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Vibration control of a flexible beam with integrated actuators and sensors

The use of system identification to determine linear Auto Regressive Moving Average eXogenous inputs (ARMAX) models for smart structures has been scarcely reported in the literature. However, these models can be used as a basis for a linear discrete-time controller design. This work presents a smart structure vibration control scheme developed using an ARMAX model of the structure and compares its performance to an empirically designed velocity feedback controller. The smart structure is comprised of piezoceramic (such as PZT) actuators and strain gauge sensors attached to a cantilever beam and interfaced to a PC, which provides the control software platform. System identification is carried out in three phases: data collection, model characterization and parameter estimation. Input-output data are collected by stimulating the piezoactuators with a bipolar square wave signal and monitoring the strain gauge response. The model is characterized with second-order plant dynamics and a least-squares estimation algorithm calculates the model parameters. The controller is designed using pole placement to achieve the desired closed-loop response. The ARMAX model is used to calculate the pole placement controllers by solution of the Diophantine equation for the prescribed closed-loop pole positions. Results show that the pole placement controller can match the performance of a velocity feedback controller and maintain this performance when the sampling rate is greatly reduced.