Performance improvement of a PEMFC system controlling the cathode outlet... Diego Feroldi (corresponding author), Maria Serra, Jordi Riera

Performance improvement of a PEMFC system controlling the cathode outlet...  Diego Feroldi (corresponding author), Maria Serra, Jordi Riera
Performance improvement of a PEMFC system controlling the cathode outlet air flow
Diego Feroldi (corresponding author), Maria Serra, Jordi Riera
Institut de Robòtica i Informàtica Industrial
Universitat Politècnica de Catalunya - Consejo Superior de Investigaciones Científicas
C. Llorens i Artigas 4, 08028 Barcelona, Spain
E-mail: dferoldi@iri.upc.edu
Telephone: 34 93 4015805; fax: 34 93 4015750
ABSTRACT
This paper presents a stationary and dynamic study of the advantages of using a regulating valve
for the cathode outlet flow in combination with the compressor motor voltage as manipulated
variables in a fuel cell system. At a given load current, the cathode input and output flowrate
determine the cathode pressure and stoichiometry, and consequently determine the oxygen partial
pressure, the generated voltage and the compressor power consumption. In order to maintain a
high efficiency during operation, the cathode output regulating valve has to be adjusted to the
operating conditions, specially marked by the current drawn from the stack. Besides, the
appropriate valve manipulation produces an improvement in the transient response of the system.
The influence of this input variable is exploited by implementing a predictive control strategy based
on Dynamic Matrix Control (DMC), using the compressor voltage and the cathode output
regulating valve as manipulated variables. The objectives of this control strategy are to regulate
both the fuel cell voltage and oxygen excess ratio in the cathode, and thus, to improve the system
performance. All the simulation results have been obtained using the MATLAB-Simulink
environment.
Keywords: PEMFC, Multivariable Control, Predictive Control, Dynamic Matrix Control, Performance
improvement
1
1. INTRODUCTION
Polymer Electrolyte Membrane (PEM) fuel cell systems are efficient devices which allow the
transformation of chemical energy stored in hydrogen to electric energy. In order to obtain this
transformation efficiently the global system, which includes several subsystems, must be considered. The
air supply is one of these subsystems, which has a great influence in the system efficiency. At the same
time, one of the most important challenges in fuel cell control is to assure sufficient amount of oxygen in
the cathode when current is drawn abruptly from the fuel cell stack. In this study the air supply subsystem
is composed by an air compressor, while the fuel supply subsystem relies on a pressurized hydrogen tank.
The hydrogen inlet flow rate is regulated by an independent control loop to maintain the working pressure
in the anode close to the pressure in the cathode. A schematic diagram of the system is showed in Fig. 1.
The PEM fuel cell system without a proper controller will not be able to withstand the load fluctuations
[1]. When an electric load is connected to the fuel cell, the control system must maintain the optimal
temperature, the membrane hydration and the partial pressure of the gases at both sides of the membrane
in order to avoid voltage degradation and fuel cell life shortening [2]. In particular, the air supply results
critical in the system performance because the oxygen reacts instantly as current is drawn, whereas the
oxygen supply is limited by the dynamics of the inlet manifold and the air compressor [3]. The operating
air pressure and the air stoichiometric ratio provided to the stack by the air supply subsystem, control the
oxygen partial pressure at the cathode catalyst layer. This partial pressure has major influence in the
cathode polarization and thus, in the conversion efficiency [4].
In several publications the control of air supply has been approached. In [5] is demonstrated the
convenience of regulating the oxygen excess ratio in the cathode to maximize the system net power. The
oxygen excess ratio or stoichiometric ratio is defined as the ratio of inlet oxygen flow to reacted oxygen
flow in the cathode. In [2], [5], [6] and [7], the control of oxygen excess ratio is approached through the
manipulation of the compressor motor voltage. In [2] and [5] feedforward control is employed,
meanwhile in [6] and [7] model based predictive control (MPC) is employed. These works indicate that
there is a severe conflict between oxygen excess control and net power dynamic response if no extra
power source is employed. This limitation arises from the fact that all the power required by the air
supply compressor comes from the fuel cell stack. In [6] supercapacitors are included as an ancillary
power source in order to support the power peaks.
