Engine air/fuel ratio sensing device

An engine air/fuel ratio sensing device for measuring the oxygen partial pressure or concentration in the exhaust gas of an engine. The device has a sensor and a control circuit coupled to each other. The sensor consists of an electrolyte oxygen pump cell and an electrolyte oxygen sensor cell, both cells having a gap portion therebetween. The control circuit provides a pumping current through a current limiting resistor to the pump cell and measures two terminal voltages across the current limiting resistor to derive the actual pump current and the internal resistance of the pump cell which are used to correct the actual pump current to a proper pump current dependent on the temperature to which the sensor is exposed, in accordance with a predetermined equation.

BACKGROUND OF THE INVENTION 
This invention relates to a device for measuring an oxygen concentration 
within an exhaust gas from an internal combustion engine etc., to sense 
the air/fuel (hereinafter abbreviated as A/F) ratio and in particular to 
an improved engine A/F ratio sensing device of an oxygen pump type 
constructed using an ion conducting solid electrolyte. 
It is hitherto well known in the art to control e.g. an engine of an 
automobile to run at a stoichiometric (theoretical) A/F ratio by sensing 
its combustion state in relation to the stoichiometric A/F ratio according 
to the variation of an electromotive force produced by the difference of 
the oxygen partial pressure between the exhaust gas and the atmosphere by 
means of an oxygen sensor constructed with an ion conducting solid 
electrolyte such as stabilized zirconia. 
When the A/F ratio which is given by the weight ratio of air to fuel is the 
stoichiometric A/F ratio of 14.7, the above type oxygen sensor can provide 
a large output variation, while outside the stoichiometric A/F ratio it 
provides a substantially null output variation. Therefore, when the engine 
is operated at an A/F ratio outside the stoichiometric A/F ratio, the 
output of such an oxygen sensor can not be utilized. 
Thus, an A/F ratio sensor of an oxygen pump type which eliminates such a 
disadvantage and enables the engine to be operated at any A/F ratio has 
already been proposed. However, such a sensor is not practical for the 
reason of an outstanding variation of its characteristic due to 
temperature variation. 
FIG. 1 shows an arrangement of an A/F ratio sensing device of an oxygen 
pump type, and FIG. 2 shows a cross sectional view of the sensor in FIG. 1 
taken along line II--II, which is disclosed in a related application Ser. 
No. 606,926 filed May 4, 1984. 
In FIG. 1, within an exhaust pipe 1 of an engine (not shown) an A/F ratio 
sensor, generally designated by a reference numeral 2, is disposed. This 
sensor 2 is formed of a solid electrolyte oxygen pump cell 3, a solid 
electrolyte oxygen sensor cell 4, and a supporting base 5. The solid 
electrolyte oxygen pump cell 3 includes an ion conducting solid 
electrolyte (stabilized zirconia) 6 in the form of a plate with a 
thickness of about 0.5 mm having platinum electrodes 7 and 8 disposed on 
the respective sides thereof. The solid electrolyte oxygen sensor cell 4, 
similar to the pump cell 3, includes an ion conductive solid electrolyte 9 
in the form of a plate having platinum electrodes 10 and 11 disposed on 
the respective sides thereof. The supporting base 5 supports the oxygen 
pump cell 3 and the oxygen sensor cell 4 so that they are oppositely 
disposed having a minute gap "d" of about 0.1 mm therebetween. 
An electronic control unit 12 is electrically coupled to the pump cell 3 
and the sensor cell 4. More specifically, the electrode 10 is connected 
through a resistor R1 to the inverting input of an operational amplifier 
A, the non-inverting input of which is grounded through a DC reference 
voltage source V. This DC reference voltage serves to control the output 
voltage of the sensor cell 4 to assume said voltage V according to the 
oxygen partial pressure difference between those within the gap and 
outside the gap. The electrode 7 is connected through a resistor Rs to the 
emitter of a transistor Tr whose collector is grounded through a DC power 
source B and whose base is connected to the output of the operational 
amplifier A and the inverting input of the operational amplifier A through 
a capacitor C. The electrodes 8 and 11 are grounded. 
U.S. Pat. No. 4,272,329 discloses the principle of an A/F ratio sensing 
device of an oxygen type. 
