Output correction method for exhaust gas ingredient-concentration sensors of proportional-output type

An output correction method for a proportional-output type O.sub.2 sensor including an oxygen concentration detecting element formed by an oxygen-pumping element and a cell element, each of the oxygen-pumping element and the cell element being composed of a wall of a solid electrolytic material having oxygen ion-conductivity, and a pair of electrodes having the wall interposed therebetween. The oxgen-pumping element is supplied with an output voltage corresponding to a difference between a voltage developed between the electrodes of the cell element and a predetermined reference voltage, and current flowing in the oxygen-pumping element is detected. A correction resistance supplies information indicative of a deviation of an air-fuel ratio detected by the sensor with respect to a predetermined reference air-fuel ratio. A correction value is determined on the basis of the information and the direction of flow of the current. The detected current is corrected by the use of the determined corrected value. A desired air-fuel ratio is calculated on the basis of the corrected current.

BACKGROUND OF THE INVENTION 
This invention relates to an output correction method for exhaust gas 
ingredient-concentration sensors of a proportional-output type adapted for 
use in internal combustion engines, and more particularly to a method of 
this kind, which enables to properly correct variations in output 
characteristic between the individual sensors. 
A method is known, in which exhaust gas concentration is sensed and the 
air-fuel ratio of a mixture supplied to an internal combustion engine is 
controlled to a desired ratio in a feedback manner responsive to the 
sensed concentration, so as to enhance the emission characteristics of the 
engine and reduce fuel consumption. As an 0.sub.2 sensor for sensing the 
concentration of oxygen contained in the exhaust gases, so called 
proportional-output type 0.sub.2 sensors are known, which generate an 
output proportional to the oxygen concentration. 
0.sub.2 sensors of this type include a limiting current type comprising a 
cell element and an oxygen-pumping element, each composed of a plate-like 
member formed of a solid electrolytic material having oxygen 
ion-conductivity, and a couple of electrodes attached to opposite side 
surfaces of the plate-like member, and which senses the air-fuel ratio of 
the mixture e.g. by pumping oxygen into and out of a gas diffsion chamber 
defined between the cell and oxygen-pumping elements. 
However, there can be variations in the output value between individual 
0.sub.2 sensors due to variations in the diameter of a gas-introducing 
slit opening into the gas diffusion chamber, or variations in the 
composition or thickness between individual solid electrolytic materials, 
or variations in the heating temperature or processing time for forming 
the materials. These variations cause variations in the air-fuel ratio 
value detected by the individual 0.sub.2 sensors. 
A method for correcting such variations in the air-fuel ratio is known e.g. 
from Japanese Provisional Utility Model Publication (Kokai) No. 60-120354, 
in which a correction resistance is connected as a circuit constant to a 
circuit connecting the oxygen-pumping element to a power source, wherein 
correction of variations in the output between individual sensors is 
carried out by changing the amount of current flowing in the circuit by 
means of the correction resistance. 
Further, another method for correcting the variations has been proposed by 
the assignee of the present application in Japanese Provisional Pat. 
Publication (kokai) No. 62-198744, in which when the output level of the 
sensor is equal to a predetermined reference value, the amount of fuel 
supplied to the engine is actually changed by a predetermined amount, and 
a correction value is calculated on the basis of a change in the output of 
the sensor resulting from the change in the amount of fuel, and the 
correction value is used to correct the sensor, thereby enabling the 
correction merely by means of calculation. 
However, the method according to Publication No. 60-120354 has the 
following disadvantage: In an 0.sub.2 sensor which can sense the air-fuel 
ratio over a wide range from the rich side to the lean side with respect 
to a stoichiometric, the output (pumping current Ip) characteristic of the 
sensor is generally such that the rate of a change in the pumping current 
Ip responsive to a change in the air-fuel ratio on the rich side is 
different from that responsive to a change of the air-fuel ratio on the 
lean side Therefore, the sensor output cannot be properly corrected on 
both the rich side and the lean side by means of a single correction 
resistance to thereby fail to detect the air-fuel ratio with accuracy. 
Consequently, this method requires the use of two correction resistances 
to correct the sensor output on both the rich side and the lean side. 
On the other hand according to the method of Publication No. 62-198744, 
although the correction of the sensor output can be effected by means of 
calculation within a microcomputer, it is required to actually change the 
amount of fuel by multiplying a normally required amount of fuel by a 
predetermined value, which will make the engine control complicated. 
SUMMARY OF THE INVENTION 
It is the object of the invention to provide an output correction method 
for exhaust gas ingredient-concentration sensors of a proportional-output 
type, which is capable of easily and properly correcting variations in the 
air-fuel ratio detected by individual sensors due to variations in output 
characteristic between the sensors, to thereby enhance the accuracy of 
detecting of the air-fuel ratio. 
To attain the above object, the present invention provides a method of 
correcting an output of an exhaust gas ingredient-concentration sensor of 
a proportional-output type including at least one oxygen concentration 
detecting element formed by an oxygen-pumping element and a cell element, 
each of the oxygen-pumping element and the cell element being composed of 
a wall of a solid electrolytic material having oxygen ion-conductivity, 
and a pair of electrodes having the wall interposed therebetween, the 
oxygen-pumping element and the cell element defining a gas 
diffusion-limiting zone therebetween, current detecting means connected to 
the oxygen-pumping element for detecting a value of current flowing 
therein, voltage applying means for applying an output voltage 
corresponding to a difference between a voltage developed between the 
electrodes of the cell element and a predetermined reference voltage to 
the oxygen-pumping element, and control means for calculating a desired 
value of an air-fuel ratio of an air-fuel mixture on the basis of the 
value of the current detected by the current detecting means. 