2
The voltage applied to the compressor motor is a suitable manipulated variable in order to control the
oxygen excess ratio in the cathode, as it is showed in [2], [5], [6] and [7]. In this paper we propose to use
a regulating valve for the cathode outlet flow in combination with the compressor motor voltage as
manipulated variables to control both the oxygen excess ratio and the stack voltage. In [2], [5], [6] and
[7], the stack output voltage is let unregulated. However, depending on the application, the regulation of
the stack output voltage would be required.
The paper is organized as follows: In Section 2 a description of the fuel cell system model employed is
done. Stationary and transient analyses of system performance are done in Sections 3 and 4, respectively.
In Section 5, a control strategy based on predictive control is proposed. The results are presented in
Section 6 and, finally, conclusions are stated in Section 7.
2. PEM FUEL CELL SYSTEM MODEL DESCRIPTION
This work utilizes the PEM fuel cell model proposed by Pukrushpan et al. [2]. This nonlinear model is
used to represent the transient behaviour of the plant in the simulation analysis. The control oriented
model for automation applications includes the transient phenomenon of the compressor, the manifold
filling dynamics (both anode and cathode), reactant partial pressures, and membrane humidity. The stack
voltage predicted by the model depends on load current, partial pressure of hydrogen and oxygen, fuel
cell temperature and the contents of water in the membrane. Spatial variations are not included and
constant properties are assumed in all volumes. Only temporary variations are present. The model also
assumes that the inlet reactant flows in the cathode and in the anode can be humidified, heated and cooled
rapidly. With respect to the considered dynamics, the model neglects the fast dynamics of the
electrochemical reactions (time constant of 10-19 s). Temperature is treated as a constant parameter
because its slow behaviour (time constant of 102 s), allowing to be regulated by its own (slower)
controller. The model represents a 75 kW fuel cell system with 381cells. For more model details see [2].
3. STATIONARY ANALYSIS
As it has been mentioned, the air supply subsystem has a strong influence in fuel cell performance. On the
one hand, an insufficient air supply may cause oxygen starvation in the cathode, which causes voltage
reduction and membrane life shortening. On the other hand, the compressor operation implies a power
consumption that diminishes the system efficiency. The system efficiency is defined as [8]:
3
η sys =
VFC ( PFC − Paux )
PFC
1.482
(1)
where the constant 1.482 results of using the higher heating value of hydrogen (ΔH=286kJmol-1), VFC is
the fuel cell voltage, PFC is the fuel cell generated power and Paux is the power consumed by the auxiliary
equipment. The compressor power represents the major consumption in the auxiliary subsystem and is the
only parasitic power considered in this work.
The operation at a higher pressure increments the generated voltage as a result of the increment in the
cathode oxygen partial pressure and anode hydrogen partial pressure:
E = 1.229 − 0.85 × 10−3 (TFC − 298.15) + 4.3085 × 10−5 TFC ⎡⎣ln( pH 2 ) + 0.5ln( pO2 ) ⎤⎦
(2)
where E is the generated voltage in a single cell in open circuit in volts, TFC is the fuel cell temperature in
Kelvin, pH2 and pO2 are the cathode partial pressure of hydrogen and oxygen, respectively, in atm.
Nevertheless, an increment in the operating pressure implies a higher consumption of power in the air
compressor, contributing to a reduction in the system efficiency. In fact, an increment in the cathode
pressure produces an increment in the supply manifold pressure and thus, an increment in the pressure
ratio across the compressor and in the compressor power consumption. The power consumed by the air
compressor is:
PCM
γ −1
⎡
⎤
C pTatm ⎢⎛ psm ⎞ γ
⎥W
=
−
1
⎜
⎟
⎥ CP
ηCP ⎢⎝ patm ⎠
⎢⎣
⎥⎦
(3)
where WCP is the compressor air flow rate, PCM is the compressor power, Tatm is the inlet air temperature
in the compressor, ηCP is the compressor efficiency, psm is the supply manifold pressure, Cp is the specific
heat capacity of air, equal to 1004 J·kg-1·K-1 and γ is the ratio of the specific heats of air equal to 1.4.
