Double Air-Fuel Ratio Sensor System Carrying Out Learning Control Operation

(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, 4,027,477, 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 is 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 upstreamside 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, however, the air-fuel ratio correction coefficient FAF may be greatly deviated from a reference value such as 1.0 due to individual differences in the characteristics of the parts of the engine, individual changes caused by aging, environmental changes, and the like. For example, when driving at a high altitude (above sea level), the air-fuel ratio correction coefficient FAF is remarkably reduced, thereby obtaining an optimum air-fuel ratio such as the stoichiometric air-fuel ratio. In this case, a maximum value and a minimum value are imposed on the air-fuel ratio correction coefficient FAF, thereby preventing the controlled air-fuel ratio from becoming overrich or overlean. Therefore, when the air-fuel ratio correction coefficient FAF is close to the maximum value or the minimum value, the margin of the air-fuel ratio correction coefficient FAF becomes small, thus limiting the compensation of a transient change of the controlled air-fuel ratio. Also, when the engine is switched from an air-fuel ratio feedback control (closed-loop control) by the upstream-side and downstream-side O.sub.2 sensors to an open-loop control, the air-fuel ratio correction coefficient FAF is made the reference value (=1.0), thereby causing an overrich or overlean condition in the controlled air-fuel ratio, and thus deteriorating the fuel consumption, the drivability, and the condition of the exhaust emissions such as HC, CO, and NO.sub.X, since the air-fuel ratio correction coefficient FAF (=0.1) during an open-loop control is, in this case, not an optimum level. Further, it takes a long time for the controlled air-fuel ratio to reach an optimum level after the engine is switched from an open control to an air-fuel ratio feedback control by the upstream-side and downstream-side O.sub.2 sensors, thus also deteriorating the fuel consumption, the drivability, and the condition of the exhaust emissions.

Accordingly, a learning control operation has been introduced into a double O.sub.2 sensor system, so that a mean value of the air-fuel ratio correction coefficient FAF, i.e., a mean value of successive values of the air-fuel ratio correction coefficient FAF immediately before skip operations is always changed around the reference value such as 1.0. Therefore, the margin of the air-fuel ratio correction coefficient FAF is always large, and accordingly, a transient change in the controlled air-fuel ratio can be compensated. Also, a difference in the air-fuel ratio correction coefficient FAF between an air-fuel ratio feedback control and an open-loop control becomes small. As a result, the deviation of the controlled air-fuel ratio in an open-loop control from its optimum level is small, and in addition, the controlled air-fuel ratio promptly reaches an optimum level after the engine is switched from an open-loop control to an air-fuel ratio feedback control.

In the above-mentioned learning control operation, a learning value FGHAC is calculated so that the mean value FAFAV of the air-fuel ratio correction coefficient FAF is brought close to the reference value such as 1.0. This learning control operation originally responds to a change of density of the air intake into the engine such as when driving at a high altitude. Therefore, a maximum value and a minimum value are also imposed on the learning value FGHAC, thereby preventing the controlled air-fuel ratio from becoming overrich or overlean due to the operation of an evaporation system. In a double O.sub.2 sensor system, however, the base air-fuel ratio is controlled by changing the deviation of the air-fuel ratio correction coefficient FAF from the reference value such as 1.0. Accordingly, since the mean value FAFAV of the air-fuel ratio correction coefficient FAF is changed by the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor even when no change occurs in the intake air density, the learning value FGHAC is changed and brought close to the maximum value or minimum value thereof. Therefore, in this case, the margin of the learning value FGHAC becomes small, and even when a change occurs in the intake air density, compensation of the change of the intake air density may be impossible, thus also deteriorating the fuel consumption, the drivability, and the condition of the exhaust emissions.

It is an object of the present invention to provide a double air-fuel ratio sensor system in an internal combustion engine in which a learning control operation is properly carried out when the intake air density is changed.

