A nonlinear model-based control method is proposed and validated for controlling, estimating and optimizing the cure in composite parts. During the cure, the exothermic reaction causes temperature gradients through the thickness that can lead to a nonuniform cure and high residual stress. A predictive control and optimization approach is proposed to ensure that temperature gradients are kept within acceptable limits and the cure state is fairly uniform, regardless of the part thickness. A reduced order process model is derived and used to formulate a dynamic inversion controller. A nonlinear observer is constructed to estimate the unknown temperature and cure states within the composite. An on-line optimizer determines the maximum allowable heating rate. The optimizer is run at discrete intervals throughout the process to account for process and part variability. The control, estimation and optimization algorithms were validated through a series of simulations and experiments of composite parts cured in a press. Parts that were cured with the proposed control method were compared with parts cured following a manufacturer’s recommended cure cycle. The results demonstrate the success of the proposed control method in achieving uniform temperature and cure, and in decreasing the residual stress, without increasing cycle time.

1.
Bogetti
,
T. A.
, and
Gillespie
,
J. W.
,
1991
, “
Two-Dimensional Cure Simulation of Thick Thermosetting Composites
,”
J. Compos. Mater.
,
25
, pp.
239
273
.
2.
Michaud
,
D. J.
,
Beris
,
A. N.
, and
Dhurjati
,
P. S.
,
2002
, “
Thick-Sectioned RTM Composite Manufacturing, Part II. Robust Cure Cycle Optimization and Control
,”
J. Compos. Mater.
,
36
, pp.
1201
1232
.
3.
Michaud
,
D. J.
,
Beris
,
A. N.
, and
Dhurjati
,
P. S.
,
2002
, “
Thick-Sectioned RTM Composite Manufacturing: Part I—In Situ Cure Model Parameter Identification and Sensing
,”
J. Compos. Mater.
,
36
, pp.
1175
1200
.
4.
Michaud
,
D. J.
,
Beris
,
A. N.
, and
Dhurjati
,
P. S.
,
1998
, “
Curing Behavior of Thick-Sectioned RTM Composites
,”
J. Compos. Mater.
,
32
, pp.
1273
1296
.
5.
Mantell, S. C., and Eriksen, C., 2001, “The Effect of Cure Path on Residual Strains in Thick Composite Parts,” in American Composites Society 16th Technical Conference on Composite Materials, Blacksburg, VA, American Composites Society.
6.
Choi
,
M. A.
,
Lee
,
M. H.
,
Chang
,
J.
, and
Lee
,
S. J.
,
1999
, “
Three-Dimensional Simulations of the Curing Step in the Resin Transfer Molding Process
,”
Polym. Compos.
,
20
, pp.
543
552
.
7.
Twardowski
,
T. E.
,
Lin
,
S. E.
, and
Geil
,
P. H.
,
1993
, “
Curing in Thick Composite Laminates: Experiment and Simulation
,”
J. Compos. Mater.
,
27
, pp.
216
250
.
8.
Ciriscioli
,
P. R.
,
Springer
,
G. S.
, and
Lee
,
W. I.
,
1991
, “
An Expert System for Autoclave Curing of Composites
,”
J. Compos. Mater.
,
25
, pp.
1542
1587
.
9.
Pillai
,
V. K.
,
Beris
,
A. N.
, and
Dhurjati
,
P. S.
,
1994
, “
Implementation of Model-Based Optimal Temperature Profiles for Autoclave Curing of Composites Using a Knowledge-Based System
,”
Ind. Eng. Chem. Res.
,
33
, pp.
2443
2452
.
10.
Dunkers
,
J. P.
,
Flynn
,
K. M.
,
Parnas
,
R. S.
, and
Sourlas
,
D.
,
2002
, “
Development of a Model Assisted Feedback Control Algorithm for Liquid Composite Molding, and Evaluation of Controller Robustness
,”
Composites, Part A
,
33
, p.
841
841
.
11.
