Double air-fuel ratio sensor system having improved exhaust emission characteristics

In a double air-fuel sensor system including two air-fuel ratio sensors upstream and downstream of a catalyst converter provided in an exhaust gas passage, an air-fuel ratio feedback control parameter is calculated in accordance with the output of the downstream-side air-fuel ratio sensor in an air-fuel ratio feedback control mode therefor, and an actual air-fuel ratio is adjusted in accordance with the output of the upstream-side air-fuel ratio sensor and the air-fuel ratio feedback control parameter. In this air-fuel ratio feedback control mode, a large allowable range is imposed on the air-fuel ratio feedback control parameter. In a non air-fuel ratio feed control mode for the downstream-side air-fuel ratio sensor, a small allowable range is imposed on the air-fuel ratio feedback control parameter which, in this case, is unchangeable.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a method and apparatus for feedback 
control of an air-fuel ratio in an internal combustion engine having two 
air-fuel ratio sensors upstream and downstream of a catalyst converter 
disposed within an exhaust gas passage. 
2. Description of the Related Art 
Generally, in a feedback control of the air-fuel ratio sensor (O.sub.2 
sensor) system, a base fuel amount TAUP is calculated in accordance with 
the detected intake air amount and detected engine speed, and the base 
fuel amount TAUP is corrected by an air-fuel ratio correction coefficient 
FAF which is calculated in accordance with the output of an air-fuel ratio 
sensor (for example, an O.sub.2 sensor) for detecting the concentration of 
a specific component such as the oxygen component in the exhaust gas. 
Thus, an actual fuel amount is controlled in accordance with the corrected 
fuel amount. The above-mentioned process is repeated so that the air-fuel 
ratio of the engine is brought close to a stoichiometric air-fuel ratio. 
According to this feedback control, the center of the controlled air-fuel 
ratio can be within a very small range of air-fuel ratios around the 
stoichiometric ratio required for three-way reducing and oxidizing 
catalysts (catalyst converter) which can remove three pollutants CO, HC, 
and NO.sub.X simultaneously from the exhaust gas. 
In the above-mentioned O.sub.2 sensor system where the O.sub.2 sensor is 
disposed at a location near the concentration portion of an exhaust 
manifold, i.e., upstream of the catalyst converter, the accuracy of the 
controlled air-fuel ratio is affected by individual differences in the 
characteristics of the parts of the engine, such as the O.sub.2 sensor, 
the fuel injection valves, the exhaust gas recirculation (EGR) valve, the 
valve lifters, individual changes due to the aging of these parts, 
environmental changes, and the like. That is, if the characteristics of 
the O.sub.2 sensor fluctuate, or if the uniformity of the exhaust gas 
fluctuates, the accuracy of the air-fuel ratio feedback correction amount 
FAF is also fluctuated, thereby causing fluctuations in the controlled 
air-fuel ratio. 
To compensate for the fluctuation of the controlled air-fuel ratio, double 
O.sub.2 sensor systems have been suggested (see: U.S. Pat. Nos. 3,939,654, 
4,O27,477, 4,130,095, 4,235,204). In a double O.sub.2 sensor system, 
another O.sub.2 sensor is provided downstream of the catalyst converter, 
and thus an air-fuel ratio control operation is carried out by the 
downstream-side O.sub.2 sensor in addition to an air-fuel ratio control 
operation carried out by the upstream-side O.sub.2 sensor. In the double 
O.sub.2 sensor system, although the downstream-side O.sub.2 sensor has 
lower response speed characteristics when compared with the upstream-side 
O.sub.2 sensor, the downstream-side O.sub.2 sensor has an advantage in 
that the output fluctuation characteristics are small when compared with 
those of the upstream-side O.sub.2 sensor, for the following reasons: 
(1) On the downstream side of the catalyst converter, the temperature of 
the exhaust gas is low, so that the downstream-side O.sub.2 sensor is not 
affected by a high temperature exhaust gas. 
(2) On the downstream side of the catalyst converter, although various 
kinds of pollutants are trapped in the catalyst converter, these 
pollutants have little affect on the downstream side O.sub.2 sensor. 
(3) On the downstream side of the catalyst converter, the exhaust gas is 
mixed so that the concentration of oxygen in the exhaust gas is 
approximately in an equilibrium state. 
Therefore, according to the double O.sub.2 sensor system, the fluctuation 
of the output of the upstream-side O.sub.2 sensor is compensated for by a 
feedback control using the output of the downstream-side O.sub.2 sensor. 
Actually, as illustrated in FIG. 1, in the worst case, the deterioration 
of the output characteristics of the O.sub.2 sensor in a single O.sub.2 
sensor system directly effects a deterioration in the emission 
characteristics. On the other hand, in a double O.sub.2 sensor system, 
even when the output characteristics of the upstream-side O.sub.2 sensor 
are deteriorated, the emission characteristics are not deteriorated. That 
is, in a double O.sub.2 sensor system, even if only the output 
characteristics of the downstream-side O.sub.2 are stable, good emission 
characteristics are still obtained. 