According to the present invention, in a double air-fuel ratio sensor system including two O.sub.2 sensors upstream and downstream of a catalyst converter provided in an exhaust passage, an actual air-fuel ratio is adjusted by using the output of the upstream-side O.sub.2 sensor and the output of the downstream-side O.sub.2 sensor. In this system, when a change of an air-fuel ratio correction amount or a change of an air-fuel ratio feedback control parameter calculated in accordance with the output of the downstream-side air-fuel ratio sensor is small, a learning correction amount is calculated so that a mean value of the air-fuel ratio correction amount is brought close to a reference value. The actual air-fuel ratio is further adjusted in accordance with the learning correction amount. That is, according to the present invention, when the change of the air-fuel ratio correction amount or the air-fuel ratio feedback control parameter by the downstream-side air-fuel ratio sensor is so small that the air-fuel ratio feedback control by the downstream-side air-fuel ratio sensor is sufficiently stable, a learning control operation is carried out. In this case, this learning control operation originally can respond to a change of the intake air density. Otherwise, a learning control operation is prohibited, so that the air-fuel ratio feedback control by the downstream-side air-fuel ratio sensor is prominently carried out.

The present invention will be more clearly understood from the description as set forth below with reference to the accompanying drawings, wherein:

FIG. 1 is a graph showing the emission characteristics of a single O.sub.2 sensor system and a double O.sub.2 sensor system;

FIG. 2 is a schematic view of an internal combustion engine according to the present invention;

FIGS. 3, 3A, 3B, 3C, 4, 6, 6A, 6B, 6C, 7, 8A, 8B, 9, 12, 12A, 12B, 13, 14A, 14B, 15, 18, and 20 are flow charts showing the operation of the control circuit of FIG. 2;

FIGS. 5A through 5D are timing diagrams explaining the flow chart of FIGS. 3, 3A, 3B and 3C;

FIGS. 10A through 10H, and FIGS. 11A, 11B, and 11C are timing diagrams explaining the flow charts of FIGS. 3, 3A, 3B, 3C, 4, 6, 6A, 6B, 6C, 7 8A, and 8B;

FIGS. 16A through 16I and FIGS. 17A, 17B, and 17C are timing diagrams explaining the flow charts of FIGS. 3, 4, 13, 14A, 14B, and 15; and

FIGS. 19A through 19D are timing diagrams explaining the flow chart of FIG. 18.

In FIG. 2, 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 taken 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 sensor 5 and 6 for detecting the angle of the crankshaft (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, though not shown in FIG. 2.

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 it 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 them to the A/D converter 101 of the control circuit 10.

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, 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, an interface 102 of the control circuit 10.

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 never 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 date Q of the airflow meter 3 and the coolant temperature date 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. 2 will be now explained.

FIG. 3 is a routine for calculating a first air-fuel ratio feedback correction amount FAF1 in accordance with the output of the upstream-side O.sub.2 sensor 13 executed at every predetermined time period such as 4 ms.

At step 301, it is determined whether or not all 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/nonactivation 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 verse. 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 to step 329, in which the amount FAF1 is caused to be 1.0 (FAF1=1.0), thereby carrying out an open-loop control operation.

Contrary to the above, at step 301, if all of the feedback control conditions are satisfied, the control proceeds to step 302.

At step 302, 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 303, the voltage V.sub.1 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 is lean, the control proceeds to step 304, which determines whether or not the value of a first delay counter CDLY1 is positive If CDLY1>0, the control proceeds to step 305, which clears the first delay counter CDLY1, and then proceeds to step 306. If CDLY1.ltoreq.0, the control proceeds directly to step 306. At step 306, the first delay counter CDLY1 is counted down by 1, and at step 307, it is determined whether or not CDLY1<TDL1. Note that TDL1 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 307, only when CDLY1<TDL1 does the control proceed to step 308, which causes CDLY1 to be TDL1, and then to step 309, which causes a first air-fuel ratio flag F1 to be "0" (lean state). On the other hand, if V.sub.1 >V.sub.R1, which means that the current air-fuel ratio is rich, the control proceeds to step 310, which determines whether or not the value of the first delay counter CDLY1 is negative. If CDLY1<0, the control proceeds to step 311, which clears the first delay counter CDLY1, and then proceeds to step 312. If CDLY1.gtoreq.0, the control directly proceeds to 312. At step 312, the first delay counter CDLY1 is counted up by 1, and at step 313, it is determined whether or not CDLY1>TDR1. Note that TDR1 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 313, only when CDLY1>TDR1 does the control proceed to step 314, which causes CDLY1 to be TDR1, and then to step 315, which causes the first air-fuel ratio flag F1 to be "1" (rich state).

