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Control of a Non-uniform Flexible Beam: Identification of First Two Modes

Phuong-Tung Pham, Gyoung-Hahn Kim, Quoc Chi Nguyen*, and Keum-Shik Hong
International Journal of Control, Automation, and Systems, vol. 19, no. 11, pp.3698-3707, 2021

Abstract : This paper presents an experimental study implementing the input shaping control of the first two modes of the vibration of a non-uniform flexible cantilever beam having a translating base. Examples of a moving cantilever beam appear in many industrial systems. Vibration suppression of the beam has important implications for improving the effectiveness of such systems. The equations of motion of the cantilever beam, including the moving base, are developed using the extended Hamilton principle. The partial differential equation representing the beam’s dynamics is then transformed into a finite-dimensional model using the Galerkin method. Accordingly, the modal parameter identification procedure is established based on experimental modal analysis. Under the estimated modal parameters, including the natural frequency and damping ratio, single- and two-mode input shaping controllers of three different types (zero vibration, zero vibration derivative, and zero vibration derivative-derivative) are designed for vibration suppression of the beam. Experimental results are discussed, reporting that the two-mode shaper’s vibration suppression was superior to the single-mode shaper. In contrast, the two-mode shaper’s settling time has slightly increased compared to that of the single-mode shaper.

Keyword : "Experimental modal analysis, flexible beam, input shaping control, modal parameter identification, non-uniform beam, vibration suppression."

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