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Research Papers

Resonance Tracking of Continua Using Self-Sensing Actuators

[+] Author and Article Information
Dominik Kern1

Chair for Engineering Mechanics (ITM),  Karlsruhe Institute of Technology (KIT), Karlsruhe 76131, Germanykern@kit.edu

Tobias Brack

Chair for Engineering Mechanics (ITM),  Karlsruhe Institute of Technology (KIT), Karlsruhe 76131, Germanybrack@imes.mavt.ethz.ch

Wolfgang Seemann

Chair for Engineering Mechanics (ITM),  Karlsruhe Institute of Technology (KIT), Karlsruhe 76131, Germanyseemann@kit.edu

1

Corresponding author.

J. Dyn. Sys., Meas., Control 134(5), 051004 (Jun 05, 2012) (9 pages) doi:10.1115/1.4006224 History: Received April 28, 2011; Revised February 06, 2012; Published June 05, 2012; Online June 05, 2012

This paper proposes and develops an innovative method to solve the resonance tracking problem for actuator and sensor applications to obtain maximum power transmission or signal selectivity using a modified phase-locked loop (PLL). The tracking of a higher eigenfrequency is very useful in some cases, but it is more challenging than the excitation of the only eigenfrequency of a 1-DoF system. The resonances are identified through employing their characteristic phase difference. The conventional PLL was modified to track a certain phase difference without deviation. The closed loop is a nonlinear control system due to the conversion between harmonic signals and phase signals. However, a model simplification to linear elements allows the goal oriented determination of the controller parameters. The advantages of self-sensing in combination with resonance tracking are attractive for practical applications such as ultrasonic motors and compact force sensors. The conducted experiments approved the effectiveness of the resonant excitation of higher oscillation modes of continua using self-sensing actuators.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

A prestressed, clamped–clamped beam with piezoelectric transducers (MFC type) on both sides of the middle section (l1  < x < l2 )

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Figure 2

FRF for the unstressed and with Fv  = 100 N prestressed beam

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Figure 3

Bridge circuit for self-sensing assuming the electrically equivalent model of the piezoelectric material [19]

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Figure 4

Structure of the conventional PLL [23]

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Figure 5

Linear (solid line boxes) and nonlinear elements (dashed line boxes) in the closed-loop

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Figure 6

Root-locus plot of the modified PLL without mechanical system as function of KP for three values of TN  = KP /KI , the root loci of the chosen parameters are marked (crosses)

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Figure 7

The basin of attraction around the resonance frequencies (red dot) is bounded by the neighboring antiresonance frequencies (blue asterisk)

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Figure 8

Transient responses of the simplified model tracking a frequency step and the full model tracking a step of the beam’s eigenfrequency

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Figure 9

Photograph of the experimental setup

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Figure 10

Signal flow scheme of the self-sensing experiments

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Figure 11

FRF using self-sensing for the unstressed and with Fv  = 200 N prestressed beam

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Figure 12

Tracking the second eigenfrequency in conventional mode (no self-sensing) for different controller parameters

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Figure 13

Tracking the fourth eigenfrequency with self-sensing in the experiment: (a) continuously increasing the prestress; (b) step changes of the prestress (step up at t = 4 s, step down at t = 5.25 s)

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