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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr1 Model Predictive Control of a Powder Coating Curing Process: an Application of the MPC@CB Software MPC@CB © Software by: Kamel Abid, Pascal Dufour, Isabelle Bombard, Pierre Laurent CCC’07, Zhangjiajie, July, 27-29 2007

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr2 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Experimental results 7. Conclusions & perspectives Outline

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr3 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Experimental results 7. Conclusions & perspectives Outline

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr4 Painting applications in: building (outdoor and indoor), furniture, cars accessories … Need to decrease pollution due to the painting: organic solvent based coating are replaced by powder coatings Quite recently, UV-curable powder coatings and low- temperature coatings designed for heat sensitive substrates have appeared on the coatings market. But few studies on curing kinetics, thermal modelling and control of such powder coating curing process: trajectory tracking or minimization of curing time or … Control problem statement

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr5 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Experimental results 7. Conclusions & perspectives Outline

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr6 First principle PDE model Schematic drawing of the “substrat+powder” sample Powder coatings = fine particles of: resin + cross-linker in thermosetting or thermoplastic powder coatings + pigments + extenders + flow additives and fillers to achieve specific properties (color, ….)

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr7 1. 1.Thermal model based on the Fourier law of heat conduction uses: 1. 1.the temperature variable varying in the thickness of the powder coated metal sample 2. 2.the degree of cure conversion variable (ranging from 0+ to 1 at the end) 2. 2.A non linear PDE Boundary control problem has to be tackled First principle PDE model

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr8 First principle PDE model [Bombard et al, 2006] Tp(z,t) = temperature across the powder film thickness ep = film thickness (~0.1 mm) x(z,t) = degree of cure Ts(z,t) = temperature across the substrate es = film thickness (~1 mm) 0t,e0,z x)(1xek C ΔHe z t)(z,T Cρ λ t t)(z,T p nm ) t)(z,RT E ( 0 pp 0p 2 p 2 p pc,p p a 0t,ee,ez z t)(z,T Cρ λ t t)(z,T spp 2 s 2 pss sc, s

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr9 First principle PDE model [Bombard et al, 2006] 3 boundary conditions for the temperature: Manipulated variable 0t 0,z at )Tt)(z,(Th)Tt)(z,(Tσε(t)φα z t)(z,T λ extpp 4 4 ppir p p 0t,ez at z t)(z,T λ z t)(z,T λ p p sc, p p 0t,eez at )Tt)(z,(Th)Tt)(z,(Tσε z t)(z,T λ sp extss 4 4 ss s s

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr10 First principle PDE model [Bombard et al, 2006] The degree of cure x(z,t) of the powder: Initial conditions: 0t,e0,z x)(1xek t t)x(z, p nm ) t)(z,RT E ( 0 p a 0t],ee[0,zTt)(z,Tt)(z,T spextsp 0t],e[0,z0t)x(z, p

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr11 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Experimental results 7. Conclusions & perspectives Outline

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr12 Advantages: - constraints (such as manipulated variables physical limitations, constraints due to operating procedures or safety reasons…) may be specified - a model aims to predict the future behavior of the process and the best one is chosen by a correct optimal control of the manipulated variables. Drawbacks: - computational time needed may limit online use - suboptimal solutions - how to handle unfeasibilities Model predictive control strategy

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr13 Model predictive control strategy The function f means: trajectory tracking, processing time minimization, productivity function …

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr14 Originaly developed for nonlinear PDE model control Main idea: decrease the online time needed to compute the PDE model based control Approach: Input constraints: hyperbolic transformation Output constraints: exterior penalty method Linearization + sensitivites computed off line On line use of a time varying linear model On line resolution of a penalized (and so unconstrained) optimization control problem : a modified Levenberg Marquardt Algorithm Model predictive control strategy [Dufour et al, IEEE TCST 11(5) 2003]

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr15 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Experimental results 7. Conclusions & perspectives Outline

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr16 1. 1. Developed under Matlab, MPC@CB© solves any user defined : trajectory tracking problem operating time minimization problem any cost function input/output constraint handled 2. 2. Any user defined continuous model (SISO, MISO, SIMO, MIMO model), including large scale PDE model 3. 3. Easy to introduce a user defined observer 4. 4. Easy to apply the software for simulation or real time application MPC@CB ©: flexibility/ease for a quick use in control ! MPC@CB© software main features

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr17 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Experimental results 7. Conclusions & perspectives Outline

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr18 Minimization of the curing time, with magnitude+velocity constraints on u(t) + output contraint yp(t) : horizon=6, sampling time = 1s Simulation results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr19 Minimization of the curing time, with magnitude+velocity constraints on u(t) + output contraint yp(t) : horizon=6, sampling time = 1s Simulation results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr20 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Experimental results 7. Conclusions & perspectives Outline

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr21 Temperature trajectory tracking, with magnitude+velocity constraints on u(t) : horizon=6, sampling time = 1s Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr22 Temperature trajectory tracking, with magnitude+velocity constraints on u(t) : horizon=6, sampling time = 1s Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr23 Temperature trajectory tracking, with magnitude+velocity constraints on u(t) : horizon=6, sampling time = 1s Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr24 Temperature trajectory tracking, with magnitude+velocity constraints on u(t) : horizon=14, sampling time = 1s Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr25 Temperature trajectory tracking, with magnitude+velocity constraints on u(t) : horizon=14, sampling time = 1s Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr26 Temperature trajectory tracking, with magnitude+velocity constraints on u(t) : horizon=14, sampling time = 1s Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr27 Temperature trajectory tracking: influence of the horizon over the results Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr28 1. 1.Control problem statement 2. 2.First principle PDE model 3. Model predictive control strategy 4. MPC@CB© software main features 5. Simulation results 6. Experimental results 7. Conclusions & perspectives Outline

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr29 The real time control of powder curing is possible : temperature trajectory tracking Experimental control of PDE system by a general MPC@CB© software has been shown Conclusions Perspectives Minimization of the powder curing time under constraints: an observer is under development MPC@CB© may be used for any process: since its development, it is currently used for control of polymer production, vial lyophilisation, pasta drying. To use MPC@CB©: dufour@lagep.univ-lyon1.fr

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr30 Thank you Any questions ?

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr31 Temperature trajectory tracking, with magnitude+velocity constraints on u(t) : horizon=6, sampling time = 1s Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr32 Temperature trajectory tracking, with magnitude+velocity constraints on u(t) : horizon=14, sampling time = 1s Experimental results

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Université de Lyon- CNRS-LAGEP, France Paper CCC07-0506 dufour@lagep.univ-lyon1.fr33

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