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Research Papers

Multimode Modified Positive Position Feedback to Control a Collocated Structure

[+] Author and Article Information
Ehsan Omidi

Department of Mechanical Engineering,
The University of Alabama,
Box 870276,
Tuscaloosa, AL 35487
e-mail: eomidi@crimson.ua.edu

S. Nima Mahmoodi

Department of Mechanical Engineering,
The University of Alabama,
Box 870276,
Tuscaloosa, AL 35487
e-mail: nmahmoodi@eng.ua.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 2, 2013; final manuscript received November 5, 2014; published online December 10, 2014. Assoc. Editor: May-Win L. Thein.

J. Dyn. Sys., Meas., Control 137(5), 051003 (May 01, 2015) (7 pages) Paper No: DS-13-1182; doi: 10.1115/1.4029030 History: Received May 02, 2013; Revised November 05, 2014; Online December 10, 2014

Multimode modified positive position feedback (MMPPF) is proposed to suppress vibrations at multi-resonance frequencies in flexible collocated structures. Typically, flexible structures have large numbers of active modes in low frequency bandwidths, which make them susceptible to multi-frequency resonant vibrations. Hence, it is essential for the controller to have effective suppression on all participating modes. The MMPPF controller consists of a first- and a second-order compensator for each mode, as they are all set parallel for all active modes. Because of suppression performance sensitivity to controller gain parameters, proper gain selection is essential. Here, the linear quadratic regulator (LQR) approach and a proposed method called M-norm are used for gain optimization of the MMPPF controller. The optimized controller is then evaluated experimentally using a cantilever beam, enhanced by a piezoelectric actuator. According to the obtained results, the MMPPF controller reduces vibration amplitudes to the expected lower level, under both LQR and M-norm optimization methods. In some cases, vibration amplitude at the place of piezo-actuator is reduced to even less than the vibration amplitude level of the disturbance input at clamped end.

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Figures

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Fig. 1

Schematic view of the enhanced flexible structure

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Fig. 2

Block diagram of closed-loop MMPPF collocated system

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Fig. 3

Root locus plot of the resonant system with MMPPF controller, “x” denotes poles and “o” denotes zeros: (a) without the feed-through term and (b) with the feed-through term

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Fig. 4

Frequency analysis of the influence of the feed-through term

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Fig. 5

Experimental test setup

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Fig. 6

Response of the cantilever beam to a chirp signal

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Fig. 7

FFT plot of the vibration disturbance amplitude at the base

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Fig. 8

FFT plot of the vibration amplitude of the uncontrolled system

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Fig. 9

FFT plot of vibration amplitude for LQR-optimized MMPPF controller

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Fig. 10

FFT plot of vibration amplitude for M-norm optimized MMPPF controller

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Fig. 11

Input voltage to the piezoelectric actuator for vibration suppression: (a) MMPPF-LQR optimized approach and (b) MMPFF- M-norm approach

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