Next, at step 316, 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 317 to 321, which carry out a learning control operation and a skip operation.

That is, at step 317, it is determined whether or not a learning control execution flag F.sub.G is "1". The learning control execution flag F.sub.G will be explained later with reference to FIGS. 7 and 8. Only if F.sub.G ="1", does the control proceed to step 318 which carries out a learning control operation, which will be explained later with reference to FIG. 4.

At step 319, if the flag F1 is "0" (lean) the control proceeds to step 320, which remarkably increases the correction amount FAF by a skip amount RSR. Also, if the flag F1 is "1" (rich) at step 517, the control proceeds to step 321, which remarkably decreases the correction amount FAF by the skip amount RSL.

On the other hand, if the first air-fuel ratio flag F1 is not reversed at step 316, the control proceeds to step 322 to 324, which carries out an integration operation. That is, if the flag F1 is "0" (lean) at step 322, the control proceeds to step 323, which gradually increases the correction amount FAF1 by a rich integration amount KIR. Also, if the flag F1 is "1" (rich) at step 322, the control proceeds to step 324, which gradually decreases the correction amount FAF1 by a lean integration amount KIL.

The correction amount FAF1 is guarded by a minimum value 0.8 at steps 325 and 326, and by a maximum value 1.2 at steps 327 and 328, thereby also preventing the controlled air-fuel ratio from becoming overrich or overlean.

The correction amount FAF1 is then stored in the RAM 105, thus completing this routine of FIG. 3 at step 330.

The learning control at step 318 of FIG. 3 is explained with reference to FIG. 4.

At step 401, a mean value FAFAV of the air-fuel ratio correction coefficient FAF1 is calculated by

where FAF1.sub.0 is a value of the air-fuel ratio correction coefficient FAF1 fetched previously at a skip operation. That is, the mean value FAF1AV is a mean value of two successive values of the air-fuel ratio correction coefficient FAF1 immediately before the skip operations. Note that the mean value FAF1AV can be obtained by four or more successive maximum and minimum values of the air-fuel ratio correction coefficient FAF1. At step 402, in order to prepare the next execution,

At step 403, a difference between the mean value FAF1AV and a reference value, which, in this case, is a definite value such as 1.0 corresponding to the stoichiometric air-fuel ratio, is calculated by:

Note that the definite value 1.0 is the same as the value of the air-fuel ratio correction coefficient FAF1 in an open-loop control by the upstream side O.sub.2 sensor 13 (see step 329 of FIG. 3).

At step 404, it is determined whether the difference .DELTA.FAF is positive. As a result, if .DELTA.FAF>0, then the base air-fuel ratio before the execution of the next skip operation is too rich. Then, at step 405, the learning correction amount FGHAC is increased by

where .DELTA.FGHAC is a definite value. Then, at steps 406 and 407, the learning correction amount FGHAC is guarded by a maximum value such as 1.05. Contrary to this, if .DELTA.FAF.ltoreq.0, then the base air-fuel ratio before the execution of the next skip operation is too lean. Then, at step 408, a learning correction amount FGHAC is decreased by

Then, at steps 409 and 410, the learning correction amount FGHAC is guarded by a minimum value such as 0.90.

Then, the learning correction amount FGHAC is stored in the backup RAM 106 at step 411 and the routine of FIG. 4 is completed by step 412.

Note that it is possible to renew the learning correction amount FGHAC, only if .vertline..DELTA.FAF.vertline.>X (positive value).

Thus, according to the learning control routine of FIG. 4, the learning correction amount FGHAC is calculated so that the air-fuel ratio correction coefficient FAF1 is brought close to the reference value such as 1.0.

