomenon that appears as the suppression of vibration propagation in mechanical systems through containment of vibration at its source. Previous research has involved the appearance of mode localization in periodic systems, or systems with multiple identical units coupled to each other in like fashion. Small perturbations in the properties of the units, weak coupling between the units, and minimal damping can combine to produce the phenomenon in periodic systems. Feedback control, however, makes mode localization a possibility in any multi-degree-of-freedom system, periodic or not. This work examines the viability of using mode localization as a means of vibration control in multi-degree-of-freedom systems. The research was centered around an experimental test system consisting of five pendula coupled together with torsional springs. One may configure the test rig as an ordered periodic system or as a disordered one with localized modes. Development of the equations of motion for the system led to calculation of the system's eigenproperties. Experimental tests for determining the eigenproperties verified the equations of motion and demonstrated the presence of localized modes The goal of the research is to apply control efforts to the ordered periodic system so that its eigenproperties match those of the disordered system with localized modes; in other words, the controlled periodic system should behave like the disordered system. The control efforts are provided by three dc motors which, through gear trains, provide torque inputs to three of the pendula in the system. Experimental work revealed, however, that Coulomb friction in the control actuators and unwanted structural flexibility in the pendulum system detrimentally dominated the dynamics of the controlled system. Efforts to alleviate the effects of the friction and flexibility have proven unsuccessful to date, warranting continued work to evaluate the practicality of vibration control through mode localization.