The method according to the invention is characterized by comprising the 
following steps: 
(1) supplying the control means with information indicative of a deviation 
of the air-fuel ratio detected by the sensor with respect to a 
predetermined reference air-fuel ratio; 
(2) determining a correction value on the basis of the information and a 
direction of flow of the current; 
(3) correcting the detected value of the current by the use of the 
determined correction value; and 
(4) calculating the desired value of the air-fuel ratio on the basis of the 
corrected value of the current. 
Preferably, a single value is supplied to the control means as the 
information, and when the current flows in one direction, the correction 
value is set to a first predetermined value based on the single value, 
while when the current flows in the opposite direction, the correction 
value is set to a second predetermined value obtained by multiplying the 
first predetermined value by a predetermined number of times. 
Specifically, the current flows in the one direction when the air-fuel 
ratio detected by the sensor is on one of a rich side and a lean side with 
respect to a stoichiometric ratio, while the current flows in the opposite 
direction when the detected value of the air-fuel ratio is on the other of 
the rich side and the lean side. 
The information may be a value of at least one correcting resistance which 
is disconnected from the current detecting means and the voltage applying 
means. 
The above and other objects, features, and advantages of the invention will 
be more apparent from the ensuing detailed description taken in 
conjunction with the accompanying drawings.

DETAILED DESCRIPTION 
The invention will now be described in detail with reference to the 
drawings showing an embodiment thereof. 
FIG. 1 shows the entire arrangement of a fuel supply control system 
employing an oxygen concentration sensor to which the method of the 
invention is applied. 
In FIG. 1, reference numeral 100 designates a body(sensor element section) 
of the oxygen concentration sensor (hereinafter called "the 0.sub.2 
sensor") 1. The sensor body 100 is arranged within an exhaust system of an 
engine, not shown, in which a three-way catalyst is arranged for purifying 
ingredients HC, CO, and NOx contained in the exhaust gases emitted from 
the engine. 
As shown in FIG. 2 in detail, the sensor body 100 is in the form of a 
rectangular parallelepiped, and comprises a basic body 20 formed of a 
solid electrolytic material having oxygen ion-conductivity (e.g. zirconium 
dioxide (ZrO.sub.2). 
The sensor body 100 shown in FIG. 2 is a type which has two oxygen 
concentration detecting elements longitudinally arranged, each having a 
cell element and an oxygen pumping element. The basic body 20 of the 
sensor body 100 has first and second walls 21, 22 extending parallel with 
each other, between which first and second gas diffusion chambers, 
23.sub.1, 23.sub.2 serving as gas diffusion-limiting zones are defined. 
The first gas diffusion chamber 23.sub.1 is communicated with an exhaust 
pipe, not shown, of the engine through a first slit 24.sub.1 which is 
disposed such that exhaust gases in the exhaust pipe can be guided into 
the first gas diffusion chamber 23.sub.1 through the slit 24.sub.1. The 
exhaust gases within the first gas diffusion chamber 23.sub.1 is 
introduced into the second gas diffusion chamber 23.sub.2 through a second 
slit 24.sub.2 communicating between the two chambers 23.sub.1 and 
23.sub.2. An air reference chamber 26 to be supplied with air or reference 
gas is defined between the first wall 21 and an outer wall 25 disposed 
adjacent the first wall 21 and extending parallel therewith. 
In order to detect oxygen concentration within the first gas diffusion 
chamber 23.sub.1, a couple of electrodes (first electrodes) 27.sub.1 a, 
27.sub.1 b formed of platinum (Pt) are mounted on opposite side surfaces 
of the first wall 21, which cooperate with the first wall 21 to form a 
cell element (sensing cell) 28.sub.1 for the first oxygen concentration 
detecting element, while another couple of electrodes 29.sub.1 a, 29.sub.a 
b are similarly mounted on opposite side surfaces of the second wall 22, 
which cooperate with the second wall 22 to form an oxygen-pumping element 
(pumping cell) 30.sub.1 for the first oxygen concentration detecting 
element. 
On the other hand, in order to detect oxygen concentration within the 
second gas diffusion chamber 23.sub.2, a cell element 28.sub.2 for the 
second oxygen concentration detecting element having a couple of 
electrodes 27.sub.2 a, 27.sub.2 b, and an oxygen-pumping element 30.sub.2 
for the second oxygen concentration detecting element having a couple of 
electrodes 29.sub.2 a, 29.sub.2 b are respectively mounted on the first 
and second walls 21, 22, similarly to the cell element 28.sub.1 and the 
oxygen-pumping element 30.sub.1. 
A heater (heating element) 31 is provided on an outer side surface of the 
outer wall 25, for heating the cell element 28.sub.1, 28.sub.2 and the 
oxygen-pumping elements 30.sub.1, 30.sub.2 to activate them. 
The electrodes 27.sub.1 b and 29.sub.1 b for the first oxygen concentration 
detecting element, which are located on the first gas diffusion chamber 
23.sub.1 side, are connected with each other (in the embodiment, they are 
connected by a suitable electrically conductive member 32.sub.1), and are 
connected to an inverting input terminal of an operational amplifier 41 
through a line 1. 
On the other hand, the other electrode 27.sub.1 a of the cell element 
28.sub.1 for the first oxygen concentration detecting element is connected 
to an inverting input terminal of a differential amplifier circuit 
42.sub.1 for the first oxygen concentration detecting element. The 
differential amplifier circuit 42.sub.1 forms voltage applying means 
together with a reference voltage source 43.sub.1 connected to a 
non-inverting input terminal thereof for applying to the oxygen-pumping 
element 30.sub.1 a voltage corresponding to the difference between a 
voltage (cell element voltage) developed between the electrodes 72.sub.1 a 
and 27.sub.1 b of the cell element 28.sub.1 (in the embodiment, the sum of 
a voltage on the line 1 and the cell element voltage) and a reference 
volta V.sub.so from the reference voltage source 43.sub.1. 