In operation, when the oxygen partial pressure within the gap portion 
between the cells 3 and 4 is the same as the oxygen partial pressure 
outside the gap portion, the sensor cell 4 generates no electromotive 
force. Therefore, the inverting input of the operational amplifier A 
receives no voltage and, accordingly the operational amplifier A provides 
as an output therefrom a maximum voltage corresponding to the reference 
voltage V to the base of the transistor Tr. Therefore, the transistor Tr 
is made conductive to cause a pump current Ip to flow through the 
electrodes 7 and 8 of the pump cell 3 from the voltage source B. Then the 
pump cell 3 pumps oxygen present in the gap portion "d" into the exhaust 
pipe 1. As a result, the sensor cell 4 develops an electromotive force "e" 
thereacross according to the oxygen partial pressure difference on both 
sides of the cell 4. 
Therefore, the oxygen sensor cell 4 applies the electromotive force "e" 
generated across the electrodes 10 and 11 to the inverting input of the 
operational amplifier A through the resistor R1. The operational amplifier 
A provides an output now proportional to the difference between the 
electromotive force "e" and the reference DC voltage V applied to the 
non-inverting input. The output of the operational amplifier A drives the 
transistor Tr to control the pump current Ip. 
Thus, the electromotive force "e" approaches the reference voltage V. 
Accordingly, the control unit 12 reaches an equilibrium state and serves 
to provide a pump current Ip necessary for keeping the electromotive force 
"e" at the predetermined reference voltage V. The resistor Rs serves to 
provide an output corresponding to the pump current Ip supplied from the 
DC power source B as a pump current supply means. The pump current Ip 
corresponds to an A/F ratio value. This pump current Ip is converted into 
a voltage by the resistor Rs and is sent to a fuel control unit (not 
shown) so that the fuel control unit may be controlled at a desired A/F 
ratio. The resistance of the resistor Rs is selected so as to prevent the 
pump current Ip from flowing excessively from the DC power source B. The 
capacitor C forms an integrator associated with the operational amplifier 
A and serves to make the electromotive force "e" precisely coincident with 
the reference voltage V. 
One example of the static characteristics of an A/F ratio sensing device of 
an oxygen pump type thus constructed in the form of a negative feedback 
control is shown in FIG. 3. A solid line indicates a characteristic of 
pump current Ip as a function of A/F ratio when the A/F ratio sensor 2 is 
exposed at 600.degree. C. while a dotted line indicates a characteristic 
at 800.degree. C. It is found that such a characteristic variation gives 
rise to the thermal variation of the ion conductivity of the ion 
conducting solid electrolytes 6 and 9, respectively forming the solid 
electrolyte oxygen pump cell 3 and the solid electrolyte oxygen sensor 
cell 4. Experiments reveal that as the temperature of the A/F ratio sensor 
is varied over a temperature range of an engine exhaust gas, the current 
Ip, flowing through the oxygen pump cell 3, corresponding to the same A/F 
ratio varies up to several ten percentages thereof, resulting in an 
unpractical A/F ratio sensor. 
On the other hand, FIG. 4 shows a temperature dependency of the electrical 
resistance of the ion conducting solid electrolytes 6 and 9. Since this 
characteristic is common to various solid electrolytes, the application of 
this characteristic shown in FIG. 4 enables the temperature variation of 
the A/F ratio sensor to be corrected. 
SUMMARY OF THE INVENTION 
It is accordingly an object of the invention to provide an A/F ratio 
sensing device of an oxygen pump type, free from such a thermal 
characteristic variation as above noted, by the detection of the thermal 
characteristic variation the A/F ratio sensor per se from the variation of 
its internal resistance and by the correction of same. 