In the above-mentioned double O.sub.2 sensor system, for example, an 
air-fuel ratio feedback control parameter such as a rich skip amount RSR 
and/or a lean skip amount RSL is calculated in accordance with the output 
of the downstream-side O.sub.2 sensor, and an air-fuel ratio correction 
amount FAF is calculated in accordance with the output V.sub.1 of the 
upstream-side O.sub.2 sensor and the air-fuel ratio feedback control 
parameter as illustrated in FIGS. 2A and 2B (see: U.S. Ser. Nos. 831,566 
and 848,580). In this case, the air-fuel ratio feedback control parameter 
is stored in a backup random access memory (RAM). Therefore, when the 
downstream-side O.sub.2 sensor is brought to a non-activation state or the 
like to stop the calculation of the air-fuel ratio feedback control 
parameter by the downstream-side O.sub.2 sensor, the air-fuel ratio 
correction amount FAF is calculated in accordance with the output of the 
upstream-side O.sub.2 sensor and the air-fuel ratio feedback control 
parameter which was calculated in an activation state of the 
downstream-side O.sub.2 sensor (i.e., an air-fuel ratio feedback control 
mode for the downstream-side O.sub.2 sensor) and was stored in the backup 
RAM. 
In the above-mentioned double O.sub.2 sensor system, however, when the 
control is transferred from an air-fuel ratio feedback control mode for 
the downstream-side O.sub.2 sensor to an open-loop control mode for the 
downstream-side O.sub.2 sensor, the air-fuel ratio feedback control 
parameter may be so large or small that an air-fuel ratio feedback control 
by the upstream-side O.sub.2 sensor using the air-fuel ratio feedback 
control parameter invites overcorrection of the air-fuel ratio. That is, 
in an air-fuel ratio feedback mode for the upstream-side O.sub.2 sensor, 
when the catalyst converter is not completely activated or when the 
upstream-side O.sub.2 sensor is not completely activated, the air-fuel 
ratio may be made overrich or overleaned, thus increasing the HC and CO 
emissions or the NO.sub.X emission. Also, in an air-fuel ratio feedback 
control mode for the upstream-side O.sub.2 sensor, when the engine is in 
an idling state, the air-fuel ratio may be greatly fluctuated, thus 
reducing the drivability characteristics. Note that the idling state is 
usually one condition of the air-fuel ratio feedback control mode for the 
downstream-side O.sub.2 sensor, but is not a condition of the air-fuel 
ratio feedback control mode for the upstream-side O.sub.2 sensor. 
Also, in the air-fuel ratio feedback control mode for the upstream-side 
O.sub.2 sensor and in the open-loop control mode for the downstream-side 
O.sub.2 sensor, it is possible to control the actual air-fuel ratio in 
accordance with the output of the upstream-side O.sub.2 sensor and an 
air-fuel ratio feedback control parameter which is a fixed value. In this 
case, however, the air-fuel ratio feedback control parameter calculated in 
the air-fuel ratio feedback mode does not reflect the control of the 
air-fuel ratio in the open-loop control mode for the downstream-side 
O.sub.2 sensor at all, and accordingly, it is impossible to obtain an 
optimum air-fuel ratio such as the stoichiometric air-fuel ratio in the 
open-loop control mode. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a double air-fuel ratio 
sensor system having improved exhaust emission characteristics and having 
improved drivability characteristics in an air-fuel ratio feedback control 
mode for an upstream-side air-fuel ratio sensor, but in an open-loop 
control mode for a downstream-side air-fuel ratio sensor. 
According to the present invention, in an air-fuel ratio feedback control 
mode for the downstream-side air-fuel ratio sensor which, in this case, 
includes an air-fuel ratio feedback control mode for the upstream-side 
air-fuel ratio sensor, an air-fuel ratio feedback control parameter is 
calculated in accordance with the output of the downstream-side air-fuel 
ratio sensor, and an actual air-fuel ratio is adjusted in accordance with 
the output of the upstream-side air-fuel ratio sensor and the air-fuel 
ratio feedback control parameter. In this air-fuel ratio feedback control 
mode, a large allowable range is imposed on the air-fuel ratio feedback 
control parameter, and in a non air-fuel ratio feed control mode for the 
downstream-side air-fuel ratio sensor, a small allowable range is imposed 
on the air-fuel ratio feedback control parameter which is, in this case, 
unchangeable. 
As a result, since the allowable range of the air-fuel ratio feedback 
control parameter is large in the air-fuel ratio feedback mode for the 
downstream-side O.sub.2 sensor, effective use is made of a double air-fuel 
ratio sensor system is effectively made use of. On the other hand, in the 
open-loop control mode for the downstream-side O.sub.2 sensor 15, and in 
the air-fuel ratio feedback control mode for the upstream-side O.sub.2 
sensor 13, since the allowable range of the air-fuel ratio feedback 
control parameter is small, the deviation of the air-fuel ratio from the 
stoichiometric air-fuel ratio is small, thus improving the HC, CO, and 
NO.sub.X emission characteristics, the drivability characteristics, and 
the fuel consumption.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In FIG. 3, which illustrates an internal combustion engine according to the 
present invention, reference numeral 1 designates a four-cycle spark 
ignition engine disposed in an automotive vehicle. Provided in an 
air-intake passage 2 of the engine 1 is a potentiometer-type airflow meter 
3 for detecting the amount of air drawn into the engine 1 to generate an 
analog voltage signal in proportion to the amount of air flowing 
therethrough. The signal of the airflow meter 3 is transmitted to a 
multiplexer-incorporating analog-to-digital (A/D) converter 101 of a 
control circuit 10. 
