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Research Papers

Decentralized Vibration and Shape Control of Structures With Colocated Sensors and Actuators

[+] Author and Article Information
A. H. Ghasemi

Department of Mechanical Engineering,
University of Michigan,
2350 Hayward Street,
Ann Arbor, MI 48109
e-mail: ghasemi@umich.edu

Jesse B. Hoagg

Department of Mechanical Engineering,
University of Kentucky,
271 Ralph G. Anderson Building,
Lexington, KY 40506-0503
e-mail: jhoagg@engr.uky.edu

T. M. Seigler

Department of Mechanical Engineering,
University of Kentucky,
281 Ralph G. Anderson Building,
Lexington, KY 40506-0503
e-mail: tmseigler@uky.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 27, 2015; final manuscript received December 17, 2015; published online January 18, 2016. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 138(3), 031011 (Jan 18, 2016) (11 pages) Paper No: DS-15-1044; doi: 10.1115/1.4032344 History: Received January 27, 2015; Revised December 17, 2015

This paper introduces a decentralized shape and vibration controller for structures with large and potentially unknown system order, model-parameter uncertainty, and unknown disturbances. Controller implementation utilizes distributed, colocated, and independent actuator–sensor pairs. Controller design requires knowledge of the relative degrees of the actuator and sensor dynamics and upper bounds on the diagonal elements of system's high-frequency gain matrix. Closed-loop performance is determined by a parameter gain, which can be viewed as the cutoff frequency of a low-pass filter. For sufficiently large parameter gain, the closed-loop performance is arbitrarily small. Numerical examples are used to demonstrate the application and effectiveness of the decentralized controller, and we present experimental results for a setup consisting of a cantilever beam with piezoelectric actuators and strain-gauge sensors.

Copyright © 2016 by ASME
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Figures

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Fig. 1

Open-loop system. The open-loop system consists of astructure, m identical actuators, and m identical sensors. Theactuators are commanded by the controls u1, … ,um and applyactuation inputs ua,1, … ,ua,m to the structure. The sensors yield measurements y1, … , ym of the structure outputs yq,1, … , yq,m. The structure is subject to the unknown disturbance w, and the sensors are subject to the unknown measurement noise σ1, … , σm.

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Fig. 2

Closed-loop system. Each decentralized filtered-dynamic-inversion controller ui uses local feedback yi of the colocated measurement and local feedforward ri.

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Fig. 3

Frame structure with point sensing and actuation. Three actuators apply point forces at the mid-points of each member, and three colocated sensors measure the structure displacements at the same positions. Unknown point disturbance forces are also applied at the same location as the control forces. The control objective is to attenuate the midpoint displacement measurements.

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Fig. 4

Closed-loop vibration response of the frame structure. Attenuation of the midpoint displacements is improved as k increases.

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Fig. 5

Control inputs to the frame structure. As k increases, the control inputs converge to the cancellations of the disturbance forces w1=4 sin 2πt N,w2=2 sin 3πt N, and w3=4 sin πt N.

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Fig. 6

Vibration response of the frame structure using PPF and D-FDI controllers. D-FDI can significantly attenuate vibrations in comparison with the PPF.

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Fig. 7

Control inputs to the frame structure of the PPF and D-FDI controllers. The control inputs of D-FDI converge to the cancellations of the disturbance forces w1=4 sin 2πt N,w2=2 sin 3πt N, and w3=4 sin πt N.

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Fig. 8

Simply supported beam with point sensing and actuation. Actuators apply point forces the quarter-points of the beam, and the sensors measure the displacements at the same locations. A broadband disturbance force acts at the beam's midpoint. The control objective is to make yq,1 and yq,2 track the outputs of local reference models.

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Fig. 9

Shape control of the beam. As k increases the shape of the beam converges to the first mode shape of a simply supported beam where w(xb, t) is the beam deflection and xb is the distance from the left support. Error bars represent standard deviation of the mean shape.

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Fig. 10

Shape control of the beam. As k increases the shape of the beam converges to the second mode shape of a simply supported beam where w(xb, t) is the beam deflection and xb is the distance from the left support. Error bars represent standard deviation of the mean shape.

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Fig. 11

Shape control of the beam using PI and D-FDI controllers. In the presence of actuator/sensor dynamics, the performance of the PI controller is limited in comparison with the D-FDI. With a large enough k, the beam's shape converges to the first and second mode shapes of a simply supported beam using D-FDI. Error bars represent standard deviation of the mean shape.

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Fig. 12

Mass–spring–dashpot system. Actuators provide forces uA and uC, and colocated sensors measure the displacements qA and qC. The control objective is to control displacements qA and qC such that they follow reference commands rA and rC, respectively, despite the unknown disturbance forces wB and wC.

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Fig. 13

Closed-loop vibration response of the mass–spring–dashpot system. Command following improves as k increases.

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Fig. 14

Control inputs for Fig. 13, where the disturbance forces wB=sin 4πt N and wC=sin(2πt+π/4) N

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Fig. 15

Closed-loop vibration response of the mass–spring–dashpot system with broadband measurement noise. Command following improves as k increases.

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Fig. 16

Control inputs to the mass–spring–dashpot system with broadband measurement noise. The amplitude and frequency content of the control signal is increases relative to noiseless case of Fig. 14.

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Fig. 17

Experiment setup. Piezoelectric actuators apply strains to the top surface, and colocated strain-gauge sensors measure strain at the bottom surface. The piezoelectric actuators are used to provide both the control and the disturbance. The objective is to attenuate the strain-gauge measurements.

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Fig. 18

Single-input single-output (SISO) experiment with a third-order controller and two disturbance inputs. The actuator farthest from the fixed end is used for control, while both actuators produce sinusoidal disturbances at different frequencies. Note that ymax is defined as maxt∈[0,15]|y(t)| across all three trials.

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Fig. 19

Strain-gauge measurements for multiple-input multiple-output (MIMO) experiment with third-order local controllers and two disturbance inputs. Both actuators use third-order decentralized controllers, while both actuators produce sinusoidal disturbances at different frequencies. Note that yi,max is defined as maxt∈[0,15]|yi(t)| across all three trials.

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