Method for estimating the oxygen concentration in internal combustion engines
A method for estimating the oxygen concentration in an internal combustion engine that includes, but is not limited to an intake manifold, an exhaust manifold, an EGR system, a throttle valve, an air mass sensor for measuring a fresh air flow ({dot over (m)} thr ) entering the intake manifold through the throttle valve, and cylinders. The method includes, but is not limited to the steps of estimating the total gas flow ({dot over (m)} o ) entering the cylinders, calculating the EGR gas flow ({dot over (m)} egr ), calculating the air fraction (f — air — em ) of the gas flowing in the exhaust manifold, calculating the air mass (m im — air ) entering the cylinders based on the air fraction (f — air — em ) in the exhaust manifold, on the total gas flow ({dot over (m)} o ) entering the cylinders, on the EGR gas flow ({dot over (m)} egr ) and on the fresh air flow ({dot over (m)} thr ), calculating the total mass (m im ) in the intake manifold based on the fresh air flow ({dot over (m)} thr ), on the EGR gas flow ({dot over (m)} egr ) and on the total gas flow ({dot over (m)} o ) entering the cylinders, calculating the air fraction (f air — im ) in the intake manifold based on the air mass (m im — air ) entering the cylinders and the total mass (m im ) in the intake manifold, and calculating the oxygen mass concentration ([O 2 ] m — im ) in the intake manifold based on the air fraction (f air — im ) in the intake manifold.
1. A method for estimating an oxygen concentration in an internal combustion engine comprising an intake manifold, an exhaust manifold, an EGR system, a throttle valve, an air mass sensor for measuring a fresh air flow ({dot over (m)} thr ) entering the intake manifold through the throttle valve, and a plurality of cylinders, the comprising the steps of:
estimating a total gas flow ({dot over (m)} o ) entering the plurality of cylinders;
calculating an EGR gas flow ({dot over (m)} egr );
calculating an air fraction (f — air — em ) of a gas flowing in the exhaust manifold;
calculating a air mass (m im — air ) entering the plurality of cylinders based at least in part on the air fraction (f — air — em ) in the exhaust manifold, the total gas flow ({dot over (m)} o ) entering the plurality of cylinders, the EGR gas flow ({dot over (m)} egr ), and the fresh air flow ({dot over (m)} air );
calculating a total mass (m im ) in the intake manifold based at least in part on the fresh air flow ({dot over (m)} thr ), the EGR gas flow ({dot over (m)} egr ), and the total gas flow ({dot over (m)} o ) entering the plurality of cylinders;
calculating the air fraction (f air — im ) in the intake manifold based at least in part on the air mass (m im — air ) entering the plurality of cylinders and the total mass (m im ) in the intake manifold; and
calculating a oxygen mass concentration ([O 2 ] m — im ) in the intake manifold based on the air fraction (f air — im ) in the intake manifold.
2. The method of claim 1 , wherein an estimation of the total gas flow ({dot over (m)} o ) entering the plurality of cylinders and of the EGR gas flow ({dot over (m)} egr ) comprise the steps of:
determining an estimated pressure (p im ) and a measured pressure (p im — sens ) in the intake manifold; and
estimating a theoretical total gas flow ({dot over (m)} oTH ) entering the plurality of cylinders.
3. The method according to any of claim 2 , wherein the theoretical total gas flow ({dot over (m)} oTH ) entering the plurality of cylinders is calculated according to the following equation:
m
.
oTH
=
p
im
R
im
T
im
η
vol
V
d
N
eng
120
where η vol is a volumetric efficiency of the internal combustion engine, N eng is a speed engine (rpm) and V d is an engine displacement.
4. The method according to any of the claim 2 , wherein the total gas flow ({dot over (m)} o ) entering the plurality of cylinders is calculated according to the following equation:
{dot over (m)} o ={dot over (m)} oTH +P.I. ( p im — sens −p im )
where P.I. is a predetermined proportional-integral controller.
5. The method of claim 1 , wherein an estimation of the total gas flow ({dot over (m)} o ) entering the plurality of cylinders and of the EGR gas flow ({dot over (m)} egr ) comprises the steps of:
determining an estimated pressure (p im ) and a measured pressure (p im — sens ) in the intake manifold;
estimating a theoretical EGR gas flow ({dot over (m)} egrTH ); and
estimating a theoretical total gas flow ({dot over (m)} oTH ) entering the plurality of cylinders.
6. The method of the claim 1 , further comprising the step of determining an estimated temperature (T im ) in the intake manifold,
wherein an estimated pressure (p im ) in the intake manifold is calculated according to the following equation:
p
im
=
R
im
m
im
T
im
V
im
(
10
)
where V im is a constant representative of a geometrical volume of the intake manifold, and R im is the constant R of the gas.
7. The method of the claim 6 , further comprising the steps of measuring a temperature (T im — sens ) in the intake manifold,
wherein the estimated temperature (T im ) in the intake manifold is calculated according to the following equations:
T
im
_
ideal
=
p
im
_
sens
V
im
R
im
m
im
{
T
im
_
obs
=
(
L
.
P
.
F
)
T
im
T
im
=
T
im
_
ideal
+
P
..
I
.
(
T
im
_
sens
-
T
im
_
obs
)
where V im is a constant representative of the geometrical volume of the intake manifold, R im is the constant R of the gas, L.P.F is a predetermined low pass filter and T im — obs is an observed temperature value generated by a low pass filter model taking into account a temperature sensor time constant.