In the embodiment, the reference volta V.sub.so of the sum of the cell 
element voltage developed across the cell element 28.sub.1 when the 
air-fuel ratio of a mixture supplied to the engine is equal to a 
stoichiometric mixture ratio, e.g. 0.45 volts and a predetermined 
reference voltage, hereinafter referred to, applied to a non-inverting 
input terminal of the operational amplifier 41. 
The differential amplifier circuit 24.sub.1 has an output thereof connected 
to the electrode 29.sub.1 a of the oxygen-pumping element 30.sub.1 remote 
from the first gas diffusion chamber 23.sub.1 by way of a switch 44.sub.1 
of a switching circuit 44. The switching circuit 44 is controlled to close 
or open in dependence on activation and non-activation of the sensor body 
100 as well as on operating conditions of the engine. More specifically, 
when the sensor body 100 is inactivated, both of the switches 44.sub.1 and 
44.sub.2 are opened, and on the other hand, when it is activated, one of 
the switches is closed in response to operating conditions of the engine. 
The non-inverting input terminal of the operational amplifier circuit 41 is 
connected to a reference voltage source 45 to be supplied with the 
predetermined reference voltage therefrom. A current detecting resistance 
46 for detecting pumping current Ip is connected between an output 
terminal of the operational amplifier circuit 41 and the line 1 or an 
inverting input terminal of the operational amplifier circuit 41. That, is 
the resistance 46 also serves as the negative feedback resistance of the 
operational amplifier circuit 41. 
In the operational amplifier circuit 41 connected as above, provided that 
there is no offset in the output of the circuit 41, when the air-fuel 
ratio is equal to the stoichiometric ratio, no pumping current Ip flows in 
the line 1 and is applied to the inverting input terminal of the circuit 
41 according to the input level setting for the differential amplifier 
42.sub.1, and then the output voltage is equal to the reference potential 
at the non-inverting input terminal and an electric potential at the 
inverting input terminal is also equal to the reference potential. On the 
other hand, when the air-fuel ratio is not equal to the stoichiometric 
ratio, pumping current is supplied to the inverting input terminal, and an 
output voltage is generated at the output of the circuit 41, which 
corresponds to the amplification degree or factor (even if it is 1) 
determined by the value of the resistance 46. Although the output voltage 
varies in response to the magnitude of the pumping current Ip, the 
potential at the inverting input terminal is maintained at a constant 
value substantially equal to the reference potential at the non-inverting 
input terminal due to the action of the operational amplifier 41. 
More specifically, with the above described construction, when no pumping 
current Ip flows in the line 1, i.e. Ip is zero, the output voltage 
I.sub.PVW of the operational amplifier 41 (i.e. the voltage at one end of 
the resistance 46) is made equal to the reference voltgage V.sub.REF from 
the reference voltage source 45, and at the same time a voltage V.sub.CENT 
applied to the inverting input terminal (i.e. the voltage in the line 1 
and at the other end of the resistance 46) is made equal to the reference 
voltage V.sub.REF. 
Further, even when the pumping current Ip is not zero and varies within the 
lean side or within the rich side in response to the air-fuel ratio of the 
supplied mixture, as hereinafter referred to, the voltage at the inverting 
input terminal of the operational amplifier 41 or at the other end of the 
resistance 46 connected to the line 1, is made substantially equal to the 
voltage at the non-inverting input terminal, i.e. the reference voltage 
V.sub.REF irrespective of a change in the pumping current Ip. 
As described above, the voltage V.sub.CENT on the line 1 and accordingly at 
the other end of the resistance 46 is maintained substantially at the 
voltage V.sub.REF, irrespective of whether the pumping current Ip assumes 
zero or varies. On the other hand, the voltage at the one end of the 
resistance 46 connected to the output of the operational amplifier circuit 
41 is varied in response to the direction of the pumping current Ip (the 
positive direction or the negative direction) and the amount of the 
current Ip. Therefore, the voltage V.sub.CENT is a reference value 
(reference voltage) for detecting current flowing through the 
oxygen-pumping element and calculating the air-fuel ratio based on the 
detected current value. 
In this sense, the potential on the line 1 is not the earth potential, but 
the whole system including the line 1 and the current detecting resistance 
46 is raised in potential from the ground level by the reference voltage 
V.sub.REF. Consequently, when the pumping current Ip is determined from a 
potential difference between the opposite ends of the current detecting 
resistance 46, that is, from the respective voltages V.sub.CENT and 
I.sub.PVW, as hereinafter described, the reference value V.sub.CENT as 
well as the other end voltage I.sub.PVW are always positive voltages, 
irrespective of whether the pumping current Ip flows in the positive 
direction or in the negative direction in response to the air-fuel ratio, 
thereby facilitating the calculation of the air-fuel ratio. 
Further, the raising-up of the reference voltage of the pumping current 
detecting system to the constant reference voltage as above is 
advantageous for avoiding erroreous detecting of the current due to noise, 
especially high level noise such as ignition pulse noise of the engine. 
The voltage V.sub.REF of the reference voltage source 45 of the operational 
amplifier circuit 41 is set at a predetermined voltage (e.g. 205 volts) 
also for ensuring the above described advantage. 
The second oxygen concentration detecting element of the sensor body 100 
has a similar construction to the first oxygen concentration detecting 
element. That is, in the voltage applying circuit and the switching 
circuit 44, there are respectively provided a differential amplifier 
circuit 42.sub.2 a reference voltage source 43.sub.2, and the 
aforementioned switch 44.sub.2. The switch 44.sub.2 is connected to the 
outer side electrode 29.sub.2 a of the oxygen-pumping element 30.sub.2, 
and the respective inner side electrodes 27.sub.2 b and 29.sub.2 b of the 
cell element 28.sub.2 and the oxygen-pumping element 30.sub.2 are both 
connected to the line 1, so that, during the use of the second oxygen 
concentration detecting element, the pumping current Ip flowing through 
the oxygen-pumping element 30.sub.2 flows in the line 1. 
