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Research Papers

Model-Based Robust Optimal Control for Layer-By-Layer Ultraviolet Processing of Composite Laminates

[+] Author and Article Information
Admu Yebi

Mem. ASME
Clemson University—International
Center for Automotive Research,
4 Research Dr.,
Greenville, SC 29607
e-mail: ayebi@clemson.edu

Beshah Ayalew

Associate Professor
Mem. ASME
Clemson University—International Center for
Automotive Research,
4 Research Dr., CGEC342,
Greenville, SC 29607
e-mail: beshah@clemson.edu

Srikanth Pilla

Assistant Professor
Clemson University—International Center
for Automotive Research,
4 Research Dr., CGEC340,
Greenville, SC 29607
e-mail: spilla@clemson.edu

Xiaoyan Yu

Clemson University—International Center
for Automotive Research,
4 Research Dr.,
Greenville, SC 29607
e-mail: xyu4@clemson.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 20, 2015; final manuscript received September 12, 2016; published online November 11, 2016. Assoc. Editor: Jingang Yi.

J. Dyn. Sys., Meas., Control 139(2), 021008 (Nov 11, 2016) (11 pages) Paper No: DS-15-1327; doi: 10.1115/1.4034782 History: Received July 20, 2015; Revised September 12, 2016

This paper first discusses some experimental verification of proposed ultraviolet (UV) radiation curing process models and then it outlines a robust process optimization and control scheme for layer-by-layer UV processing of a thick composite laminate. The experiments include UV transmission, cure kinetics, and in situ temperature measurements for UV curing of a one-dimensional (1D) composite material sample. The validated models are used to motivate how optimizing the layer-by-layer curing process can help address the challenge of maintaining through-cure due to the in-domain attenuation of the UV input during thick-part fabrication. The key insight offered is to model the layer-by-layer deposition and curing process as a multimode hybrid dynamic system with a growing spatial domain, where the interlayer hold times and the UV intensity at each layer addition can be taken as the augmented control variables to be selected optimally. Specifically, the control input is set to have feed forward and output feedback components, which act on the UV intensity at each layer and are constructed to track a reference surface temperature trajectory. The feedback gains at each layer addition are designed by posing a robust optimization problem that penalizes the sensitivity of the objective function to process uncertainties. It is illustrated using simulation analyses that augmented control with robust optimal static feedback of UV intensity at each layer and nominal optimization of the interlayer hold times gives very close tracking of a desired final cure level distribution in the presence of parametric uncertainty.

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References

Figures

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Fig. 1

Schematic for a UV curing process model

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Fig. 2

Measured isothermal heat flow for varying photoinitiator

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Fig. 3

Measured isothermal heat flow for varying curing temperature

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Fig. 4

Measured isothermal heat flow for varying UV intensity

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Fig. 5

Comparison of measured and predicted cure rate for varying curing temperature: (a) T = 25 °C, (b) T = 50 °C, and (c) T = 80 °C

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Fig. 6

Comparison of simulated and measured temperature: (a) top surface temperature, (b) bottom surface temperature, and (c) simulated cure conversion

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Fig. 7

A hybrid system formulation of the layer-by-layer curing process with closed-loop control

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Fig. 8

Final cure level profile with +10 % parameter deviation in E2 and −10 % parameter deviation in B¯

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Fig. 9

Optimized interlayer hold times for nominal optimization case (Case 2)

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Fig. 10

Control input of UV intensity for robust optimization case (Case 3)

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Fig. 11

Sensitivity of the final cure state (dα/dθ is normalized with respect to its maximum)

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Fig. 12

Convergence of computational algorithm (with β=0.25)

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