The compressor motor voltage as a control input allows regulating the oxygen partial pressure in the
cathode. Augmenting the compressor voltage the oxygen partial pressure increases. However, the
compressor power consumption also increases. Thus, it is important to employ a complementary way to
increment the oxygen partial pressure. A diminution of the area of the valve that closes the cathode air
flow contributes to increase the cathode pressure and at the same time, contributes to decrease the air
flow, the stoichiometry, and the oxygen concentration. The consumption of the compressor has two
opposite trends: the trend to increase due to the pressure rise and the trend to decrease due to the flow
reduction. When all these effects are taken into account, there is a positive balance in the total efficiency
diminishing the valve area as we can observe analyzing the polarization (Fig. 2), efficiency (Fig. 3),
4
power compressor consumption (Fig. 4) and oxygen partial pressure curves (Fig. 5) plotted for two
different valve areas and a certain compressor voltage (Vcm = 140V). It is important to note that the
increase in the efficiency is not for all current densities. When the current density is high the flow and
concentration reduction have a greater influence than the pressure increase and the result is a decrease in
the oxygen partial pressure. In effect, the oxygen consumption is higher at higher current densities:
WO2 , rct =
M O2 n A
4F
i
(4)
where WO2,rct is the rate of oxygen reacted, MO2 is the molar mass of oxygen equal to 32 x 10-3 kg mol-1, n
is the cell’s number, A is the active cell area equal to 381 cm2, F is Faraday number equal to 96485 C and
i is the current density. Hence, the oxygen molar fraction in the cathode will be lower because of the
oxygen starvation.
Depending on the operating pressure, the increment in efficiency happens along different current density
ranges. With low operating pressures (lower compressor voltage, Vcm) the system efficiency increment
due to the valve closure occurs only at low current densities, whereas with higher operating pressures
(higher compressor voltage) the increment in system efficiency occurs along greater current densities
ranges. This can be seen in Fig. 6 to Fig. 8. For Vcm = 100V the efficiency increment occurs only for
current densities below 0.34 A·cm-2 (Fig. 6), for Vcm = 140V the increment occurs for current densities
below 0.67 A·cm-2 (Fig. 3), while for Vcm = 180V the increment occurs for al the current densities
analysed (Fig. 7). As can be seen in Fig. 8 for Vcm = 180V, the oxygen partial pressure rise, as a result of
diminishing the valve area, occurs at all current densities. In Fig. 9, it can be seen how the efficiency
changes with At for values between 20 to 40 cm2.
As a conclusion of this stationary analysis, it can be stated that the cathode output valve area as well as
the compressor motor voltage have to be adjusted in order to have high efficiency.
4. TRANSIENT ANALYSIS
Besides the possible performance improvement observed in the stationary analysis there is also an
improvement in the transient behaviour using the cathode air flow valve as a manipulated variable. A
preliminary transient analysis is made employing a DMC control strategy (the details of this control
strategy are explained in the next section). The controlled variable in this analysis is the stack voltage. A
stack current disturbance from 200A to 210A is applied to the fuel cell system in order to compare the
disturbance rejection capability of the system. A comparison between the transient responses obtained
5
using only the compressor voltage as a control variable and the one obtained by using the opening valve
area in combination with the compressor voltage is showed in Fig 10. The later shows a better behaviour
with a reduction in the stack voltage time response from 0.6s to 0.4s.
5. CONTROL STRATEGY
The advantages of using the opening valve area together with the compressor voltage are exploited
implementing a control strategy. This control strategy is based in Dynamic Matrix Predictive Control
(DMC) and has two control objectives: i) to regulate the oxygen excess ratio in the cathode, λO2, and ii)
the generated voltage, VFC. As we explained before, the control of λO2 is an indirect way to control the
system efficiency [5]. The load current, IFC, is considered as a disturbance to the fuel cell system. The
compressor motor voltage by itself is not able to control both control objectives. Nevertheless, with the
addition of the opening valve area control variable, At, this problem is solved. Therefore, the manipulated
variables are: u1 = Vcm and u2 = At.
The DMC uses the step response to model the process, taking into account only the p first samples until
the response tends to a constant value, assuming therefore that the process is asymptotically stable. Thus,
the predicted output can be expressed as:
(5)
ŷ = Gu + f
where:
⎛ g1
⎜
⎜ g2
⎜ M
G=⎜
⎜ gm
⎜ M
⎜
⎜g
⎝ p
0
g1
M
g m −1
M
g p −1
⎞
⎟
⎟
⎟
⎟
L
g1 ⎟
O
M ⎟
⎟
L g p − m +1 ⎟⎠
L
L
O
0
0
M
(6)
is the dynamic matrix constructed from the coefficients gi obtained from the step response with prediction
horizon p and control horizon m, u is the future control vector and f is free response, that means, the
response that not depends of future control movements [9].