The output voltage I.sub.PVW of the operational amplifier circuit 41 and 
the voltage V.sub.CENT on the line 1, at the opposite ends of the current 
detecting resistance 46, are supplied to an input port 401 of an 
electronic control unit (hereinafter called "the ECU") 4 and are at the 
same time supplied to respective inputs of a differential amplifier 
circuit 47. 
The differential amplifier circuit 47 amplifies the difference between the 
voltage V.sub.CENT and the output voltage I.sub.PVW of the operational 
amplifier circuit 41, and thus serves to improve the accuracy of a signal 
indicative of a voltage detected from pumping current Ip which assumes 0 
or a value close thereto, i.e. where the air-fuel ratio is within a 
predetermined range about the stoichiometric air-fuel ratio of the 
mixture. In the differential amplifier circuit 47, the I.sub.PVW signal is 
amplified by a predetermined magnification .alpha., e.g. 5 times, to be 
produced as a voltage I.sub.PVN. 
The output voltage I.sub.PVN of the differential amplifier circuit 47 is 
obtained by the following equation, and is also supplied to the input port 
401: 
EQU I.sub.PVN =-5(I.sub.PVW -V.sub.CENT)+V.sub.CENT (l) 
Therefore, three voltage signals, i.e. V.sub.CENT as the reference voltage, 
I.sub.PVW, and I.sub.PVN are supplied to the input port 401 for 
calculating the air-fuel ratio based on the pumping current Ip. Although 
the pumping current can be detected by using only the voltages V.sub.CENT 
and I.sub.PVW, it can be more accurately detected by additionaly using the 
voltage I.sub.PVN when the air-fuel ratio is in the vicinity of the 
stoichiometric air-fuel ratio of the mixture in which the pumping current 
Ip assumes small values. 
Also supplied to the input port 401 is variation correcting value 
information for correcting variations between sensor bodies used. This 
information may be supplied individually for each of the first and second 
oxygen concentration detecting elements, if the sensor body 100 has two 
oxygen detecting elements as in the illustrated embodiment of the 
invention. Specifically, the information may be supplied by utilizing 
label correction resistances 48.sub.1 and 48.sub.2, as shown in FIG. 3. 
The values of the label correction resistances 48.sub.1 and 48.sub.2 are 
set to values corresponding to variations in the characteristics of sensor 
bodies compared with a standard sensor body. The degree of variation in 
the characteristics of individual sensor body is indicated by a label 
indicative of its resistance value. The label correction resistances 
48.sub.1 and 48.sub.2 are used together with the sensor body 100 used. 
That is, for instance, they maY be provide within a connecting coupler, 
not shown, arranged in a wire harness, not shown, connecting the sensor 
body 100 to the ECU 4, hereinafter referred to. When the sensor body 100 
is electrically connected to the ECU 4, respective one ends of the 
resistances 48.sub.1, 48.sub.2 are connected to a predetermined voltage 
source Vcc, as shown in FIG. 3, whereby the variation correcting value 
information corresponding to their resistance values is inputted through 
the other ends of the resistances. 
The input port 401 of the ECU 4 is provided therein with an A/D 
(analog-to-digital) converter, which converts the above-mentioned input 
analog signals to digital signals. 
The ECU 4 is supplied with respective output signals from throttle valve 
opening (.theta.th) sensor 10, and an intake pipe absolute pressure (PBA) 
sensor 12 as engine parameter sensors, which have then their voltage 
levels shifted to a predetermined level by a level shifter circuit 402 and 
successively applied to the A/D converter 404 through a multiplexer 403. 
The A/D converter 404 of the input port 401 supplies the 
digitally-converted data to a central processing unit (hereinafter called 
"the CPU") 406 via a data bus 405. 
An output signal from an engine speed (Ne) sensor 14 is applied to a 
waveform shaper circuit 407 to have its pulse waveform shaped, and the 
shaped signal is supplied to the CPU 406 as a top-dead center position 
(TDC) signal, as well as to a counter 408. The counter 408 counts the time 
interval between an immediately preceding pulse of the TDC signal and a 
present pulse of same, inputted thereto from the Ne sensor 14. The counted 
value Me is proportional to the reciprocal of the actual engine rotational 
speed Ne. The counter 408 supplies the counted value Me to the CPU 406 via 
the data bus 405. 
Further connected to the CPU 406 via the data bus 405 are a read-only 
memory (hereinafter called "the ROM") 409, and a random access memory 
(hereinafter called "the RAM") 4IU, and driving circuits 4I2-4I4. The RAM 
410 temporarily stores results of calculations executed within the CPU 
406, while the ROM 409 stores a control program to be executed within the 
CPU 406 for calculation of a fuel injection period T.sub.OUT of fuel 
injection valves 11, and other various programs, as well as various maps 
and tables. 
The CPU 406 determines whether to energize or deenergize the heater 31 and 
whether to close or open the switches 44.sub.1 and 44.sub.2, and then 
supplies driving signals corresponding to the determinations to the heater 
31 and the switching circuit 44 via the driving circuits 41.sub.2 and 
41.sub.3. 
The CPU 406 determined operation conditions of the engine such as a 
feedback control condition, based on the aforementioned various engine 
parameter signals including an output signal from the 0.sub.2 sensor 1, 
and calculates the fuel injection period of the fuel injection valves 11 
in synchronism with TDC signal pulses in response to the determined engine 
operation conditions, based on a control program, not shown, by the use of 
the following equation (2): 
EQU T.sub.OUT =Ti.times.K.sub.02 .times.K.sub.1 +K.sub.2 (2) 
where Ti represents a basic fuel injection period, which is calculated from 
a Ti map, not shown, stored in the ROM 409, in response e.g. to the 
absolute pressure PBA within the engine intake pipe, and the engine 
rotational speed Ne. K.sub.O2 represents an air-fuel ratio correction 
coefficient, which is determined in response to oxygen concentration in 
the actual exhaust gases, based on a control program, not shown, when the 
engine is in the feedback control region, while it is set to a 
predetermined value when the engine is in an open loop control region. 
