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Research Papers

Modeling and Control of Torsional Beam Vibrations: A Wave-Based Approach

[+] Author and Article Information
M. Moallem

Mechatronics Systems Engineering,  Simon Fraser University Surrey, 250–13450 102nd Avenue, Surrey BC V3T 0A3, Canada

J. Vib. Acoust 130(2), 021014 (Mar 21, 2008) (5 pages) doi:10.1115/1.2776338 History: Received August 28, 2006; Revised July 26, 2007; Published March 21, 2008

This paper presents a wave-based modeling and control approach for suppressing torsional vibrations of an elastic shaft driven by a motor at one end and an inertial load at the other end. A two-port network model representing the dynamics of torsional displacements is obtained starting from the partial differential equations governing a shaft in torsion. By incorporating appropriate boundary conditions, the infinite dimensional transfer function of the system is obtained. Furthermore, the system is represented by delay elements that can be used for simulation purposes. An inversion-based controller that can be used to suppress vibrations while rotating the shaft according to a specific trajectory is then developed. The performance of the controller is further studied using numerical simulations.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Shaft with a circular cross section under torsion

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Figure 2

Two-port representation in the time domain: El(l,t−T)=Ω(l,t−T)−ZcΓ(l,t−T), Eo(0,t−T)=Ω(0,t−T)+ZcΓ(0,t−T)

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Figure 3

Two-port representation of a shaft with a torque input and an inertial load impedance

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Figure 4

Pole and zero locations obtained using Eqs. 24,25, respectively

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Figure 5

Simulation results for a rigid-body based conventional controller

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Figure 6

Simulation results for the proposed controller

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