Disposed in a distributor 4 are crank angle sensors 5 and 6 for detecting 
the angle of the crank-shaft (not shown) of the engine 1. 
In this case, the crank-angle sensor 5 generates a pulse signal at every 
720.degree. crank angle (CA) while the crank-angle sensor 6 generates a 
pulse signal at every 30.degree. CA. The pulse signals of the crank angle 
sensors 5 and 6 are supplied to an input/output (I/O) interface 102 of the 
control circuit 10. In addition, the pulse signal of the crank angle 
sensor 6 is then supplied to an interruption terminal of a central 
processing unit (CPU) 103. 
Additionally provided in the air-intake passage 2 is a fuel injection valve 
7 for supplying pressurized fuel from the fuel system to the air-intake 
port of the cylinder of the engine 1. In this case, other fuel injection 
valves are also provided for other cylinders, but are not shown in FIG. 3. 
Disposed in a cylinder block 8 of the engine 1 is a coolant temperature 
sensor 9 for detecting the temperature of the coolant. The coolant 
temperature sensor 9 generates an analog voltage signal in response to the 
temperature THW of the coolant and transmits that signal to the A/D 
converter 101 of the control circuit 10. 
Provided in an exhaust system on the downstream-side of an exhaust manifold 
11 is a three-way reducing and oxidizing catalyst converter 12 which 
removes three pollutants CO, HC, and NO.sub.X simultaneously from the 
exhaust gas. 
Provided on the concentration portion of the exhaust manifold 11, i.e., 
upstream of the catalyst converter 12, is a first O.sub.2 sensor 13 for 
detecting the concentration of oxygen composition in the exhaust gas. 
Further, provided in an exhaust pipe 14 downstream of the catalyst 
converter 12 is a second O.sub.2 sensor 15 for detecting the concentration 
of oxygen composition in the exhaust gas. The O.sub.2 sensors 13 and 15 
generate output voltage signals and transmit those signals to the A/D 
converter 101 of the control circuit 10. 
Reference 16 designates a throttle valve, and 17 an idle switch for 
detecting whether or not the throttle valve 16 is completely closed. 
The control circuit 10, which may be constructed by a microcomputer, 
further comprises a central processing unit (CPU) 103, a read-only memory 
(ROM) 104 for storing a main routine and interrupt routines such as a fuel 
injection routine, an ignition timing routine, tables (maps), constants, 
etc., a random access memory 105 (RAM) for storing temporary data, a 
backup RAM 106, a clock generator 107 for generating various clock 
signals, a down counter 108, a flip-flop 109, a driver circuit 110, and 
the like. 
Note that the battery (not shown) is connected directly to the backup RAM 
106 and, therefore, the content thereof is not erased even when the 
ignition switch (not shown) is turned off. 
The down counter 108, the flip-flop 109, and the driver circuit 110 are 
used for controlling the fuel injection valve 7. That is, when a fuel 
injection amount TAU is calculated in a TAU routine, which will be later 
explained, the amount TAU is preset in the down counter 108, and 
simultaneously, the flip-flop 109 is set. As a result, the driver circuit 
110 initiates the activation of the fuel injection valve 7. On the other 
hand, the down counter 108 counts up the clock signal from the clock 
generator 107, and finally generates a logic "1" signal from the carry-out 
terminal of the down counter 108, to reset the flip-flop 109, so that the 
driver circuit 110 stops the activation of the fuel injection valve 7. 
Thus, the amount of fuel corresponding to the fuel injection amount TAU is 
injected into the fuel injection valve 7. 
Interruptions occur at the CPU 103 when the A/D converter 101 completes an 
A/D conversion and generates an interrupt signal; when the crank angle 
sensor 6 generates a pulse signal; and when the clock generator 107 
generates a special clock signal. 
The intake air amount data Q of the airflow meter 3 and the coolant 
temperature data THW of the coolant sensor 9 are fetched by an A/D 
conversion routine(s) executed at every predetermined time period and are 
then stored in the RAM 105. That is, the data Q and THW in the RAM 105 are 
renewed at every predetermined time period. The engine speed Ne is 
calculated by an interrupt routine executed at 30.degree. CA, i.e., at 
every pulse signal of the crank angle sensor 6, and is then stored in the 
RAM 105. 
The operation of the control circuit 10 of FIG. 3 will be now explained. 
FIG. 4 is a routine for calculating a first air-fuel ratio feedback 
correction amount FAF1 in accordance with output of the upstream-side 
O.sub.2 sensor 13 executed at every predetermined time period such as 4 
ms. 