In order to accomplish this object, the present invention provides an 
air/fuel ratio sensing device for an engine comprising an air/fuel sensor 
means having a gap portion for introducing an exhaust gas of the engine, a 
solid electrolyte oxygen pump cell for controlling an oxygen partial 
pressure within the gap portion, and a solid electrolyte oxygen sensor 
cell for producing an electromotive force corresponding to the difference 
between the oxygen partial pressure in the exhaust gas within the gap 
portion and the oxygen partial pressure in the exhaust gas outside the gap 
portion; and a control circuit means, coupled to the sensor means, having 
a current amplifier means for supplying to the oxygen pump cell a pump 
current necessary for keeping the oxygen partial pressure at a 
predetermined value, and a resistor inserted in the electrical path 
through which the pump current flows for limiting the pump current to a 
predetermined value, the control circuit means further comprising: a 
voltage measuring means, connected to the resistor, for measuring and 
providing as outputs therefrom the terminal voltage across the resistor 
and the terminal voltage across the oxygen pump cell, a computing means, 
connected to the voltage measuring means, for calculating from the 
terminal voltage across the resistor and the resistance of the resistor a 
first value corresponding to the pump current and for calculating from the 
first value and the terminal voltage across the oxygen pump cell a second 
value corresponding to the internal resistance of the oxygen pump cell, 
and a calibrating means, connected to the computing means, for providing 
as an air/fuel signal therefrom a third value obtained by calibrating the 
first value in accordance with a predetermined relationship including the 
first value and the second value as a parameter. 
The calibrating means preferably comprises a storage means for storing a 
plurality of typical values representative of the first and second values 
as well as numerical values respectively corresponding to the combinations 
of the first and second values, and a computing means for searching four 
of the numerical values respectively corresponding to the combinations of 
respective two typical values sandwiching the respective values of the 
first and second values and for calculating a numerical value, as the 
third value, corresponding to the combination of the first and second 
values by means of an interpolating operation from the four numerical 
values. 
The calibrating means calculates the third value (Ipo) from a calibrating 
equation Ipo=Ip(1+J.times.1nR/Ro).sup.C by using the first value (Ip) and 
second value (R), Ro, J, and C being constants. Also, the calibrating 
means calculates the third value (Ipo) from a calibrating equation 
Ipo=Ip{1+CJ.times.1n(R-Ro)/Ro} by using the first value (Ip) and second 
value (R), Ro, J, and C being constants. The constant C is preferably in 
the range of about 0.75-1.0.

Throughout the figures, the same reference numerals indicate identical or 
corresponding portions. 
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
One preferred embodiment of an A/F ratio sensing device of an oxygen pump 
type for an engine in accordance with the present invention will now be 
described in detail with reference to the accompanying drawings, 
particularly FIGS. 5 and 6. 
In FIG. 5, the difference between the arrangement of this invention and 
that of FIG. 1 is the provision of a control unit 12'. More specifically, 
this control unit 12', in addition to the control unit 12 having the same 
arrangement as that shown in FIG. 1, includes an A/D converter 13 of a two 
channel type, and computing portions 14-18. The two inputs of the A/D 
converter 13 are connected across the resistor Rs. The input of the 
computing portion 14 is connected to one output of the A/D converter 13 to 
calculate a terminal voltage v1-v2 across the resistor Rs. The input of 
the computing portion 15 is connected to the output of the computing 
portion 14 to calculate the pump current Ip by dividing v1-v2 by the 
resistance Rs. The one input of the computing portion 16 is connected to 
the other output of the A/D converter 13 and the other input of same is 
connected to the output of the computing portion 15 to calculate the 
internal resistance R of the oxygen pump cell 3 by dividing the terminal 
voltage v2 across the oxygen pump cell 3 by the pump current Ip. The two 
inputs of the computing portion 18 are respectively connected to the 
outputs of the computing portions 15 and 16 to calculate a proper pump 
current Ipo by correcting the pump current Ip with respect to the internal 
resistance R. 
In the arrangement of FIG. 5, the terminal voltages v1 and v2 of the 
resistor Rs are given by the following equations: 
EQU v1=Ip(Rs+R) (1) 
EQU v2=IpR (2) 
The terminal voltages v1 and v2 are respectively converted into digital 
signals by the A/D converter 13 for the facilitation of the computation 
processes, and the digitalized terminal voltages v1 and v2 are provided 
for the computing portion 14 which calculates the difference between the 
terminal voltages v1 and v2. This difference is divided by the resistance 
Rs in the computing portion 15 whose output therefore assumes 
(v1-v2)/Rs={Ip(Rs+R)-IpR}/Rs=Ip from equations (1) and (2), resulting in 
the calculation of the pump current Ip. In the computing portion 16, the 
terminal voltage v2 is divided by the output of the computing portion 15, 
i.e., Ip. Therefore, the output of the computing portion 16 assumes 
v2/Ip=IpR/Ip=R from equation (2), resulting in the calculation of the 
internal resistance R of the oxygen pump cell 3. This internal resistance 
R together with the pump current Ip are inputed to the computing portion 
18 in which the pump current Ip is corrected, i.e., calibrated to the pump 
current Ipo in a reference temperature To. The calibration is made on the 
basis of the relationship as described hereinbelow. 
