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Research Papers

Adaptive Piezoelectric Vibration Control With Synchronized Switching

[+] Author and Article Information
J. C. Collinger

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

J. A. Wickert1

Department of Mechanical Engineering, Iowa State University, Ames, IA 50011wickert@iastate.edu

L. R. Corr

 Bechtel Bettis, Inc., West Mifflin, PA 15122

Numerical values used for the model parameters in simulation are listed in Table 1.

1

Corresponding author.

J. Dyn. Sys., Meas., Control 131(4), 041006 (May 18, 2009) (8 pages) doi:10.1115/1.3117189 History: Received September 09, 2007; Revised December 18, 2008; Published May 18, 2009

An autonomous vibration controller that adapts to variations in a system’s mass, stiffness, and excitation, and that maximizes dissipation through synchronized switching is described. In the model and laboratory measurements, a cantilever beam is driven through base excitation and two piezoelectric elements are attached to the beam for vibration control purposes. The distributed-parameter model for the beam-element system is discretized by using Galerkin’s method, and time histories of the system’s response describe the controller’s attenuation characteristics. The system is piecewise linear, and a state-to-state modal analysis method is developed to simulate the coupled dynamics of the beam and piezoelectric circuit by mapping the generalized coordinates between the sets of modes for the open-switch and closed-switch configurations. In synchronized switching control, the elements are periodically switched to an external resonant shunt, and the instants of optimal switching are identified through a filtered velocity signal. The controller adaptively aligns the center frequency of a bandpass filter to the beam’s fundamental frequency through a fuzzy logic algorithm in order to maximize attenuation even with minimal a priori knowledge of the excitation or the system’s mass and stiffness parameters. In implementation, the controller is compact owing to its low inductance and computational requirement. The adaptive controller attenuates vibration over a range of excitation frequencies and is robust to variations in system parameters, thus outperforming traditional synchronized switching.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Model of a cantilever beam and attached piezoelectric elements that is subjected to base excitation

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Figure 2

Schematic of the piezoelectric elements that are switched to a resonant shunt

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Figure 3

Mapping between the open (light line type) and closed (heavy line type) switch configurations: (a) resonant response of the cantilever beam’s tip, (b) phase trajectory for the first vibration mode (f1=81 Hz), and (c) phase trajectory for the second vibration mode (f2=370 Hz). The points labeled 1–4 are the instants at which the switch opens or closes.

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Figure 4

Variation of the performance index J with respect to the bandpass filter’s center frequency

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Figure 5

Fuzzy logic membership functions that are used to quantify (a) J and (b) the change in J

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Figure 6

Schematic of the experimental test stand with block diagram implementation of adaptive synchronized switching with fuzzy logic control

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Figure 7

Beam tip response with fuzzy control implementation and excitation at its fundamental frequency: (a) simulated and (b) measured tip velocity of the beam with control (light) and without (dark), (c) simulated (-○-) and measured ( ∗) evolution of the performance index, and (d) simulated (-○-) and measured ( ∗) evolution of the filter’s center frequency

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Figure 8

Beam tip response with fuzzy control implementation and suboptimal placement of the filter’s initial condition (f0=56 Hz): (a) simulated and (b) measured tip velocity of the beam with control (light) and without (dark), (c) simulated (-○-) and measured ( ∗) evolution of the performance index, and (d) simulated (-○-) and measured ( ∗) evolution of the filter’s center frequency

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Figure 9

Beam tip response with fuzzy control implementation and suboptimal placement of the filter’s initial condition (f0=112 Hz): (a) simulated and (b) measured tip velocity of the beam with control (light) and without (dark), (c) simulated (-○-) and measured ( ∗) evolution of the performance index, and (d) simulated (-○-) and measured ( ∗) evolution of the filter’s center frequency

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Figure 10

Beam tip response with fuzzy control implementation and on-line filter adaptation to impose stepwise changes 81 Hz–71 Hz–81 Hz in the structure’s fundamental frequency: (a) simulated and (b) measured tip velocity of the beam with control (light) and without (dark), (c) simulated (-○-) and measured ( ∗) evolution of the performance index, and (d) simulated (-○-) and measured ( ∗) evolution of the filter’s center frequency

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