The operation by the flow chart of FIG. 3 will be further explained with reference to FIGS. 5A through 5D. As illustrated in FIG. 5A, when the air-fuel ratio A/F1 is obtained by the output of the upstream-side O.sub.2 sensor 13, the first delay counter CDLY1 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/F1' (F1) is changed at time t.sub.2 after the rich delay time period TDR1. Similarly, at time t.sub.3, even when the air-fuel ratio A/F1 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 TDL1. However, at time t.sub.5, t.sub.6, or t.sub.7, when the air-fuel ratio A/F1 is reversed within a smaller time period than the rich delay time period TDR1 or the lean delay time period TDL1, the delay air-fuel ratio A/F1' is reversed at time t.sub.8. That is, the delayed air-fuel ratio A/F1' is stable when compared with the air-fuel ratio A/F1. Further, as illustrated in FIG. 5D, at every change of the delayed air-fuel ratio A/F1' from the rich side to the lean side, or vice versa, the correction amount FAF1 is skipped by the skip amount RSR or RSL, and also, the correction amount FAF1 is gradually increased or decreased in accordance with the delayed air-fuel ratio A/F1'.

Air-fuel ratio feedback control operations by the downstream-side O.sub.2 sensor 15 will be explained. There are two types of air-fuel ratio feedback control operations by the downstream-side O.sub.2 sensor 15, i.e., the operation type in which a second air-fuel ratio correction amount FAF2 is introduced thereinto, and the operation type 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 TDR1 and the lean delay time period TDL1), 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 larger than the lean delay time period (TDR1>(-TDL1)), the controlled air-fuel ratio becomes richer, and if the lean delay time period becomes larger than the rich delay time period ((-TDL1)>TDR1), the controlled air-fuel ratio becomes leaner. Thus, the air-fuel ratio can be controlled by changing the rich delay time period TDR1 and the lean delay time period (-TDL1) 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 of the 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.

A double O.sub.2 sensor system into which a second air-fuel ratio correction amount FAF2 is introduced will be explained with reference to FIGS. 6, 7, 8A, 8B, and 9.

FIG. 6 is a routine for calculating a second air-fuel ratio feedback correction amount FAF2 in accordance with the output of the downstream-side O.sub.2 sensor 15 executed at every predetermined time period such as 1 s.

At step 601, it is determined all the feedback control (closed-loop control) conditions by the downstream-side O.sub.2 sensor 15 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.; and

(iii) the power fuel incremental amount FPOWER is 0.

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 also proceeds to steps 631, 632, and 633 thereby carrying out an open-loop control operation. That is, at step 631, the first air-fuel ratio correction coefficient FAF2 is made a reference value such as 1.0. Also, at step 632, the rich skip amount RSR and the lean skip amount RSL are both made a definite value RS1, i.e., RSR=RSL=RS1. Further, at step 633, the rich integration amount KIR and the lean integration amount KIL are both made a definite value KI1, i.e., KIR=KIL=KI1. According to steps 632 and 633, the air-fuel ratio feedback control by the upstream-side O.sub.2 sensor 13 makes it possible for the first air-fuel ratio correction coefficient FAF1 to be changed symmetrically with respect to the mean value thereof, so that, if the air-fuel ratio feedback control by the downstream-side, O.sub.2 sensor 15 is opened, the mean value FAF1 calculated at step 401 of FIG. 4 exactly indicates a mean value of the first air-fuel ratio correction coefficient FAF1. Thus, erroneous calculation of the learning correction amount FGHAC can be prevented.

Contrary to the above, at step 601, if all of the feedback control conditions are satisfied, the control proceeds to step 602.

At step 602, 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 603, the voltage V 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.

Step 604 through 615 correspond to step 304 through 315, respectively, of FIG. 3, thereby performing a delay operation upon the determination at step 603. Here, a rich delay time period is defined by TDR2, and a lean delay time period is defined by TDL2. As a result of the delayed determination, if the air-fuel ratio is rich a second air-fuel ratio flag F2 is caused to be "1", and if the air-fuel ratio is lean, a second air-fuel ratio flag F2 is caused to be "0".