At step 401, it is determined whether or not all of the feedback control 
(closed-loop control) conditions by the upstream-side O.sub.2 sensor 13 
are satisfied. The feedback control conditions are as follows: 
(i) the engine is not in a starting state; 
(ii) the coolant temperature THW is higher than 50.degree. C.; 
(iii) the power fuel incremental amount FPOWER is 0; and 
(iv) the upstream-side O.sub.2 sensor 13 is in an activated state. 
Note that the determination of activation/non-activation of the 
upstream-side O.sub.2 sensor 13 is carried out by determining whether or 
not the coolant temperature THW.gtoreq.70.degree. C., or by whether or not 
the output of the upstream-side O.sub.2 sensor 13 is once swung, i.e., 
once changed from the rich side to the lean side, or vice versa. Of 
course, other feedback control conditions are introduced as occasion 
demands. However, an explanation of such other feedback control conditions 
is omitted. 
If one of more of the feedback control conditions is not satisfied, the 
control proceeds to step 428, in which the amount FAF is caused to be 1.0 
(FAF=1.0), thereby carrying out an open-loop control operation. Note that, 
in this case, the amount FAF can be a value or a mean value immediately 
before the open-loop control operation. That is, the amount FAF or a mean 
value FAF thereof is stored in the backup RAM 106, and in an open-loop 
control operation, the value FAF or FAF is read out of the backup RAM 106. 
Contrary to the above, at step 401, if all of the feedback control 
conditions are satisfied, the control proceeds the step 402. 
At step 402, an A/D conversion is performed upon the output voltage V.sub.1 
of the upstream-side O.sub.2 sensor 13, and the A/D converted value 
thereof is then fetched from the A/D converter 101. Then at step 403, the 
voltage V1 is compared with a reference voltage V.sub.R1 such as 0.45 V, 
thereby determining whether the current air-fuel ratio detected by the 
upstream-side O.sub.2 sensor 13 is on the rich side or on the lean side 
with respect to the stoichiometric air-fuel ratio. 
If V.sub.1 .ltoreq.V.sub.R1, which means that the current air-fuel ratio 
upstream of the catalyst converter 12 is lean, the control proceeds to 
step 404, which determines whether or not the value of a delay counter 
CDLY is positive. If CDLY&gt;0, the control proceeds to step 405, which 
clears the delay counter CDLY, and then proceeds to step 406. If 
CDLY.ltoreq.0, the control proceeds directly to step 406. At step 406, the 
delay counter CDLY is counted down by 1, and at step 407, it is determined 
whether or not CDLY&lt;TDL. Note that TDL is a lean delay time period for 
which a rich state is maintained even after the output of the 
upstream-side O.sub.2 sensor 13 is changed from the rich side to the lean 
side, and is defined by a negative value. Therefore, at step 407, only 
when CDLY&lt;TDL does the control proceed to step 408, which causes CDLY to 
be TDL, and then to step 409, which causes a first air-fuel ratio flag F1 
to be "0" (lean state). On the other hand, if V.sub.1 &gt;V.sub.R1, which 
means that the current air-fuel ratio upstream of the catalyst converter 
12 is rich, the control proceeds to step 410, which determines whether or 
not the value of the delay counter CDLY is negative. If CDLY&lt;0, the 
control proceeds to step 411, which clears the delay counter CDLY, and 
then proceeds to step 412. If CDLY .gtoreq.0, the control directly 
proceeds to 412. At step 412, the delay counter CDLY is counted up by 1, 
and at step 413, it is determined whether or not CDLY&gt;TDR. Note that TDR 
is a rich delay time period for which a lean state is maintained even 
after the output of the upstream-side O.sub.2 sensor 13 is changed from 
the lean side to the rich side, and is defined by a positive value. 
Therefore, at step 413, only when CDLY&gt;TDR does the control proceed to 
step 414, which causes CDLY to the TDR, and then to step 415, which causes 
the first air-fuel ratio flag F1 to be "1" (rich state). 
Next, at step 416, it is determined whether or not the first air-fuel ratio 
flag F1 is reversed, i.e., whether or not the delayed air-fuel ratio 
detected by the upstream-side O.sub.2 sensor 13 is reversed. If the first 
air-fuel ratio flag F1 is reversed, the control proceeds to steps 417 to 
419, which carry out a skip operation. 
At step 417, if the flag F1 is "0" (lean) the control proceeds to step 418, 
which remarkably increases the correction amount FAF by an effective skip 
amount ERSR. Also, if the flag F1 is "1" (rich) at step 417, the control 
proceeds to step 419, which remarkably decreases the correction amount FAF 
by an effective skip amount ERSL. Note that the effective skip amounts 
ERSR and ERSL are calculated by the routine of FIG. 6 and are stored in 
the RAM 105. 
On the other hand, if the first air-fuel ratio flag F1 is not reversed at 
step 416, the control proceeds to steps 420 to 422, which carries out an 
integration operation. That is, if the flag F1 is "0" (lean) at step 420, 
the control proceeds to step 421, which gradually increases the correction 
amount FAF by a rich integration amount KIR. Also, if the flag F1 is "1" 
(rich) at step 420, the control proceeds to step 422, which gradually 
decreases the correction amount FAF by a lean integration amount KIL. Note 
that, in this case, KIR (KIL)&lt;ERSR (ERSL). 