Tam, A. S., and Gutowski, T. G., 1989, “Nonlinear Process Controller for Curing a Thermoset Composite,” in International SAMPE Symposium and Exhibition Book, Covina, CA.
12.
Soucy, K. A., and Holt, B. R., 1992, “Modeling, Estimation and Control of Polymer Composite Processing,” American Control Conference.
13.
White
,
S. R.
, and
Hahn
,
H. T.
,
1993
, “
Cure Cycle Optimization for the Reduction of Processing-Induced Residual Stresses in Composite Materials
,”
J. Compos. Mater.
,
27
, pp.
1352
1378
.
14.
Ramakrishnan
,
B.
,
Zhu
,
L.
, and
Pitchumani
,
R.
,
2000
, “
Curing of Composites Using Internal Resistive Heating
,”
J. Manuf. Sci. Eng.
,
122
, pp.
124
131
.
15.
Rai
,
N.
, and
Pitchumani
,
R.
,
1997
, “
Rapid Cure Simulation Using Artificial Neural Networks
,”
Composites, Part A
,
28
, pp.
847
859
.
16.
Demirci, H. H., and Coulter, J. P., 1994, “Intelligent Control of Resin Transfer Molding Processes (RTM) Utilizing Neural Networks and Nonlinear Optimization Methods,” ASME Proceedings on Design and Performance of Composite Materials, MD-52.
17.
Astrom, K. J., and Wittenmark, B., 1989, Adaptive Control, Reading, Addison-Wesley, MA.
18.
Doyle
, III,
F. J.
,
1998
, “
Nonlinear Inferential Control for Process Applications
,”
ASME J. Process Control
,
8
, pp.
339
353
.
19.
Henson, M. A., and Seborg, D. E., eds., 1997, Nonlinear Process Control, Prentice–Hall, Englewood Cliffs, NJ.
20.
Isidori, A., 1989, Nonlinear Control Systems, 1989: Springer-Verlag, Berlin.
21.
Vidyasagar, M., 1978, Nonlinear Systems Analysis, Prentice–Hall, Englewood Cliffs, NJ.
22.
Enns
,
D.
,
Bugajski
,
D.
,
Hendrick
,
R.
, and
Stein
,
G.
,
1994
, “
Dynamic Inversion: An Evolving Methodology for Flight Control Design
,”
Int. J. Control
,
59
, pp.
71
91
.
23.
Kang
,
W.
, and
Krener
,
A. J.
,
1992
, “
Extended Quadratic Controller Normal Form and Dynamic State Feedback Linearization of Nonlinear Systems
,”
SIAM J. Control Optim.
,
30
, pp.
1319
1337
.
24.
Kolavennu
,
S.
,
Palanki
,
S.
, and
Cockburn
,
J. C.
,
2001
, “
Nonlinear Control of Nonsquare Multivariable Systems
,”
Chem. Eng. Sci.
,
56
, pp.
2103
2110
.
25.
Kolavennu
,
S.
,
Palanki
,
S.
, and
Cockburn
,
J. C.
,
2001
, “
Robust Controller Design for Multivariable Nonlinear Systems Via Multi-Model H2/H¥ Synthesis
,”
Chem. Eng. Sci.
,
56
, pp.
4339
4349
.
26.
Luenberger
,
D. G.
,
1971
, “
An Introduction to Observers
,”
IEEE Trans. Autom. Control
,
AC-16
, pp.
596
602
.
27.
Kwakernaak, H., and Sivan, R., 1972, Linear Optimal Control Systems, Wiley Interscience, New York, Vol. XXV.
28.
Soroush
,
M.
,
1997
, “
Nonlinear State-Observer Design with Application to Reactors
,”
Chem. Eng. Sci.
,
52
, pp.
387
404
.
29.
Daoutidis
,
P.
, and
Kravaris
,
C.
,
1994
, “
Dynamic Output Feedback Control of Minimum-Phase Multivariable Nonlinear Processes
,”
Chem. Eng. Sci.
,
49
, pp.
433
447
.
30.
