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Research Papers

Building Vibration Control by Active Mass Damper With Delayed Acceleration Feedback: Multi-Objective Optimal Design and Experimental Validation

[+] Author and Article Information
Yuan-Guang Zheng

School of Mathematics and Information Science,
Nanchang Hangkong University,
Nanchang 330063, China

Jing-Wen Huang

College of Information Science and Technology,
Beijing University of Chemical Technology,
Beijing 100029, China

Ya-Hui Sun

State Key Laboratory for Strength and Vibration,
Xian Jiaotong University,
Xian 710049, China

Jian-Qiao Sun

School of Engineering,
University of California, Merced,
Merced, CA 95343
e-mail: jqsun@ucmerced.edu

1Corresponding authors.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 8, 2017; final manuscript received December 12, 2017; published online February 22, 2018. Assoc. Editor: Nicole Kessissoglou.

J. Vib. Acoust 140(4), 041002 (Feb 22, 2018) (7 pages) Paper No: VIB-17-1410; doi: 10.1115/1.4038955 History: Received September 08, 2017; Revised December 12, 2017

The building structural vibration control by an active mass damper (AMD) with delayed acceleration feedback is studied. The control is designed with a multi-objective optimal approach. The stable region in a parameter space of the control gain and time delay is obtained by using the method of stability switch and the numerical code of NDDEBIFTOOL. The control objectives include the setting time, total power consumption, peak time, and the maximum power. The multi-objective optimization problem (MOP) for the control design is solved with the simple cell mapping (SCM) method. The Pareto set and Pareto front are found to consist of two clusters. The first cluster has negative feedback gains, i.e., the positive acceleration feedback. We have shown that a proper time delay can enhance the vibration suppression with controls from the first cluster. The second cluster has positive feedback gains and is located in the region which is sensitive to time delay. A small time delay will deteriorate the control performance in this cluster. Numerical simulations and experiments are carried out to demonstrate the analytical findings.

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Figures

Grahic Jump Location
Fig. 2

Positive roots of F(ω) = 0

Grahic Jump Location
Fig. 3

The stable region of Eq. (5) and the Pareto set of the MOP (15). The label n denotes the number of the eigenvalues with positive real part of the characteristic equation D(λ) = 0, the region with n = 0 is the stable region Ωs, and D⊂{Ωs} is the time-delay-independent stable region. The Pareto set includes two clusters, the first cluster is composed of red points on the left side, and the second cluster is composed of blue points at the lower right edge.

Grahic Jump Location
Fig. 1

The shake table and the plant. xf (m) represents the floor horizontal deflection relative to the ground. xc (m) denotes the cart linear position relative to the floor of the building. xt (m) is the shake table position relative to the ground, which represents the excitation to the plant. (Reproduced with permission from Quanser2)

Grahic Jump Location
Fig. 8

The real part of the eigenvalues of D(λ) = 0 with k = 0.55 and variation of τ

Grahic Jump Location
Fig. 9

Time series of the closed-loop system (5) with k = 0.55 and different time delay τ. (Top) Numerical simulation. (Bottom) Experimental results.

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Fig. 4

The Pareto front of the MOP (15) includes two clusters. The first cluster is denoted by red circles, and the second cluster is denoted by blue circles. (Top left) The Pareto front in (ts, tp, Et)-space. (Top right) The Pareto front projected in (ts, Et)-space. (Bottom left) The Pareto front projected in (Et, tp)-space. (Bottom right) The Pareto front projected in (ts, tp)-space.

Grahic Jump Location
Fig. 5

The real part of the eigenvalues of D(λ) = 0 with k = −0.25 and variation of τ

Grahic Jump Location
Fig. 6

Time series of the closed-loop system (5) with k = −0.25 and different time delay τ. (Top) Numerical simulation. (Bottom) Experimental results.

Grahic Jump Location
Fig. 7

Time series of the system (5) with no control (k = 0). (Left) Numerical simulation. (Right) Experimental results.

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