Research Doctorate - Doctor of Philosophy (PhD) / Mechanical systems experience undesirable vibration in response to environmental and operational forces. Slight vibrations can limit the accuracy of sensitive instruments or cause error in micro- and nano-manufacturing processes. Larger vibrations, as experienced by load bearing structures, can cause fatigue and contribute to mechanical failure. The suppression of vibration is a necessity in many scientific and engineering applications. Piezoelectric and electromagnetic transducers have been employed in countless applications as sensors, actuators, or both. In cases where traditional passive mechanical vibration control is inadequate, piezoelectric and electromagnetic actuators have been used within feedback control systems to suppress vibration. A counter-active force is applied in response to a measured vibration. In this work, a new approach to the control of mechanical vibration is introduced. By presenting an appropriately designed electrical impedance to the terminals of a piezoelectric or electromagnetic transducer, vibration in the host structure can be suppressed. Standard LQG, H2, and H∞ synthesis techniques are employed to facilitate the design of optimal shunt impedances. No feedback sensor or auxiliary transducer is required. Vibration control problems are typically based on the minimization of displacement or velocity at a single point. For spatially distributed systems, such as aircraft wings, any single point may not suitably represent the overall structural vibration. Spatial system identification is introduced as a method for procuring global models of flexible structures. Spatial models can be used to properly specify the performance objective of an active vibration control system. Experimental results are presented throughout to clarify and validate the concepts presented.

This study presented the design and implementation of a spatial Hinf controller to suppress the free and forced vibrations of a cantilevered smart beam. The smart beam consists of a passive aluminum beam with surface bonded PZT (Lead-Zirconate-Titanate) patches. In this study, the PZT patches were used as the actuators and a laser displacement sensor was used as the sensor. In the first part of the study, the modeling of the smart beam by the assumed-modes method was conducted. The model correction technique was applied to include the effect of out-of-range modes on the dynamics of the system. Later, spatial system identification work was performed in order to clarify the spatial characteristics of the smart beam. In the second part of the study, a spatial Hinf controller was designed for suppressing the first two flexural vibrations of the smart beam. The efficiency of the controller was verified both by simulations and experimental implementation. As a final step, the comparison of the spatial and pointwise Hinf controllers was employed. A pointwise Hinf controller was designed and experimentally implemented. The efficiency of the both controllers was compared by simulations.