The DMC controller objective is to minimize the difference between the consignees, w(t), and the process
outputs in a least square sense with the possibility of including a penalty term on the control signal:
p
m
J = ∑ R [ yˆ(t + j | t ) − w(t + j ) ] + ∑ Q [ Δu (t + j − 1) ]
j =1
2
2
j =1
6
(7)
where R and Q are diagonal weight matrixes. With the matrix R it is possible to compensate the different
ranges of values in the process outputs, meanwhile the matrix Q allows to give different weights to the
control signals.
If there are no restrictions in the manipulated variables, the minimization of the cost function J can be
realized making its derivative equal to zero, resulting:
U = (G T RG+Q)-1G T R(w-f)
(8)
Such as all the predictive control strategies, only the first element in the control vector calculated is sent
to the plant. In the next iteration the sequence of control is calculated again using actualized information
from the plant. The theoretical bases of the method are given in detail in [9].
There is a great interaction between the manipulated variables and the controlled variables, which makes
difficult the realization of a decentralized control of the system [10]. The DMC resolves efficiently the
interaction problem between manipulated variables and controlled variables. The multivariable controller
implemented employs in his control algorithm an extended dynamic matrix that takes into account the
interactions:
G12 ⎞
⎛G
G = ⎜ 11
⎟
⎝ G21 G22 ⎠
(9)
where each matrix Gij contains the coefficients of the i-th step response corresponding to the j-th input.
The matrix R and Q have now the following form:
⎛R
R=⎜ 1
⎜0
⎝
0⎞
⎛ Q1 0 ⎞
⎟; Q =⎜
⎟
⎟
⎜0 Q ⎟
R2 ⎠
⎝
2⎠
(10)
where Ri and Qi are diagonal matrixes of dimension p x p and m x m respectively. Thus, a centralized
multivariable controller it is proposed, which take into account the interactions between manipulated and
controlled variables.
6. RESULTS
The control horizon m, the prediction control p, and the matrixes R and Q were adjusted, in the control
algorithm, to achieve an adequate dynamic behaviour of the fuel cell system. The values of R and Q have
a strong influence on the transient response obtained. This is especially true for the weight matrix Q,
which reduces the control effort. The higher are the values in Q, the lower is the control effort, but the
7
response time is greater. The values chosen of Q and R are: Q1 = diag(1,1,…,1), Q2 =diag(0.5,0.5,…,0.5),
R1 = diag (5,5,…,5), R2=(1,1,…,1). The values of m and p are 100 and 15, respectively.
The internal model utilized by the DMC controller has been obtained through the linearization of the
nonlinear model described in Section 2 around the operating point corresponding Vcm = 187.5V, At = 20
cm2, Ist = 190A, which gives a net power of 40 kW.
The simulation results of the controlled system with variations in the load current are presented in Fig. 12
to Fig 15. In Fig. 11 the perturbation profile is showed. Fig. 12 and Fig. 13 show the controlled variables
(λO2 and VFC), while Fig. 14 and Fig. 15 show the manipulated variables (Vcm and At). As can be observed
in the figures, the implemented controller has a good disturbance rejection: the stack voltage response has
a peak (3.5% of VFC variation for 15% of IFC variation) that disappears in less than 0.5s, and the oxygen
excess ratio response presents a peak (30% of λO2 variation for the same IFC variation) that vanishes in
less than 1s.
The controller performance can be improved if the disturbance is measured and a step disturbance model
is included in the control model used to predict the plant outputs. Comparisons between measured and
non-measured disturbance approaches have been made. In Fig. 16 and Fig. 17 details of voltage stack and
oxygen excess ratio responses are showed, respectively. The results obtained show a substantial
improvement in the generated voltage response. The oxygen excess ratio response could be changed by
adjusting the values of the weight matrixes.
The control algorithm implements a compensation mechanism to rectify the inevitable model errors and
deal with non-measured disturbances. This compensation mechanism utilizes output values, and thus,
assures zero error at steady-state.
The simulation analysis shows a good performance in a wide operating range around the linearization
point despite the internal controller model is linear.
