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Research Papers

Multi-Objective Optimization of Piezoelectric Actuator Placement for Shape Control of Plates Using Genetic Algorithms

[+] Author and Article Information
Rajesh Kudikala

Department of Mechanical Engineering, IIT Kanpur, Kanpur, 208016 Indiakudikala@iitk.ac.in

Deb Kalyanmoy

Department of Mechanical Engineering, IIT Kanpur, Kanpur, 208016 Indiadeb@iitk.ac.in

Bishakh Bhattacharya

Department of Mechanical Engineering, IIT Kanpur, Kanpur, 208016 Indiabishakh@iitk.ac.in

J. Mech. Des 131(9), 091007 (Aug 18, 2009) (11 pages) doi:10.1115/1.3160313 History: Received December 10, 2008; Revised May 27, 2009; Published August 18, 2009

Shape control of adaptive structures using piezoelectric actuators has found a wide range of applications in recent years. In this paper, the problem of finding optimal distribution of piezoelectric actuators and corresponding actuation voltages for static shape control of a plate is formulated as a multi-objective optimization problem. The two conflicting objectives considered are minimization of input control energy and minimization of mean square deviation between the desired and actuated shapes with constraints on the maximum number of actuators and maximum induced stresses. A shear lag model of the smart plate structure is created, and the optimization problem is solved using an evolutionary multi-objective optimization algorithm: nondominated sorting genetic algorithm-II. Pareto-optimal solutions are obtained for different case studies. Further, the obtained solutions are verified by comparing them with the single-objective optimization solutions. Attainment surface based performance evaluation of the proposed optimization algorithm has been carried out.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Aluminum plate with 20 locations for the actuators

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Figure 2

Finite element model of the plate with actuators at the chosen locations

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Figure 3

Actuator presence/absence criteria

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Figure 4

Initial and desired shapes of the plate (case 1)

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Figure 5

Pareto-optimal solutions with optimal locations of the actuators (case 1)

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Figure 6

Actuated and desired shapes at PO solution A

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Actuated and desired shapes at PO solution G

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Figure 8

Actuated and desired shapes at PO solution D

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Figure 9

Initial and desired shapes of the plate (case 2)

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Pareto-optimal solutions with optimal locations of the actuators (case 2)

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Actuated and desired shapes at PO solution A

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Actuated and desired shapes at PO solution G

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Actuated and desired shapes at PO solution D

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Skew cantilever plate with 14 locations for the actuators

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Figure 15

Initial and desired shapes of the skew plate (case 3)

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Figure 16

Pareto-optimal solutions from NSGA-II with optimal locations of the actuators (case 3)

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Figure 17

Comparison of the desired and actuated shapes at PO solution A

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Figure 18

Comparison of the desired and actuated shapes at PO solution H

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Figure 19

Comparison of the desired and actuated shapes at PO solution I

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Figure 20

Comparison of the desired and actuated shapes at PO solution G

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Figure 21

Initial and desired shapes of the skew plate (case 4)

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Figure 22

Pareto-optimal solutions from NSGA-II with optimal locations of the actuators (case 4)

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Figure 23

Comparison of the desired and actuated shapes at PO solution A

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Figure 24

Comparison of the desired and actuated shapes at PO solution C

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Figure 25

Comparison of the desired and actuated shapes at PO solution B

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Figure 26

Comparison of the responses from FEM and experiments (3)

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Figure 27

Nondominated solutions in five runs (case 1)

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Figure 28

Nondominated solutions in five runs (case 2)

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Figure 29

Nondominated solutions in five runs (case 3)

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Figure 30

Nondominated solutions in five runs (case 4)

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Figure 31

The summary attainment surfaces (case 1)

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Figure 32

The summary attainment surfaces (case 2)

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Figure 33

The summary attainment surfaces (case 3)

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Figure 34

The summary attainment surfaces (case 4)

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