The correction amount FAF is guarded by a minimum value 0.8 at steps 423 
and 424. Also the correction amount FAF is guarded by a maximum value 1.2 
at steps 425 and 426. Thus, the controlled air-fuel ratio is prevented 
from becoming overlean or overrich. 
The correction amount FAF is then stored in the RAM 105, thus completing 
this routine of FIG. 4 at steps 428. 
The operation by the flow chart of FIG. 4 will be further explained with 
reference to FIGS. 5A through 5D. As illustrated in FIG. 5A, when the 
air-fuel ratio A/F is obtained by the output of the upstream-side O.sub.2 
sensor 13, the delay counter CDLY is counted up during a rich state, and 
is counted down during a lean state, as illustrated in FIG. 5B. As a 
result, a delayed air-fuel ratio corresponding to the first air-fuel ratio 
flag F1 is obtained as illustrated in FIG. 5C. For example, at time 
t.sub.1, even when the air-fuel ratio A/F is changed from the lean side to 
the rich side, the delayed air-fuel ratio A/F' (F1) is changed at time 
t.sub.2 after the rich delay time period TDR. Similarly, at time t.sub.3, 
even when the air-fuel ratio A/F is changed from the rich side to the lean 
side, the delayed air-fuel ratio F1 is changed at time t.sub.4 after the 
lean delay time period TDL. However, at time t.sub.5, t.sub.6, or t.sub.7, 
when the air-fuel ratio A/F is reversed within a shorter time period than 
the rich delay time period TDR or the lean delay time period TDL, the 
delay air-fuel ratio A/F' is reversed at time t.sub.8. That is, the 
delayed air-fuel ratio A/F' is stable when compared with the air-fuel 
ratio A/F. Further, as illustrated in FIG. 4D, at every change of the 
delayed air-fuel ratio A/F' from the rich side to the lean side, or vice 
versa, the correction amount FAF is skipped by the skip amount ERSR or 
ERSL, and in addition, the correction amount FAF is gradually increased or 
decreased in accordance with the delayed air-fuel ratio A/F'. 
Air-fuel ratio feedback control operations by the downstream-side O.sub.2 
sensor 15 will be explained. There is a type of air-fuel ratio feedback 
control operations by the downstream-side O.sub.2 sensor 15 in which an 
air-fuel ratio feedback control parameter in the air-fuel ratio feedback 
control operation by the upstream-side O.sub.2 sensor 13 is variable. 
Further, as the air fuel ratio feedback control parameter, there are 
nominated a delay time period TD (in more detail, the rich delay time 
period TDR and the lean delay time period TDL), a skip amount RS (in more 
detail, the rich skip amount RSR and the lean skip amount RSL), an 
integration amount KI (in more detail, the rich integration amount KIR and 
the lean integration amount KIL), and the reference voltage V.sub.R1. 
For example, if the rich delay time period becomes longer than the lean 
delay time period (TDR&gt;(-TDL)), the controlled air-fuel becomes richer, 
and if the lean delay time period becomes longer than the rich delay time 
period ((-TDL)&gt;TDR), the controlled air-fuel ratio becomes leaner. Thus, 
the air-fuel ratio can be controlled by changing the rich delay time 
period TDR and the lean delay time period (-TDL) in accordance with the 
output of the downstream-side O.sub.2 sensor 15. Also, if the rich skip 
amount RSR is increased or if the lean skip amount RSL is decreased, the 
controlled air-fuel ratio becomes richer, and if the lean skip amount RSL 
is increased or if the rich skip amount RSR is decreased, the controlled 
air-fuel ratio becomes leaner. Thus, the air-fuel ratio can be controlled 
by changing the rich skip amount RSR and the lean skip amount RSL in 
accordance with the output downstream-side O.sub.2 sensor 15. Further, if 
the rich integration amount KIR is increased or if the lean integration 
amount KIL is decreased, the controlled air-fuel ratio becomes richer, and 
if the lean integration amount KIL is increased or if the rich integration 
amount KIR is decreased, the controlled air-fuel ratio becomes leaner. 
Thus, the air-fuel ratio can be controlled by changing the rich 
integration amount KIR and the lean integration amount KIL in accordance 
with the output of the downstream-side O.sub.2 sensor 15. Still further, 
if the reference voltage V.sub.R1 is increased, the controlled air-fuel 
ratio becomes richer, and if the reference voltage V.sub.R1 is decreased, 
the controlled air-fuel ratio becomes leaner. Thus, the air-fuel ratio can 
be controlled by changing the reference voltage V.sub.R1 in accordance 
with the output of the downstream-side O.sub.2 sensor 15. 
There are various merits obtained by the control of the air-fuel ratio 
feedback control parameters by the output V.sub.2 of the downstream-side 
O.sub.2 sensor 15. For example, when the delay time periods TDR and TDL 
are controlled by the output V.sub.2 of the downstream-side O.sub.2 sensor 
15, it is possible to precisely control the air-fuel ratio. Also, when the 
skip amounts RSR and RSL are controlled by the output V.sub.2 of the 
downstream-side O.sub.2 sensor 15, it is possible to improve the response 
speed of the air-fuel ratio feedback control by the output V.sub.2 of the 
downstream-side O.sub.2 sensor 15. Of course, it is possible to 
simultaneously control two or more kinds of the air-fuel ratio feedback 
control parameters by the output V.sub.2 of the downstream-side O.sub.2 
sensor 15. 