7. CONCLUSIONS
High efficiency level, long life cycle and good transient behaviour are fundamental issues for the success
of fuel cell systems in energy and automotive market. Through a steady-state analysis it is showed that
the system efficiency, in most of the current density range, can be improved by manipulating the cathode
outlet air flow valve. The dynamic analysis performed also shows a transient response improvement with
this additional manipulated variable. Taking advantage of these facts, this article proposes a control
8
strategy based on predictive control (DMC) that uses the compressor motor voltage together with the
cathode air flow valve area as manipulated variables. The controlled variables are the stack voltage and
the oxygen excess ratio. To predict the future process response, the control strategy makes use of a
process model that is easily obtainable through step response. The simulation analysis shows an
appropriate dynamic response, which can still be improved with the inclusion of the disturbance model.
The control objectives have been accomplished with reduced control effort. This effort can be further
reduced modifying the values of the matrix Q. This is particularly important because of practical
limitations in the manipulated variables.
Acknowledgments
This work has been funded partially by the project CICYT DPI2004-06871-C02-01 of the Spanish
Government, and the support of the Department of Universities, Investigation and Society of Information
of the Generalitat de Catalunya.
NOMENCLATURE
A
fuel cell active area (cm2)
At
cathode output valve area (cm2)
Cp
specific heat capacity of air (1004 J·kg-1·K-1)
E
single cell open circuit voltage (V)
F
Faraday number (96485 C)
f
output free response
G
controller dynamic matrix
gi
dynamic matrix coefficients
I
stack current (A)
i
current density (A cm-2)
J
cost function
MO2
oxygen molar mass (32 x 10-3 kg mol-1)
m
control horizon
n
number of cells in the stack
P
power (W)
9
p
prediction horizon
pO2,pH2 oxygen and hydrogen partial pressure (Pa)
Q, R
weight matrixes
T
temperature (K)
t
time (s)
u
control variable
U
future control vector
V
voltage (V)
W
flow rate (kg s-1)
w
output setpoint
ŷ
predicted output
Subscripts and superscripts
atm
atmospheric
aux
auxiliary
CM
compressor motor
CP
compressor
i, j
index
FC
fuel cell
rct
reacted
sys
system
T
transposed
Greek letters
γ
ratio of the specific heats of air (1.4)
ΔH
higher heating value of hydrogen (286 kJ)
η
efficiency
λO2
oxygen excess ratio
10
References
[1] S. Yerramalla, A. Davari, A. Feliachi, T, Biswas, J. of Power Sources, 124 (2003) pp. 104-113.
[2] J. Pukrushpan, H. Peng, A. Stefanopoulou, J. of Dynamics Systems, Measurement, and Control. 126
(2004) 14-25.
[3] J. Larminie, A. Dicks, Fuel Cell systems explained, Wiley, New York, 2000, pp.
[4] D. Friedman, R. Moore, Electrochemical Society Proceedings, 27 (1998) pp. 407-423.
[5] M. Grujicic, K. Chittajallu, E. Law, J. Pukrushpan, J. of Power and Energy, 218 (2004) 487-499.
[6] A. Vahidi, A. Stefanopoulou, H. Peng, Proceedings of the American Control Conference, (2004) 834839.
[7] J. Golbert, D. Lewin, J. of Power Sources, 135 (2004) 135-151.
[8] F. Barbir, PEM Fuel Cells: Theory and Practice, Elsevier, 2005, pp. 280-288.
[9] E. Camacho, C. Bordons, Model Predictive Control, Springer-Verlag, Londres, 1999, pp. 33-39.