When the pump current Ip is controlled so as to keep the electromotive 
force "e" of the oxygen sensor cell 10 at a constant value, the 
relationships 
EQU e=(RT/4F)1n(Pa/Pv) (3) 
EQU Ip=(4eDA/KTL)(Pa-Pv) (4) 
are established. Equation (3) is the famous Nernst's equation wherein Pa 
and Pv respectively designate oxygen partial pressures inside and outside 
the gap "d" as parameters representative of A/F ratio. It is to be noted 
that R designates the gas constant, F the Faraday's constant, and T 
temperature. Equation (4) indicates a relationship given at the time when 
a rate of oxygen pumped out of the gap "d" by the pump current Ip 
equilibrates with a rate of oxygen flown in the gap "d" by diffusion, in 
which e designates the electric charge of electron, D the diffusion 
coefficient, A the cross sectional area of the opening of the gap "d", K 
the Boltzmann's constant, and L the effective diffusion path length. From 
equations (3) and (4), we obtain 
EQU Ip=(4eDA/KTL)Pa (5) 
On the other hand, it is known that the diffusion coefficient D of gas is 
proportional to the 1.75th power of temperature. Therefore, assuming the 
proportion constant be G, D=GT.sup.1.75 is given. By substituting this in 
equation (5), we obtain 
EQU Ip=(4eGA/KL)T.sup.0.75 .times.Pa (6) 
Namely, it is found that the pump current Ip is proportional to the oxygen 
partial pressure Pa, i.e., A/F ratio and the 0.75th power of temperature 
T. In equation (6), assuming the pump current at the reference temperature 
To be Ipo, we obtain 
EQU Ipo=(4eGA/KL)To.sup.0.75 .times.Pa (7) 
From equations (6) and (7), we obtain 
EQU Ipo=Ip(To/T).sup.0.75 (8) 
Equation (8) indicates that the pump current Ip at an arbitrary temperature 
T can be calibrated to the pump current Ipo at the reference temperature 
To. It is to be noted that various experiments show that since equation 
(8) can not realize a precise calibration due to some effect caused by the 
structure of the sensor as well as temperature ununiformity and so on, it 
is desirable to express 
EQU Ipo=Ip(To/T).sup.C (9) 
and to determine the exponent C based on practically measured data. Also in 
the arrangement of FIG. 5, it has been found according to experiments that 
C is preferably in the order of 0.75-1.0. 
On the other hand, it is known that the relationship between the internal 
resistance R of the solid electrolyte and temperature T is given by 
EQU To/T=1+(To/B).times.1nR/Ro (10) 
It is to be noted that Ro designates a resistance which the solid 
electrolyte exhibits at the reference temperature To and B is a constant. 
By substituting equation (10) in equation (9), we get 
EQU Ipo=Ip(1+J.times.1nR/Ro).sup.C (11) 
where J=To/B. Hence, the computing portion 18 performs the calculation of 
equation (11) by using the pump current Ip which is the output of the 
computing portion 15 and the resistance R which is the output of the 
computing portion 16, thereby determining the pump current Ipo at the 
reference temperature To. 
It is to be noted that if a micro-processor which is hard to perform a 
logarithm calculation or an exponential calculation is used as the 
computing portion 18, the pump current Ipo at the reference temperature To 
may be simply determined by the following equation 
EQU Ipo=Ip{1+CJ(R-Ro)/Ro} (12) 
which is a first order equation approximated instead of equation (11). 
Also, an interpolating calculation may be made in the computing portion 18 
by using map data shown in FIG. 6 and stored in a memory in the computing 
portion 18. The abscissa of the map data denotes typical points R1, R2, 
R3, --, Rn, Rn+1, --of the resistance R and the ordinate denotes typical 
points Ip1, Ip2, Ip3, --, Ipn, Ipn+1, --of the pump current Ip. Each of 
the cross points of the typical points on the abscissa and the ordinate 
indicates the pump current Ipo calibrated corresponding to the reference 
resistance Ro, i.e., the reference temperature To. 
