Synthesis and implementation of sensor-less shunt controllers for piezoelectric and electromagnetic vibration control

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.