A double O.sub.2 sensor system, in which an air-fuel ratio feedback control 
parameter of the first air-fuel ratio feedback control by the 
upstream-side O.sub.2 sensor is variable, will be explained with reference 
to FIGS. 6 and 7. In this case, the skip amounts RSR and RSL as the 
air-fuel ratio feedback control parameters are variable. 
FIG. 6 is a routine for calculating the effective skip amounts ERSR and 
ERSL in accordance with the output V.sub.2 of the downstream-side O.sub.2 
sensor 15 executed at every predetermined time period such as 1 s. 
At steps 601 through 605, it is determined whether or not all of the 
feedback control (closed-loop control) conditions by the downstream-side 
O.sub.2 sensor 15 are satisfied. For example, at step 601, it is 
determined whether or not the feedback control conditions by the 
upstream-side O.sub.2 sensor 13 are satisfied. At step 602, it is 
determined whether or not the coolant temperature THW is higher than 
70.degree. C. At step 603, it is determined whether or not the throttle 
valve 16 is open (LL="0"). At step 604, it is determined whether or not 
the output V.sub.2 of the downstream-side O.sub.2 sensor 15 has been once 
changed from the lean side to the rich side or vice versa. At step 605, it 
is determined whether or not a load parameter such as Q/Ne is larger than 
a predetermined value X.sub.1. Of course, other feedback control 
conditions are introduced as occasion demands. However, an explanation of 
such other feedback control conditions is omitted. 
If one or more of the feedback control conditions is not satisfied, the 
control proceeds directly to step 623, thereby carrying out an open-loop 
control operation. 
Contrary to the above, if all of the feedback control conditions are 
satisfied, the control proceeds to step 606. At step 606, an A/D 
conversion is performed upon the output voltage V.sub.2 of the 
downstream-side O.sub.2 sensor 15, and the A/D converted value thereof is 
then fetched from the A/D converter 101. Then, at step 607, the voltage 
V.sub.2 is compared with a reference voltage V.sub.R2 such as 0.55 V, 
thereby determining whether the current air-fuel ratio detected by the 
downstream-side O.sub.2 sensor 15 is on the rich side or on the lean side 
with respect to the stoichiometric air-fuel ratio. Note that the reference 
voltage V.sub.R2 (=0.55 V) is preferably higher than the reference voltage 
V.sub.R1 (=0.45 V), in consideration of the difference in output 
characteristics and deterioration speed between the O.sub.2 sensor 13 
upstream of the catalyst converter 12 and the O.sub.2 sensor 15 downstream 
of the catalyst converter 12. However, the voltage V.sub.R2 can be 
voluntarily determined. 
At step 607, if the air-fuel ratio is lean, the control proceeds to step 
608 which resets a second air-fuel ratio flag F2. Alternatively, the 
control proceeds the step 609, which sets the second air-fuel ratio flag 
F2. 
At step 610, it is determined whether or not the second air-fuel ratio F2 
is "0". If F2="0", which means that the air-fuel ratio downstream of the 
catalyst converter 12 is lean, the control proceeds to steps 611 and 612, 
and if F2="1", which means that the air-fuel ratio downstream of the 
catalyst converter 12 is rich, the control proceeds to steps 613 and 614. 
At step 611, a rich skip amount RSR is read out of the backup RAM 106, and, 
the rich skip amount RSR is increased by a definite value .DELTA.RS such 
as 0.08% to move the air-fuel ratio to the rich side. Further, at step 
612, a lean skip amount RSL is read out of the backup RAM 106, and the 
lean skip amount RSL is decreased by the definite value .DELTA.RS to move 
the air-fuel ratio to the rich side. 
On the other hand, at step 613, the rich skip amount RSR is read out of the 
backup RAM 106, and, the rich skip amount RSR is decreased by a definite 
value .DELTA.RS to move the air-fuel ratio to the lean side. Further, at 
step 614, the lean skip amount RSL is read out of the backup RAM 106, and 
the lean skip amount RSL is increased by the definite value .DELTA.RS to 
move the air-fuel ratio to the lean side. 
The skip amounts RSR and RSL are guarded by an allowable range defined by a 
minimum value MIN1 and a maximum value MAX1 at steps 615 through 620. In 
this case, in order to effectively make use of a double O.sub.2 sensor 
system, this allowable range is larger. For example, the values MIN1 and 
MAX1 are 0% and 10%, respectively, and therefore, the allowable range is 
0% to 10% (5%.+-.5%). That is, at step 615, it is determined whether or 
not the rich skip amount RSR is within a range of MIN1 to MAX1. As a 
result, if RSR&lt;MIN1, the control proceeds to step 616 which causes RSR to 
be MIN1, and if RSR&gt;MAX1, the control proceeds to step 617 which causes 
RSR to be MAX1. Similarly, at step 618, it is determined whether or not 
the rich skip amount RSL is within the range of MIN1 to MAX1. As a result, 
if RSL&lt;MIN1, the control proceeds to step 619 which causes RSL to be MIN1, 
and if RSL&gt;MAX1, the control proceeds to step 620 which causes RSL to be 
MAX1. 