8. The method of claim 6 , further comprising the step of measuring a temperature (T thr ) of the gas flowing through the throttle valve and a temperature (T egr ) of the gas flowing through an EGR valve of the EGR system,
wherein the estimated temperature (T im ) of the intake manifold is calculated according to the following equation:
ⅆ
p
im
ⅆ
t
=
R
im
c
v
im
V
im
[
m
.
thr
T
thr
c
p
thr
+
m
.
egr
T
egr
c
p
egr
-
m
.
o
T
im
c
p
im
]
where c vim is a gas constant volume specific heat, c pim is a constant pressure gas specific heat, V im is a constant representative of the geometrical volume of the intake manifold, R im is the constant R of the gas, c pegr is a constant pressure specific heat of the EGR gas flow and c pthr is the constant pressure specific heat of a throttle air flow.
9. The method according to claim 1 , wherein the EGR gas flow ({dot over (m)} egr ) is calculated according to the following equation:
{dot over (m)} egr ={dot over (m)} oTH −{dot over (m)} thr +P ( p im — sens −p im )
where P is a predetermined proportional factor.
10. The method according to claim 1 , wherein the EGR gas flow ({dot over (m)} egr ) is calculated according to the following equation:
{dot over (m)} egr ={dot over (m)} egrTH +P.I. ( p im — sens −p im )
where P.I. is a predetermined proportional-integral controller.
11. The method according to claim 1 , wherein the air fraction (f — air — em ) of the gas flowing in the exhaust manifold is calculated according to the following equation:
f
air
_
em
=
f
air
_
im
m
.
o
-
(
A
/
F
)
st
m
.
fuel
m
.
o
+
m
.
fuel
where (A/F) st is a stoichiometric air to fuel ratio and {dot over (m)} fuel is a predetermined fuel mass introduced into the plurality of cylinders.
12. The method according to claim 1 , wherein the air mass (m im — air ) entering the plurality of cylinders is calculated according to the following equation:
ⅆ
m
im
_
air
ⅆ
t
=
m
.
thr
+
f
air
_
em
m
.
egr
-
f
air
_
im
m
.
o
13. The method according to claim 1 , wherein the total mass (m im ) is calculated according to the following equation:
ⅆ
m
im
ⅆ
t
=
m
.
thr
+
m
.
egr
-
m
.
o
14. The method according to claim 1 , wherein the air fraction (f air — im ) in the intake manifold is calculated according to the following equation:
f
air
_
im
=
m
im
_
air
m
im
15. The method according to claim 1 , wherein the oxygen mass concentration ([O 2 ] m — im ) in the intake manifold is calculated according to the following equations:
[
O
2
]
m
_
im
=
[
O
2
]
m
_
air
f
air
_
im
[
O
2
]
v
_
im
=
(
M
N
2
/
M
O
2
)
[
O
2
]
m
_
im
1
+
(
M
N
2
/
M
O
2
-
1
)
[
O
2
]
m
_
im
where [O 2 ] m — air is the oxygen mass concentration in pure air, [O 2 ] v — im is a oxygen volume concentration and M N2 and M O2 are nitrogen and oxygen molecular weights.
16. A method for estimating an oxygen concentration in an internal combustion engine comprising an intake manifold, an exhaust manifold, an EGR system, a throttle valve, an air mass sensor for measuring a fresh air flow ({dot over (m)} thr ) entering the intake manifold through the throttle valve, and a plurality of cylinders, the comprising the steps of:
estimating a total gas flow ({dot over (m)} o ) entering the plurality of cylinders;
calculating an EGR gas flow ({dot over (m)} egr );
calculating an air fraction (f — air — em ) of a gas flowing in the exhaust manifold;
calculating a air mass (m im — air ) entering the plurality of cylinders based at least in part on the air fraction (f — air — em ) in the exhaust manifold, the total gas flow ({dot over (m)} o ) entering the plurality of cylinders, the EGR gas flow ({dot over (m)} egr ), and the fresh air flow ({dot over (m)} thr );
calculating a total mass (m im ) in the intake manifold based at least in part on the fresh air flow ({dot over (m)} thr ), the EGR gas flow ({dot over (m)} egr ), and the total gas flow ({dot over (m)} o ) entering the plurality of cylinders;
calculating the air fraction (f air — im ) in the intake manifold based at least in part on the air mass (m im — air ) entering the plurality of cylinders and the total mass (m im ) in the intake manifold;
calculating an oxygen mass concentration ([O 2 ] m — im ) in the intake manifold based on the air fraction (f air — im ) in the intake manifold;
determining an estimated temperature (T im ) in the intake manifold,
wherein an estimated pressure (p im ) in the intake manifold is calculated according to the following equation:
p im =R im m im T im /V im (10)
where V im is a constant representative of a geometrical volume of the intake manifold, and R im is the constant R of the gas; and
measuring a temperature (T thr ) of the gas flowing through the throttle valve and a temperature (T egr ) of the gas flowing through an EGR valve of the EGR system, wherein the estimated temperature (T im ) of the intake manifold is calculated according to the following equation:
T
im
=
m
.
thr
T
thr
+
m
.
egr
T
egr
m
.
thr
+
m
.
egr
.