[10] M Serra, A. Husar, D. Feroldi, J. Riera, J. of Power Sources, 158 (2006) 1317–1323
11
Electric Load
DC/DC
Converter
-
+
Air Inlet Flow
H2 Inlet Flow
Air
Supply
Fuel Cell
Air Outlet
Flow
Compressor
voltage
Valve
area
Oxygen excess
ratio
Stack
voltage
Hydrogen
Supply
Load current
Fig. 1. PEM fuel cell system
1
2
Vcm = 140V; At = 20 cm
2
Vcm = 140V; At = 40 cm
0.9
Cell voltage [V]
0.8
0.7
0.6
0.5
0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
-2
Current density [A cm ]
Fig. 2. Polarization curves with Vcm = 140V and different valve area
12
0.7
0.8
0.9
45
40
35
Efficiency [%]
30
2
Vcm = 140V; At = 20 cm
25
2
Vcm = 140V; At = 40 cm
20
15
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
-2
Current density [A cm ]
0.7
0.8
0.9
Fig. 3. Efficiency curves with Vcm = 140V and different valve area
3.9
2
Vcm = 140V; At = 20 cm
2
Vcm = 140V; At = 40 cm
Compressor power [kW]
3.8
3.7
3.6
3.5
3.4
3.3
0.1
0.2
0.3
0.4
0.5
0.6
-2
Current density [A/cm ]
0.7
0.8
Fig. 4. Compressor power consumption curves with Vcm = 140V and different valve area
13
0.9
28
2
Vcm = 140V; At = 20 cm
26
2
Vcm = 140V; At = 40 cm
O2 partial pressure [kPa]
24
22
20
18
16
14
12
10
8
0.1
0.2
0.3
0.4
0.5
0.6
-2
Current density [A cm ]
0.7
0.8
0.9
Fig. 5. Oxygen partial pressure curves with Vcm = 140V and different valve area
50
2
Vcm = 100V; At = 20 cm
2
Vcm = 100V; At = 40 cm
45
Efficiency [%]
40
35
30
25
20
0
0.1
0.2
0.3
0.4
0.5
0.6
-2
Current density [A cm ]
Fig. 6. Efficiency curves with Vcm =100V and different valve area
14
0.7
0.8
0.9
45
40
35
2
Vcm = 180V; At = 20 cm
Efficiency [%]
30
2
Vcm = 180V; At = 40 cm
25
20
15
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
-2
Current density [A/cm ]
0.7
0.8
0.9
Fig. 7. Efficiency curves with Vcm =180V and different valve area
40
2
Vcm = 180V; At = 20 cm
2
Vcm = 180V; At = 40 cm
O2 partial pressure [kPa]
35
30
25
20
15
0.1
0.2
0.3
0.4
0.5
0.6
-2
Current density [A cm ]
0.7
Fig. 8. Oxygen partial pressure curves with Vcm =180V and different valve area
15
0.8
0.9
42
40
Efficiency [%]
38
36
2
At =20cm
2
At =25cm
34
2
At =30cm
2
At =35cm
32
2
At =40cm
30
0.2
0.3
0.4
0.5
0.6
-2
Current density [A cm ]
0.7
0.8
0.9
Fig. 9. Efficiency curves with Vcm =180V and different valve area
251
250.5
Vcm and At
Vcm
Stack voltage [V]
250
249.5
249
248.5
248
247.5
24.8
25
25.2
25.4
25.6
25.8
Time [s]
Fig. 10. Comparative between stack voltage responses
16
26
26.2
26.4
26.6
26.8
220
210
Ist (A)
200
190
180
170
160
0
5
10
15
20
25
30
35
20
25
30
35
Time (s)
Fig. 11. Fuel cell stack current
3
2.8
2.6
λO2
2.4
2.2
2
1.8
1.6
0
5
10
15
Time (s)
Fig. 12. Oxygen excess ratio
17
258
256
254
VFC (V)
252
250
248
246
244
242
0
5
10
15
20
25
30
35
20
25
30
35
Time (s)
Fig. 13. Fuel cell stack voltage
210
205
200
Vcm (V)
195
190
185
180
175
170
165
0
5
10
15
Time (s)
Fig. 14. Compressor motor voltage
18
35
30
20
2
At (cm )
25
15
10
5
0
0
5
10
15
20
25
30
35
Time (s)
Fig. 15. Cathode air flow opening valve area
252
251
250
Non-measured disturbance
Measured disturbance
249
VFC (V)
248
247
246
245
244
243
242
241
19
19.5
20
20.5
21
Time (s)
21.5
22
22.5
23
Fig. 16. Comparative between stack voltage response with measured and non measured disturbance
19
Non-measured disturbance
Measured disturbance
2.4
2.3
2.2
λO2
2.1
2
1.9
1.8
1.7
19
19.5
20
20.5
21
21.5
Time (s)
22
22.5
23
23.5
24
Fig. 17. Comparative between oxygen excess ratio response with measured and non measured disturbance
20
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