K.sub.1 and K.sub.2 respectively represent other correction coefficients 
and correction variables obtained in response to various engine parameter 
signals, and are set to such desired values as to optimize operating 
characteristics of the engine such as fuel consumption and accelerability. 
The CPU 406 supplies the driving signals responsive to the results of the 
above calculation to the fuel injection valves 11 via the driving circuit 
414. The air-fuel ratio is thus feedback-controlled to a desired ratio or 
stochiometric ratio during the feedback operating condition of the engine. 
The oxygen concentration is detected by the 0.sub.2 sensor in the following 
manner: 
First, when the first oxygen concentration detecting element is selected by 
the switching circuit 44, as shown in FIG. 1, the exhaust gases are 
introduced into the first gas diffusion chamber 23.sub.1 through the first 
slit 24.sub.1 with operation of the engine. This causes a difference in 
oxygen concentration between the first gas diffusion chamber 23.sub.1 and 
the air reference chamber 26 into which air is introduced. Consequently, a 
voltage (sensor voltage) corresponding to the difference is developed 
between the electrodes 27.sub.1 a and 27.sub.1 b of the cell element 
28.sub.1, which is added to the line 1 voltage V.sub.CENT and the same is 
applied to the inverting input terminal of the differential amplifier 
circuit 42.sub.1. As stated before, the reference voltage V.sub.so 
supplied to the non-inverting input terminal of the differential amplifier 
circuit 42.sub.1 is set at the sum of a voltage developed across the cell 
element 28.sub.1 when the air-fuel ratio is equal to the stoichiometric 
air-fuel ratio, and the reference voltage V.sub.REF supplied to the 
operational amplifier circuit 41. 
Therefore, when the air-fuel ratio is on the lean side, the voltage between 
the electrodes 27.sub.1 a and 27.sub.1 b of the cell element 28.sub.1 
lowers, while the line 1 voltage V.sub.CENT is maintained at V.sub.REF, so 
that the sum of the voltage between the electgrodes 27.sub.1 a and 
27.sub.1 b and the V.sub.CENT becomes lower than the reference voltage 
V.sub.so. Thus, the output level of the differential amplifier circuit 
42.sub.1 become positive, and the positive level voltage is applied to the 
oxygen-pumping element 30.sub.1 via the switch 44.sub.1. By applying the 
positive level voltage, when the oxygen-pumping element 30.sub.1 is 
activated, oxygen present within the gas diffusion chamber 23.sub.1 is 
ionized, whereby the resulting ions move through the electrode 29.sub.1 i, 
the second wall 22, and electrode 29.sub.1 a to be emitted therefrom as 
oxygen gas or pumped out of the 0.sub.2 sensor 1. This is, the direction 
of flow of the pumping current Ip from the electrode 29.sub.1 a to the 
electrode 29.sub.1 b and flows through the current-detecting resistance 46 
via the line 1. At this time, the pumping current Ip flows from the line 1 
to the output side of the operational amplifier circuit 41. 
On the other hand, when the air-fuel ratio is on the rich side, the sum of 
the voltage between the electrodes 27.sub.1 a and 27.sub.1 b of the cell 
element 28.sub.1 and the line 1 voltage V.sub.CENT becomes higher than the 
reference voltage V.sub.so, so that the output level of the differential 
amplifier circuit 42.sub.1 becomes negative. Consequently, reversely to 
the above described action, external oxygen is pumped into the gas 
diffusion chamber 23.sub.1 through the oxygen-pumping element 30.sub.1, 
and simultaneously the pumping current Ip flows from the electrode 
29.sub.1 b to the electrode 29.sub.1 a and flows through the current 
detecting resistance 46, that is, in the direction of flow of the pumping 
current Ip is reverse to that in the above case. 
When the air-fuel ratio is equal to the stoichiometric air-fuel ratio, the 
sum of the voltage between the electrodes 27.sub.1 a and 27.sub.1 b of the 
cell element 28.sub.1 and the line 1 voltage V.sub.CENT becomes equal to 
the reference voltage Vso, so that the pumping-in and out of oxygen is not 
effected, whereby no pumping current flows (that is, the pumping current 
Ip is zero). 
As described above, since the pumping-in and out of oxygen and hence the 
pumping current Ip are controlled so as to maintain the oxygen 
concentration in the gas diffusion chamber 23.sub.1 at a constant level, 
the pumping current Ip assumes a value proportional to the oxygen 
concentration of the exhaust gases on both the lean side and rich side of 
the air-fuel ratio of the supplied mixture. 
Signals for detecting the amount of the pumping current Ip flowing through 
the current-detecting resistance 46, e.g. signals indicative of respective 
voltages I.sub.PVW, V.sub.CENT, I.sub.PVN at the opposite ends of the 
resistance 46 are supplied to the ECU 4. 
Similarly to the first oxygen concentration detecting element, when the 
second oxygen concentration detecting element is used (that is, when the 
swich 44.sub.2 of the switching circuit 44 is closed, as reversely to the 
position shown in FIG. 1), the pumping-in and out of oxygen is controlled 
so as to maintain the oxygen concentration in the second gas diffusion 
chamber 23.sub.2 at a constant value, that is, the voltage between the 
electrodes 27.sub.2 a and 27.sub.2 b of the cell element 28.sub.2 is 
feedback-controlled to be maintained at a constant value, and at the same 
time the signals indicative of the voltages I.sub.PVW, V.sub.CENT, 
I.sub.PVN for detecting the pumping current Ip flowing during the feedback 
control are supplied to the ECU 4 as outputs of the second oxygen 
concentration detecting element. 