Next, at step 621, the effective rich skip amount ERSR is replaced by the 
rich skip amount RSR, and at step 622, the effective lean skip amount ERSL 
is replaced by the lean skip amount RSL. That is, 
EQU ERSR.rarw.RSR 
EQU ERSL.rarw.RSL 
Note that the skip amounts RSR and RSL are stored in the backup RAM 106, 
while the effective skip amounts ERSR and ERSL are stored in the RAM 105. 
Also, the minimum value MIN1 is a level by which the transient 
characteristics of the skip operation using the amounts RSR and RSL can be 
maintained, and the maximum value MAX1 is a level by which the drivability 
is not deteriorated by the fluctuation of the air-fuel ratio. 
Steps 623 through 632 for the open-loop control will be explained. At step 
623, the rich skip amount RSR is read out of the backup RAM 106, and a 
rich skip amount tRSR for an open-loop control is replaced by the rich 
skip amount RSR. Further, at step 624, the lean skip amount RSL is read 
out of the backup RAM 106, and a lean skip amount tRSL for an open-loop 
control is replaced by the lean skip amount RSL. That is, the skip amounts 
tRSR and tRSL for an open-loop control are the values of the skip amounts 
RSR and RSL for an air-fuel ratio feedback control immediately before an 
open-loop control is initiated. 
The skip amounts tRSR and tRSL for an open-loop control are guarded by an 
allowable range defined by a minimum value MIN2 and a maximum value MAX2 
at steps 625 through 630. In this case, in order to reduce the fluctuation 
of the air-fuel ratio by the air-fuel ratio feedback control of the output 
V.sub.1 of the upstream-side O.sub.2 sensor 13 in an open-loop control 
mode of the downstream-side O.sub.2 sensor 15, this allowable range is 
smaller as compared with the allowable range of MIN1 to MAX1. For example, 
the values MIN2 and MAX2 are 2% and 8%, respectively, and therefore, this 
allowable range is 2% to 8% (5%.+-.3%). That is, at step 625, it is 
determined whether or not the rich skip amount tRSR is within a range of 
MIN2 to MAX2. As a result, if tRSR&lt;MIN2, the control proceeds to step 626 
which causes tRSR to be MIN2, and if tRSR&gt;MAX2, the control proceeds to 
step 627 which causes tRSR to be MAX2. Similarly, at step 628, it is 
determined whether or not the rich skip amount tRSL is within the range of 
MIN2 to MAX2. As a result, if tRSL&lt;MIN2, the control proceeds to step 629 
which causes tRSL to be MIN2, and if tRSL&gt;MAX1, the control proceeds to 
step 630 which causes tRSL to be MAX2. 
Next, at step 631, the effective rich skip amount ERSR is replaced by the 
rich skip amount tRSR, and at step 632, the effective lean skip amount 
ERSL is replaced by the lean skip amount tRSL. That is, 
EQU ERSR.rarw.tRSR 
EQU ERSL.rarw.tRSL. 
Note that the skip amounts tRSR and tRSL are stored in the RAM 105. 
The routine of FIG. 6 is completed by step 633. 
FIG. 7 is a routine for calculating a fuel injection amount TAU executed at 
every predetermined crank angle such as 360.degree. CA. At step 701, a 
base fuel injection amount TAUP is calculated by using the intake air 
amount data Q and the engine speed data Ne stored in the RAM 105. That is, 
EQU TAUP.rarw..alpha..multidot.Q/Ne 
where .alpha. is a constant. Then at step 702, a warming-up incremental 
amount FWL is calculated from a one-dimensional map by using the coolant 
temperature data THW stored in the RAM 105. Note that the warming-up 
incremental amount FWL decreased when the coolant temperature THW 
increases. At step 803, a final fuel injectional amount TAU is calculated 
by 
EQU TAU.rarw.TAUP.multidot.FAF.multidot.(FWL+.beta.)+.gamma. 
where .beta. and .beta. are correction factors determined by other 
parameters such as the voltage of the battery and the temperature of the 
intake air. At step 704, the final fuel injection amount TAU is set in the 
down counter 108, and in addition, the flip-flop 109 is set to initiate 
the activation of the fuel injection valve 7. This routine is then 
completed by step 705. Note that, as explained above, when a time period 
corresponding to the amount TAU has passed, the flip-flop 109 is reset by 
the carry-out signal of the down counter 108 to stop the activation of the 
fuel injection valve 7. 
FIGS. 8A through 8D are timing diagrams for explaining the effective skip 
amounts ERSR and ERSL obtained by the flow charts of FIG. 6. In this case, 
before time t.sub.1 ', the engine is in an air-fuel ratio feedback control 
mode for the downstream-side O.sub.2 sensor 15, and after time t.sub.1 ', 
the engine is in an open-loop control mode for the downstream-side O.sub.2 
sensor 15. In the air-fuel ratio feedback control mode, when the output of 
the downstream-side O.sub.2 sensor 15 is changed as illustrated in FIG. 
