The water vapor transfer across a Nafion® membrane exhibits an undesired non-minimum phase behavior. This paper will show that even in the disturbance-to-output loop, the non-minimum phase zero adversely affects the feedback controller design because of the coupling effect between the disturbance-to-output and the input-to-output loops. The non-minimum phase zero location is influenced by the channel plate structure and the membrane material property. The structural parameters examined in this research include channel plate dimensions and heat transfer coefficients. The membrane properties studied include membrane vapor transfer properties described in the Arrhenius’ equation. A governing equation to link the non-minimum phase zero and the parameters is developed in this paper. This equation shows that the non-minimum phase zero arises from the competing heat and mass transfer dynamics, and is determined by the structural parameters and membrane properties. A sensitivity study is presented and shows that structural and material property optimization can be used with the control system design to mitigate the non-minimum phase behavior in the PEM fuel cell humidification system.

References

References
1.
He
,
W.
Yi
,
J. S.
, and
Nguyen
,
T. V.
, 2000, “
Two-Phase Flow Model of the Cathode of PEM Fuel Cells Using Interdigitated Flow Fields
,”
AIChE J.
,
46
(
10
), pp.
2053
2064
.
2.
Wang
,
Z. H.
,
Wang
,
C. Y.
, and
Chen
,
K. S.
, 2001, “
Two-phase Flow and Transport in the Air Cathode of Proton Exchange Membrane Fuel Cells
,”
J. Power Sources
,
94
(
1
), pp.
40
50
.
3.
Weber
,
A. Z.
, and
Newman
,
J.
, 2004, “
Transport in Polymer-Electrolyte Membranes
,”
J. Electrochem. Soc.
,
151
(
2
), pp.
A326
A339
.
4.
Pasaogullari
,
U.
, and
Wang
,
C. Y.
, 2004, “
Two-Phase Transport and the Role of Micro-Porous Layer in Polymer Electrolyte Fuel Cells
,”
Electrochim. Acta
,
49
(
25
), pp.
4359
4369
.
5.
Karnik
,
A. Y.
,
Sun
,
J.
,
Stefanopoulou
,
A. G.
, and
Buckland
,
J. H.
, 2009, “
Humidity and Pressure Regulation in a PEM Fuel Cell Using a Gain-Scheduled Static Feedback Controller
,”
IEEE Trans. Control Syst. Technol.
,
17
(
2
), pp.
283
297
.
6.
Chen
,
D.
, and
Peng
,
H.
, 2008 “
Non-minimum Phase Phenomenon of PEM Fuel Cell Membrane Humidifiers
,”
ASME J. Dyn. Syst. Measure. Control
,
130
(
4
), pp.
0445011
0445019
.
7.
Fruedenberg
,
J. S.
, and
Looze
,
D. P.
, 1988,
Lecture Notes in Control and Information Sciences
,
Springer-Verlag
,
Berlin
.
8.
Hauser
,
J.
,
Sastry
,
S.
, and
Meyer
,
G.
, 1992, “
Nonlinear Control Design for Slightly Non-Minimum Phase Systems: Application to V/STOL Aircraft
,”
Automatica
,
28
(
4
), pp.
665
679
.
9.
Gopalswamy
,
S.
, and
Hedrick
,
J. K.
, 1993, “
Tracking Nonlinear Non-Minimum Phase Systems Using Sliding Control
,”
Int. J. Control
,
57
(
5
), pp.
1141
1158
.
10.
Chen
,
D.
, and
Peng
,
H.
, 2005, “
A Thermodynamic Model of Membrane Humidifiers for PEM Fuel Cell Humidification Control
”,
ASME J. Measure. Control
,
127
(
3
), pp.
424
433
.
11.
Springer
,
T. E.
,
Zawodzinski
,
T. A.
, and
Gottesfeld
,
S.
, 1991, “
Polymer Electrolyte Fuel Cell Model
,”
J. Electrochem. Soc.
,
138
(
8
), pp.
2334
2342
.
12.
Pukrushpan
,
J. T.
,
Peng
,
H.
, and
Stefanopoulou
,
A. G.
, 2002,
“Simulation and Analysis of Transient Fuel Cell System Performance Based on a Dynamic Reactant Flow Model,” Proceedings of 2002 ASME International Mechanical Engineering Congress and Exposition
,
New Orleans, LA
.
13.
Nguyen
,
T. V.
, and
White
,
R. E.
, 1993, “
A Water and Heat Management Model for Proton-Exchange Membrane Fuel Cells
,”
J. Electrochem. Soc.
,
140
(
8
), pp.
2178
2186
.
14.
Sonntag
,
R. E.
Borgnakke
,
C.
and
Van Wylen
,
G. J.
, 1998,
Fundamentals of Thermodynamics
,
5th
ed.,
Wiley
,
New York
.
15.
Chen
,
D.
,
Li
,
W.
, and
Peng
,
H.
, 2008, “
An Experimental Study and Model Validation of a Membrane Humidifier for PEM Fuel Cell Humidification Control
,”
J. Power Sources
,
180
(
1
), pp.
461
467
.
16.
Fruedenberg
,
J. S.
, and
Looze
,
D. P.
, 1988,
Lecture Notes in Control and Information Sciences
,
Springer-Verlag
,
Berlin
.
17.
Skogestad
,
S.
, and
Postlethwaite
,
I.
, 1996,
Multivariable Feedback Control-Analysis and Design
,
Wiley
,
New York
.
18.
James
,
P. J.
,
McMaster
,
T. J.
,
Newton
,
J. M.
, and
Miles
,
M. J.
, 2000, “
In situ Rehydration of Perfluorosulphonate Ion-Exchange Membrane Studied by AFM
,”
Polymer
,
41
, pp.
4223
4231
.
19.
Jalani
,
N. H.
, and
Datta
,
R.
, 2005,“
The Effect of Equivalent Weight, Temperature, Cationic Forms, Sorbates, and Nanoinorganic Additives on the Sorption Behavior of Nafion
,”
J. Membrane Sci.
,
264
, pp.
167
175
.
20.
Grot
,
W. G.
, 1994, “
Perfluorinated Ion Exchange Polymers and Their Use in Research and Industry
,”
Macromol. Symposia
,
82
, pp.
161
.
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