The ECU 4 then calculates the desired air-fuel ratio based on the supplied 
signals and determines the value of the air-fuel ratio correction 
coefficient K.sub.02 in the aformentioned equation (2) based on the 
calculated desired air-fuel ratio. 
FIG. 4 shows a subroutine for calculating an output voltage V.sub.OUT 
corresponding to the pumping current Ip, which includes a process for 
correcting the output of the 0.sub.2 sensor. This program is executed in 
the ECU 4 upon generation of TDC signal pulses and in synchronism 
therewith. 
At a step 451, it is determined whether or not the output voltage I.sub.PVN 
of the differential amplifier circuit 47 is within a predetermined small 
value range with a middle value about which the voltage I.sub.PVN varies. 
That is, it is determined whether or not the value I.sub.PVN is larger 
than a first predetermined value I.sub.PVL (e.g. 2.3 volts) and at the 
same time smaller than a second predetermined value I.sub.PVH (e.g. 2.6 
volt). Depending upon the answer to the question of the step 451 it is 
determined whether to determine a voltage V.sub.lPO corresponding to the 
pumping current Ip either by using the voltage I.sub.PVW which is direct 
output of the operational amplifier circuit 41, or by using the voltage 
I.sub.PVN which is obtained by amplifying the voltage I.sub.PVW by the 
differential amplifier circuit 47. 
If the answer to the question of the step 451 is Yes, that is, if the 
voltage I.sub.PVN fulfills the condition I.sub.PVH &gt;I.sub.PVN &gt;I.sub.PVL 
(which means that the pumping current Ip assumes a small value equal to 0 
or in the vicinity of 0, and that the air-fuel ratio is within a narrow 
range about the stoichimetoric air-fuel ratio (e.g., 14.7)), the value 
I.sub.VPO is calculated by the following equation (step 452): 
EQU V.sub.IPO =I.sub.PVN =V.sub.cent =I.sub.PVERR (3) 
where V.sub.cent represents a reference voltage for the voltage V.sub.CENT 
at the one end of the current detecting resistance 46 remote from the 
output of the operational amplifier circuit 41, while I.sub.PVERR 
represents a correction value for compensating for circuit errors such as 
the offset of the operational amplifier circuit 41. 
The calculation at the step 452 is based on the following ground: 
By using the voltage I.sub.PVN which is obtained by amplifying the voltage 
I.sub.PVW by the operational amplifier circuit 47 when the voltage 
I.sub.PVN assumes a value within the small value range of the step 452, it 
is possible to enhance the accuracy of calculation of the pumping current 
Ip. If the air-fuel ratio is changed to the lean side or to the rich side 
from the above small value range where the air-fuel ratio is equal to or 
close to the stoichiometric air-fuel ratio (14.7), such change exerts a 
great influence upon the purification degree i.e. conversion efficiency of 
the three-way catalyst. Therefore, more accuracy is required in detecting 
the air-fuel ratio than when the air-fuel ratio is changed within a range 
remote from the stoichiometric air-fuel ratio. Therefore, in order to 
improve the detection accuracy in an air-fuel ratio range in the vicinity 
of the stoichiometric air-fuel ratio, the direct output voltage I.sub.PVW 
is not directly used but the amplified voltage I.sub.PVN is applied to 
calculation of the voltage value V.sub.IPO, which is obtained by 
amplifying I.sub.PVW by a predetermined number of times .alpha.. 
In the equation (3), the subtraction of the reference voltage V.sub.cent is 
effected for correcting the reference potential or zero potential. 
As stated before, the potential of the pumping current detecting system 
including the current detecting resistance 46 and the operational 
amplifier circuit 41 is raised up by the reference voltage V.sub.REF to 
always maintain the voltages at the opposite ends of the resistance 46 at 
positive levels even if the direction of flow of the pumping current Ip is 
changed. Therefore, the voltage at the end of the resistance 46 close to 
the output of the operational amplifier circuit 41 varies about the 
reference voltage V.sub.REF from the reference voltage source 45, in 
response to the direction of flow of the pumping current Ip and the amount 
of the same current. Thus, the amount of the pumping current Ip can be 
determined from the difference between the reference voltage V.sub.REF and 
the voltage varying in response to the flow of the pumping current Ip. 
Therefore, at the step 452 the reference voltage V.sub.cent is subtracted 
from the voltage I.sub.PVN. 
The reference voltage V.sub.cent corresponds to the line 1 voltage 
V.sub.CENT. If there is no circuit error in the operational amplifier 
circuit 41, etc., and the pumping current Ip is zero (that is, the 
air-fuel ratio is equal to the stoichiometric air-fuel ratio), the value 
V.sub.cent should be set to a valve equal to the reference voltage 
V.sub.REF. 
Therefore, by obtaining (I.sub.PVN -V.sub.cent), even if there is an error 
(e.g. setting error) in the voltage from the reference voltage source 45, 
or even if the voltage from the source 45 varies, the value (I.sub.PVN 
-V.sub.cent) is alwaYs zero when the actual pumping current Ip is zero. 
This correction enables detecting the pumping current accurately. Thus, 
the air-fuel ratio detection accuracy is improved especially when the 
air-fuel ratio is in the vicinity of the stoichiometric air-fuel ratio 
(14.7), in addition to the aformentioned advantage of noise proof. 
Referring again to the step 452, the correction value I.sub.PVERR is 
subtracted from (I.sub.PVN -V.sub.cent), whereby the detection accuracy 
can be further enhanced. 
Although, in the above explanation, it has been assumed that there is no 
circuit error such as the offset in the operational amplifier circuit 41, 
actually there can be such an error in the circuit 41. Especially, in the 
vicinity of the stoichiometric air-fuel ratio, the pumping current Ip 
assumes a very small value near zero, and hence the difference between the 
reference voltage and the voltage varying in response to the pumping 
current Ip becomes very small, so that such a circuit error as the offset 
greatly affects the accuracY of detection. 