8A, the determination at 610 of FIG. 6 corresponding to the second 
air-fuel ratio flag F2 is shown in FIG. 8B. As a result, as shown in FIGS. 
8C and 8D, when the determination at step 610 is lean, the effective rich 
skip amount ERSR is gradually increased at the speed of .DELTA.RS and the 
effective lean skip amount ERSL is gradually decreased at the speed of 
.DELTA.RS, and when the determination at step 610 is rich, the effective 
rich skip amount ERSR is gradually decreased at the speed of .DELTA.RS and 
the effective lean skip amount ERSL is gradually increased at the speed of 
.DELTA.RS. In this case, the effective skip amounts RSR and RSL are 
changed within a range of from MAX1 to MIN1. On the other hand, in the 
open-loop control mode, the effective skip amounts ERSR and ERSL 
calculated in the air-fuel ratio feedback control mode are held, but in 
this case, the held values are kept to be within a range of from MIN2 to 
MAX2. 
In FIG. 9, which is a modification of FIG. 6, steps 901 and 902 are 
provided instead of steps 625 through 630 of FIG. 6, thereby reducing the 
controlled range (i.e., the amplitude).DELTA.(=ERSR-ERSL ) of the 
effective skip amounts ERSR and ERSL before the open-loop control by a 
definite ratio K (&lt;1). That is, if the control center of the effective 
skip amounts is defined by ERSR=ERSL=5%, at step 901, 
EQU tRSR.rarw.5%+(tRSR-5%).multidot.K. 
Also, at step 902, 
EQU tRSL.rarw.5%+(tRSL-5%).multidot.K. 
In this case, in view of the software efficiency, the value K is preferably 
1/2 (1 bit shift operation) or 0.75 (=1/2+1/4) in accordance with a 
driving parameter. According to the routine of FIG. 9, the control range 
.DELTA. (=ERSR-ERSL ) is reduced by K in an open-loop control mode as 
compared with in an open-loop control mode. Also, if the controlled range 
.DELTA. is already small immediately before the open-loop control, the 
controlled range .DELTA. is further reduced in the open-loop control. 
In FIGS. 10, 11, and 12, which are also modifications of FIG. 6, in an 
open-loop control mode for the downstream-side O.sub.2 sensor 15, the 
allowable range (the control range) is variable in accordance with whether 
or not a driving operation such as a warming-up mode and an idling state. 
For example, when the engine is in the warming-up mode (i.e., when the 
determination at step 1001 is affirmative), the control range .DELTA. is 
reduced by K.sub.1 (FIGS. 10, 11, and 12), while when the engine is in a 
non-warming-up mode (i.e., when the determination at step 1001 is 
negative), the control range .DELTA. is reduced by K.sub.2 (&lt;K.sub.1) 
(see: steps 1003 and 1004 of FIG. 10). Alternately, the control range 
.DELTA. is within a range from MIN2 to MAX2 (see: steps 1101 to 1106 of 
FIG. 11, or the skip amounts tRSR and tRSL are fixed values such as 5% 
(see steps 1201 and 1202 of FIG. 12). According to the routines of FIGS. 
10, 11, and 12, the values tRSR and tRSL can be modified to avoid the 
smells of for example, hydrogen sulfide, from the catalyst converter 12. 
Also, the first air-fuel ratio feedback control by the upstream-side 
O.sub.2 sensor 13 is carried out at every relatively small time period, 
such as 4 ms, and the second air-fuel ratio feedback control by the 
downstream-side O.sub.2 sensor 15 is carried out at every relatively large 
time period, such as 1 s. That is because the upstream-side O.sub.2 sensor 
13 has good response characteristics when compared with the 
downstream-side O.sub.2 sensor 15. 
Further, the present invention can be applied to a double O.sub.2 sensor 
system in which other air-fuel ratio feedback control parameters, such as 
the integration amounts KIR and KIL, the delay time periods TDR and TDL, 
or the reference voltage V.sub.R1, are variable. 
Still further, a Karman vortex sensor, a heat-wire type flow sensor, and 
the like can be used instead of the airflow meter. 
Although in the above-mentioned embodiments, a fuel injection amount is 
calculated on the basis of the intake air amount and the engine speed, it 
can be also calculated on the basis of the intake air pressure and the 
engine speed, or the throttle opening and the engine speed. 
Further, the present invention can be also applied to a carburetor type 
internal combustion engine in which the air-fuel ratio is controlled by an 
electric air control value (EACV) for adjusting the intake air amount; by 
an electric bleed air control valve for adjusting the air bleed amount 
supplied to a main passage and a slow passage; or by adjusting the 
secondary air amount introduced into the exhaust system. In this case, the 
base fuel injection amount corresponding to TAUP at step 701 of FIG. 7 is 
determined by the carburetor itself, i.e., the intake air negative 
pressure and the engine speed, and the air amount corresponding to TAU at 
step 703 of FIG. 7. 
Further, a CO sensor, a lean-mixture sensor or the like can be also used 
instead of the O.sub.2 sensor.