Kantor
,
J. C.
,
1989
, “
A Finite Dimensional Nonlinear Observer for an Exothermic Stirred-Tank Reactor
,”
Chem. Eng. Sci.
,
44
, pp.
1503
1510
.
31.
Gibon-Fargeot
,
A. M.
,
Hammouri
,
H.
, and
Celle
,
F.
,
1994
, “
Nonlinear Observers for Chemical Reactors
,”
Chem. Eng. Sci.
,
49
, pp.
2287
2300
.
32.
Kazantzis
,
N.
,
Kravaris
,
C.
, and
Wright
,
R. A.
,
2000
, “
Nonlinear Observer Design for Process Monitoring
,”
Ind. Eng. Chem. Res.
,
39
, pp.
408
419
.
33.
Alvarez
,
J.
, and
Lopez
,
T.
,
1999
, “
Robust Dynamic State Estimation of Nonlinear Plants
,”
AIChE J.
,
45
, pp.
107
123
.
34.
Farza
,
M.
,
Hammouri
,
H.
,
Othman
,
S.
, and
Busawon
,
K.
,
1997
, “
Nonlinear Observers for Parameter Estimation in Bioprocesses
,”
Chem. Eng. Sci.
,
52
, pp.
4251
4267
.
35.
Farza
,
M.
,
Hammoudi
,
H.
,
Jallur
,
C.
, and
Creto
,
J.
,
1999
, “
State Observation of a Nonlinear System: Application to (Bio)Chemical Processes
,”
AIChE J.
,
45
, pp.
93
106
.
36.
Soroush
,
M.
, and
Kravaris
,
C.
,
1992
, “
Nonlinear Control of a Batch Polymerization Reactor. An Experimental Study
,”
AIChE J.
,
38
, pp.
1429
1448
.
37.
Soroush
,
M.
,
1998
, “
State and Parameter Estimations and Their Applications in Process Control
,”
Comput. Chem. Eng.
,
23
, pp.
229
245
.
38.
Soroush
,
M.
, and
Kravaris
,
C.
,
1994
, “
Nonlinear Control of a Polymerization Cstr with Singular Characteristic Matrix
,”
AIChE J.
,
40
, pp.
980
990
.
39.
Iyer
,
N. M.
, and
Farell
,
A. E.
,
1996
, “
Design of a Stable Adaptive Nonlinear Observer for an Exothermic Stirred Tank Reactor
,”
Comput. Chem. Eng.
,
20
, pp.
1141
1147
.
40.
Hojjati
,
M.
, and
Hoa
,
S. V.
,
1994
, “
Curing Simulation of Thick Thermosetting Composites
,”
Compos. Manuf.
,
5
, pp.
159
169
.
41.
Kamal
,
M. R.
, and
Sourour
,
S.
,
1973
, “
Kinetics and Thermal Characterization of Thermoset Cure
,”
Polym. Eng. Sci.
,
13
, pp.
59
64
.
42.
Calado, V. M. A., and Advani, S. G., 1999, “Thermoset Resin Cure Kinetics and Rheology,” in Processing of Composites, R. S. Dave and A. C. Loos, eds., Hanser/Gardner, Cincinatti, OH.
43.
Voorakaranam
,
S.
, and
Joseph
,
B.
,
1999
, “
Model Predictive Inferential Control with Application to a Composites Manufacturing Process
,”
Ind. Eng. Chem. Res.
,
38
, pp.
433
450
.
44.
1992, ASTM Standard E837-99: Standard Test Method for Determining Residual Stresses by the Hole-Drilling Strain-Gage Method, American Society for Testing and Materials, Philadelphia, PA.
45.
Mantell
,
S. C.
,
Ciriscioli
,
P. R.
, and
Almen
,
G.
,
1995
, “
Cure Kinetics and Rheology Models for ICI Fiberite 977-3 and 977-2 Thermosetting Resins
,”
Composites
,
14
, pp.
847
865
.
46.
Parthasarathy, S., 2002, “Real-Time Control and Optimization of Curing in Thick Sectioned Thermoset Composites,” Ph.D. thesis, Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN.
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