Therefore, to correct the offset in the circuit 41, the correction value 
I.sub.PVERR is subtracted from (I.sub.PVN -V.sub.cent) at the step 452. 
The value I.sub.PVERR is obtained by executing a subroutine, not shown. 
If the answer to the question of the step 451 is No, that is, if I.sub.PVN 
.gtoreq.I.sub.PVH or I.sub.PVN .ltoreq.I.sub.PVL is fulfilled, which means 
that the value of I.sub.PVN is out of the predetermined range, it is 
judged that the pumping current Ip has neither a value of 0 nor a small 
value in the vicinity of 0, that is, the air-fuel ratio is not in the 
vicinity of the stoichiometric air-fuel ratio (14.7). The program then 
proceeds to a step 453, in which the value V.sub.IPO is calculated by the 
following equation: 
EQU V.sub.IPO =(V.sub.CENT -I.sub.PVW).times..alpha. (4) 
where .alpha. is a predetermined value. That is, when the air-fuel ratio is 
not in the vicinity of the stoichiometric air-fuel ratio, the voltage 
I.sub.PVW value is directly used as the terminal voltage of the current 
detecting resistance 46 close to the output of the operational amplifier 
circuit 41, to calculate the difference between the line 1 voltage 
V.sub.CENT as the other terminal voltage of the resistance 46 and 
I.sub.PVW, that is, (V.sub.CENT -I.sub.PVW) to obtain the voltage 
V.sub.IPO. Therefore, in order to raise up the resulting value of 
V.sub.IPO to the same level as that of the resulting value obtained at the 
step 452, the difference (V.sub.CENT -I.sub.PVW) is multiplied by the 
predetermined value. 
Also in the calculation at the step 453, the voltage V.sub.IPO value is 
obtained by using the raised-up voltage V.sub.CENT on the line 1, that is, 
on the basis of the difference (V.sub.CENT -I.sub.PVW), so that potential 
correction is effected similarly to the step 452, whereby the voltage 
V.sub.IPO corresponding to the pumping current Ip is accurately detected 
irrespective of the influence of noise and an error in the reference 
voltage V.sub.REF. 
At a step 454, it is determined whether or not the V.sub.IPO value obtained 
at the step 452 or 453 is equal to 0, in order to judge whether or not the 
actual air-fuel ratio is equal to the stoichiometric ratio. If the answer 
is Yes, that is, if Ip is equal to zero, the program jumps to a step 455 
to execute the step 455 and a step 456, followed by termination of the 
program. 
At the step 455, the V.sub.IPO value obtained at the step 452 or 453 is 
corrected to a V.sub.IP value by being multiplied by a label resistance 
coefficient K.sub.IP. Then at the step 456, the value V.sub.IP obtained at 
the step 455 is increased by a predetermined number, e.g. 8000 in 
hexadecimal notation, to obtain a value V.sub.OUT as the output voltage. 
At the step 454, if it is determined that the value V.sub.IPO is zero, the 
value V.sub.IP obtained at the step 455 is also zero, and therefore, the 
resulting V.sub.OUT value at the step 456 is 8000 in hexadecimal notation. 
The predetermined number is a reference or middle value of the V.sub.OUT 
value When the air-fuel ratio is changed from the stoichiometric ratio to 
the lean side or to the rich side, the V.sub.OUT value is calculated by 
addition or subtraction of the present value of V.sub.IP to or from the 
middle value, in accordance with the V.sub.IP value (the V.sub.IPO value 
assumes a positive value when the air-fuel ratio is on the lean side with 
respect to the stoichiometric ratio, and a negative value when the latter 
is on the rich side, and the V.sub.IP value also assumes a positive value 
or a negative value correspondingly). 
As stated above, the voltage value V.sub.IP obtained at the step 455 is not 
made the final value, but it is increased by the predetermined number at 
the step 456. This is for preventing the V.sub.OUT value from assuming a 
value of 0 when the air-fuel ratio is equal to the stoichiometric ratio 
where the pumping current Ip is 0, to thereby enable avoiding an 
inconvenience encountered when the k.sub.02 value is determined on the 
basis of the V.sub.OUT value, e.g. when the k.sub.02 value is obtained by 
division. 
If the answer to the question of the step 454 is No, it is determined at a 
step 457 whether or not a flag FLG.sub.LCNT has been set to a value of 1. 
If the answer at the step 457 is Yes, it is determined that the first 
oxygen concentration detecting element in FIG. 1 is not being used, and 
then the program proceeds to step 458. 
The flag FLG.sub.LCNT indicates whether the first oxygen concentration 
detecting element or the second oxygen concentration detecting element is 
being used. That is, when the first oxygen concentration detecting element 
is being used the value N is set to 1, while it is set to 2 when the 
second oxygen concentration detecting element is being used. 
At the step 458, it is determined whether or not the present V.sub.IPO 
value is larger than zero (i.e. positive or negative). That is, it is 
determined whether the air-fuel ratio is on the lean side or on the rich 
side with respect to the stoichiometric ratio. 
If the answer to the question of the step 458 is Yes, that is, if the 
V.sub.IPO value is positive, it is determined that the air-fuel ratio is 
on the lean side, and then the program proceeds to a step 460, hereinafter 
referred to. On the other hand, if the answer is No, that is, if the 
V.sub.IPO value is negative, it is determined that the air-fuel ratio is 
on the rich side, and then the program proceeds to a step 459, where the 
K.sub.IP value is set to a predetermined value K.sub.LBL1R, followed by 
the program proceeding to the step 460. 
