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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Mathematical Modeling and System Identification of a Piezo-actuated, Cantilever Beam with Interferometric Measurement

Journal of Vibration Testing and System Dynamics 7(4) (2023) 447--461 | DOI:10.5890/JVTSD.2023.12.004

Jordan Kochavi, Siyuan Xing

Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, San Luis

Obispo, CA, 93407, USA

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Laser interferometers are often adopted in high-precision motion control systems but seldom used for experimental vibration analysis. This is partly because their installation and mounting are invasive to dynamical systems as opposed to non-contact position sensors such as vibrometers. However, as the industry moves towards light manufacturing structures out of economical and environmental considerations, metrology systems that already utilize laser interferometry, such as profilometry in semiconductor manufacturing, may benefit from interferometer measurement for vibration analysis. This study investigates the use of laser interferometry for vibration analysis and system identification through a piezoelectrically actuated cantilever beam mounted with a retroreflector. The dynamics of the beam, which include the piezoelectric actuator and optical measurement components are modeled through the Euler-Bernoulli beam theory. This leads to a continuous system, which is then transformed into a discrete system represented in a state-space form, through the method of separation of variables. The frequency response at the retroreflector location is obtained through the Laplace transformation of the state-space form. A recursive adaptive filter following the ARMAX structure is formulated to identify the transfer function of the discrete system from its random noise excitation. The transfer function and its frequency response is analytically predicted, then compared to the simulation and experimental results from the adaptive filter. The high-precision measurement of interferometers is well-suited for applications of signal processing such as system identification.


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