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Research Papers

Partial Differential Equation-Based Process Control for Ultraviolet Curing of Thick Film Resins

[+] Author and Article Information
Adamu Yebi

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

Beshah Ayalew

Associate Professor
Mem. ASME
International Center for Automotive Research,
Clemson University,
Greenville, SC 29607
e-mail: beshah@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 May 5, 2014; final manuscript received June 7, 2015; published online July 27, 2015. Assoc. Editor: YangQuan Chen.

J. Dyn. Sys., Meas., Control 137(10), 101010 (Jul 27, 2015) (10 pages) Paper No: DS-14-1198; doi: 10.1115/1.4030818 History: Received May 05, 2014

This paper proposes a feedback control system for curing thick film resins using ultraviolet (UV) radiation. A model-based distributed parameter control scheme is constructed for addressing the challenge of achieving through cure while reducing temperature gradients in thick films in composite laminates. The UV curing process is modeled with a parabolic partial differential equation (PDE) that includes an in-domain radiative input along with a nonlinear spatial attenuation function. The control problem is first cast as a distributed temperature trajectory-tracking problem where only surface temperature measurements are available. By transforming the original process model to an equivalent boundary input problem, backstepping boundary PDE control designs are applied to explicitly obtain both the controller and the observer gain kernels. Offline optimization may be used to generate the desired temperature trajectory, considering quality constraints such as prespecified spatial gradients and UV source limitations. The workings and the performance of the proposed control scheme are illustrated through simulations of the process model. It is shown that feedforward compensation can be added to achieve improved tracking with the PDE controller in the presence of measurement noise and other process disturbances.

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Figures

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Fig. 1

Schematic for a UV curing process model

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Fig. 2

Open-loop responses with constant ambient temperature boundary condition at the bottom: (a) nodal cure level distribution, (b) deviation of cure level between top and bottom, (c) nodal temperature distribution, and (d) deviation of temperature between top and bottom

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Fig. 3

Open-loop responses with insulated boundary condition at the bottom: (a) nodal cure level distribution, (b) deviation of cure level between top and bottom, (c) nodal temperature distribution, and (d) deviation of temperature between top and bottom

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Fig. 4

The evolution of the product of spatial input attenuation and Arrhenius components with insulated boundary condition at the bottom

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Fig. 5

Closed-loop UV curing process control system

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Fig. 8

Control gain kernel N(1,y) for different values of c

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Fig. 9

Nodal controlled cure level distribution via the proposed controller

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Fig. 12

Control input: feedforward and feedforward plus feedback (filtered)

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Fig. 6

(a) Temperature profile of the process at node (z = l) (solid line represents actual response with the proposed controller and dashed line is the reference temperature) and (b) control input

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Fig. 7

Nodal temperature distribution of the process (solid line represents actual response with the proposed controller and dashed line is the reference temperature)

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Fig. 10

Convergence of observer error (a) spatial distribution and (b) spatial 2-norm

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Fig. 11

Nodal temperature distribution of the process with feedforward, and feedback plus feedforward control in the presence of measurement noise

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