In this map data, for example, should the current Ip determined in the 
computing portion 15 be equal to Ip3 and the resistance R determined in 
the computing portion 16 be equal to R3, the value Ipon,3 stored in the 
memory in the computing portion 18 is outputed as the current Ipo. 
Further, for example, should the current Ip determined in the computing 
portion 15 be a value which is between the tabulated values Ipn and Ipn+1, 
and the resistance R determined in the computing portion 16 be a value 
which is between the tabulated values Rn and Rn+1, an interpolating step 
is performed in the portion 18 according to conventional methods. Namely, 
from the combinations of typical point Rn which is smaller than and 
closest to the resistance R and of the typical points Ipn and Ipn+1 
sandwiching the pump current Ip (i.e., the tabulated values closest to the 
current Ip), two calibrated pump currents(Ipon,n) and (Ipon+1,n) are 
retrieved by the operation of the computing portion 18. From the 
combination of the retrieved values (Ipn,Ipon,n) and (Ipn+1, Ipon+1,n), a 
pump current (Ipo,n) is determined by the interpolating operation due to 
the fact that the pump current Ip is intermediate between Ipn and Ipn+1. 
The process of the interpolating operation is well known so that the 
description thereof is omitted. 
Then, from the combinations of typical point Rn+1 which is larger than and 
closest to the resistance R and of the typical points Ipn and Ipn+1 
sandwiching the pump current Ip, two calibrated pump currents (Ipon,n+1) 
and (Ipon+1,n+1) are retrieved by the operation of the computing portion 
18. From the combination of the retrieved values (Ipn, Ipon,n+1) and 
(Ipn+1, Ipon+1,n+1), a pump current (Ipo,n+1) is determined by the 
interpolating operation due to the fact that the pump current Ip is 
intermediate between Ipn and Ipn+1. Then, from the combinations of typical 
point Rn+1 which is larger than and closest to the resistance R and of the 
typical points Ipn and Ipn+1 sandwiching the pump current Ip, two 
calibrated pump currents (Ipon,n+1) and (Ipon+1,n+1) are retrieved by the 
operation of the computing portion 18. From the combination of the 
retrieved values (Ipn, Ipon,n+1) and (Ipn+1, Ipon+ 1,n+1), a pump current 
(Ipo,n+1) is determined by the interpolating operation due to the fact 
that the pump current Ip is intermediate between Ipn and Ipn+1. 
Next, from the combination (Rn, Ipo,n) of the above determined pump current 
(Ipo,n) corresponding to the resistance Rn and the combination (Rn+1, 
Ipo,n+1) of the pump current (Ipo,n+1) corresponding to the resistance 
Rn+1, the pump current Ipo is calibrated corresponding to the resistance R 
by the interpolating operation. It is to be noted that this calibrated 
pump current Ipo has a value calibrated at the reference temperature To 
for the pump current Ip, as above described. 
The pump current Ipo thus calibrated is used as a signal representative of 
an A/F ratio whereby the A/F ratio sensing device of an oxygen pump type 
according to this invention can be disposed in the exhaust gas path which 
is not constant in temperature. 
As mentioned above, according to the A/F ratio sensing device of this 
invention, the following excellent advantages are effected: 
(1) since the pump current representative of an A/F ratio is calibrated on 
the basis of the temperature of the A/F ratio sensor, a precise A/F ratio 
signal having eliminated therefrom characteristic variation due to thermal 
variation may be always obtained; 
(2) since the temperature of the sensor is represented by the internal 
resistance of the oxygen pump cell forming the sensor, no particular 
thermal sensor is needed; 
(3) the internal resistance of the oxygen pump cell can be easily 
calculated by measuring a terminal voltage across a resistor through which 
the pump current of the oxygen pump cell flows. 
Consequently, an engine can be operated at any A/F ratio irrespective of 
temperature variation. 
It is to be noted that while this invention has been described along the 
above embodiment, it should not be limited to the shown and described 
embodiment but various modifications may be made by any one of ordinary 
skills in the art without departing from the spirit of this invention.