The predetermined value K.sub.LBLIR set at the step 455 is a correction 
coefficient used for correcting variations in output characteristic 
between individual 0.sub.2 sensors, to be applied when the air-fuel ratio 
is on the rich side with respect to the stoichiometric air-fuel ratio, 
that is, when the pumping current Ip is below zero during the use of the 
first oxygen concentration detecting element. 
The correction coefficient K.sub.LBLIR is obtained by a subroutine, not 
shown, wherein it is determined based on the value of the label correction 
resistance 48.sub.1 for the first oxygen concentration detecting element. 
The label correction resistance 48.sub.1 is provided within a coupler, not 
shown, for obtaining the correction coefficient for the first oxygen 
concentration detecting element. The resistance value of the label 
correction resistance 48.sub.1, which can be obtained by detecting current 
flowing through the resistance 48.sub.1 or voltage between opposite ends 
thereof developed when the predetermined voltage Vcc, e.g. 5V, is applied, 
is set at a value corresponding to the degree of deviation of the air-fuel 
ratio detected by an individual 0.sub.2 sensor used, with respect to the 
resistance value of a reference 0.sub.2 sensor. Therefore, the correction 
coefficient K.sub.LBLIR can be obtained by detecting the resistance value 
of the label correction resistance 48.sub.1 by means of the ECU 4. 
In the arrangement shown in FIG. 3, a single label correction resistance is 
used for each detecting element. Since the correction coefficient is set 
to different values in accordance with the direction of flow of the 
pumping current Ip (i.e. V.sub.IPO &gt;0 or V.sub.IPO &lt;0) according to the 
method of the invention, an example of which is shown in FIG. 4, even the 
use of a single label correction resistance can perform correction on both 
the lean and rich sides. 
The method of the invention is based upon the fact that the air-fuel ratio 
vs. pumping current characteristic of an 0.sub.2 sensor of the 
proportional-outout type has correlation in variation between the rich 
side and the lean side. 
Specifically, if the actual output of the sensor is, for example, deviated 
toward the rich side by a predetermined number of times. e.g. 1.3 times, 
with respect to a reference output, the actual output on the lean side is 
also deviated by a predetermined number of times which is correlated with 
the degree of deviation of the output toward the rich side. 
Therefore, even in the case that the detected pumping current Ip is 
corrected by the use of the label correction resistance which is not 
connected to the voltage applying means and the pumping current detecting 
circuit (the resistances 48.sub.1 and 48.sub.2 are not circuit constants 
in the above circuits), as shown in FIG. 3, a correction value may be, for 
instance, determined on the rich side from the actual label correction 
resistance value when the pumping current Ip value is negative, while a 
correction value on the lean side may be determined by multiplying the 
correction value determined on the rich side by a predetermined number of 
times, or vice versa. Thus, even a single correction resistance can enable 
correction on both the rich side and the lean side. 
In FIG. 4, as an example, the amount of correction is made different 
between the lean side and the rich side in such a manner that the K.sub.IP 
value is set to a value of 1 on the lean side, while it is set to 
K.sub.LBLIR on the rich side. 
The use of a single correction resistance is advantageous in the 
arrangement of FIG. 3 wherein the label correction resistance 48 is 
accommodated within the coupler, since the coupler which accommodates only 
one correction resistance can be made compact. 
Referring again to FIG. 4, at the step 460, a deterioration correction 
coefficient K.sub.CAL is set to a predetermined value K.sub.CAL1 for the 
first oxygen concentration detecting element, followed by execution of the 
steps 455 and 456 and then termination of the program. 
The deterioration correction coefficient K.sub.CAL is provided for 
correcting a change in the output characteristic of the sensor due to a 
change in the flow resistance through the slit 24 caused by a reduction in 
the diameter of the slit with oxides contained in the exhaust gases and 
deposited on the inner peripheral surface thereof. The value of the 
coefficient K.sub.CAL is obtained in accordance with a subroutine, not 
shown. The amount of deterioration correction to be effected on the rich 
side is the same as that on the lean side. This correction is especially 
useful for enhancing the accuracy of detection of the air-fuel ratio when 
it is applied to the 0.sub.2 sensor with two oxygen detecting elements as 
shown in FIGS. 1 and 2. 
If the answer to the question at the step 457 is No, it is judged that the 
second oxygen concentration detecting element is now being used. On this 
occasion, another label correction resistance 48.sub.2 for the second 
oxygen concentration detecting element (in FIG. 3) is used for the sensor 
variation correction such that the K.sub.IP value is set to a second 
predetermined value K.sub.LBL2R for the second oxygen concentration 
detecting element (step 461), and the K.sub.CAL value is set to a second 
predetermined value K.sub.CAL2 for the second oxygen concentration 
detecting element (step 462). followed by termination of the program. 
Although in the embodiment of the invention described as above, two oxygen 
concentration detecting elements are used, the invention is not limited to 
this, but it is also applicable to an 0.sub.2 sensor having a single 
detecting element corresponding to the first detecting element shown in 
FIGS. 1 and 2. 
Further, a device for supplying the correction value to the ECU 4 is not 
limited to a coupler as used in the FIG. 3 embodiment. 
Further, although in the embodiment of FIG. 4 the K.sub.IP value is set to 
1 on the lean side and set to K.sub.LBL1R on the rich side, it may be set 
on the rich side to K.sub.LBL1R which is obtained based on the actual 
resistance value of a label resistance used, while it may be set on the 
lean side to KLBL1R.times.K(0&lt;K&lt;2). 
As described above, according to the invention, the amount of correction of 
variations in the output characteristic of an 0.sub.2 sensor is varied in 
accordance with the direction of flow of the pumping current Ip detected 
for calculating the air-fuel ratio, so that the output of the sensor can 
be easily corrected on both the rich side and the lean side, thereby 
obtaining the accuracy of detection of the air-fuel ratio over the entire 
range of the air-fuel ratio.