Proper orthogonal decomposition-based control of transverse beam vibrations: experimental implementation

Linear quadratic Gaussian (LQG) compensator control of transverse vibrations was implemented on an aluminum cantilevered beam in a "smart structure" paradigm. The beam was mounted with two self-sensing self-actuating piezoceramic patches. The Euler-Bernoulli beam equation was discretized via a Galerkin type approximation (referred to as the full-order model). To reduce the size of the resulting finite-dimensional approximating system, the proper orthogonal decomposition (POD) was employed as a reduced basis method. A reduction of dimension from 34 to 2 was obtained through the model reduction technique. Feedback control based on the reduced order system was implemented in real time using a dSpace DS1103 control system. Experimental results indicate that POD-based control achieves comparable control attenuation with full-order model-based control.

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