Next, at step 616, it is determined whether or not the second air-fuel ratio flag F2 is reversed, i.e., whether or not the delayed air-fuel ratio detected by the downstream-side O.sub.2 sensor 15 is reversed. If the second air-fuel ratio flag F2 is reversed, the control proceeds to steps 617 to 620 which carry out a learning control determination and a skip operation. The learning control determination step 617 will be later explained with reference to FIG. 7. At step 618, it is determined whether or not the flag F2 is "0". That is, if the flag F2 is "0" (lean) at step 618, the control proceeds to step 619, which remarkably increases a second correction amount FAF2.sub.i during an air-fuel ratio feedback control by skip amount RS2. Also, if the flag F2 is "1" (rich) at step 618, the control proceeds to step 620, which remarkably decreases the second correction amount FAF2.sub.i by the skip amount RS2.

On the other hand, if the second air-fuel ratio flag F2 is not reversed at step 616, the control proceeds to steps 621 to 623, which carries out an integration operation. That is, if the flag F2 is "0" (lean) at step 621, the control proceeds to step 622, which gradually increases the second correction amount FAF2.sub.i by an integration amount KI2. Also, if the flag F2 is "1" (rich) at step 621, the control proceeds to step 623, which gradually decreases the second correction amount FAF2.sub.i by the integration amount KI2.

Note that the skip amount RS2 is larger than the integration amount KI2.

The second correction amount FAF2.sub.i is guarded by a minimum value 0.8 at steps 624 and 625, and by a maximum value 1.2 at steps 626 and 627, thereby also preventing the controlled air-fuel ratio from becoming overrich or overlean.

At step 628, the second air-fuel ratio correction coefficient FAF2.sub.i during an air-fuel ratio feedback control is made the second air-fuel ratio correction coefficient FAF2, i.e.,

At step 629, the rich skip amount RSR and the lean skip amount RSL are made definite values RSR.sub.1, and RSL.sub.1 (RSR.sub.1 .noteq.RSL.sub.1), respectively, and at step 630, the rich integration amount KIR and the lean integration amount KIL are made definite values KIR.sub.1 and KIL.sub.1 (KIR.sub.1 .noteq.KIL.sub.1), respectively. Note that the values RSR.sub.1, RSL.sub.1, KIR.sub.1, and KIL.sub.1 are determined in view of the characteristics of the engine parts.

The values FAF2, RSR, RSL, KIR, and KIL are then stored in the RAM 105, thus completing this routine of FIG. 6 at step 634.

The learning control determination step 617 of FIG. 6 will be explained below with reference to FIG. 7. Note that, as explained above, the routine of FIG. 7 is carried out at every switching of the delayed output the second air-fuel ratio flag F2 of the downstream-side O.sub.2 sensor 15, i.e., at every switching of the second air-fuel ratio correction coefficient FAF2. At step 701, a mean value FAF2 of the second air-fuel ratio correction coefficient FAF2 is calculated by

where FAF2.sub.0 is a value of the second air-fuel ratio correction coefficient FAF2 immediately before a previous switching of the second air-fuel ratio flag F2.

At step 702, a blunt value FAF2AVX of the mean value FAF2 is calculated by ##EQU1## At step 703, a counter C is counted up by 1 in order to measure the number of switchings of the second air-fuel ratio flag F2, and at step 704, it is determined whether or not the counter C exceeds a predetermined value C.sub.0. If C>C.sub.0, the control proceeds to step 705, and if C.ltoreq.C.sub.0, the control directly proceeds to step 712.

At step 705, a change .DELTA.FAF2AVX of the blunt value FAF2AVX is calculated by

where FAF2AVX0 is a value of the blunt value FAF2AVX at a previous execution of this step 705. At step 706, it is determined whether or not the change .DELTA.FAF2AVX is larger than a definite value A. As a result, if .DELTA.FAF2AVX>A, the control proceeds to step 707 which resets the learning control execution flag F.sub.G (F.sub.G ="0"), thereby prohibiting a learning control. Otherwise, the control proceeds to step 708 which determines whether or not the other learning control conditions are satisfied. The other learning control conditions are as follows:

(i) the coolant temperature THW is higher than 70.degree. C. and lower than 90.degree. C.; and

(ii) the deviation .DELTA.Q of the intake air amount is smaller than a predetermined value.

Of course, other learning control conditions are also introduced as occasion demands. If one or more of the learning control conditions are not satisfied, the control proceeds to step 707, and if all the learning control conditions are satisfied, the control proceeds to step 709 which sets the learning control execution flag F.sub.G (F.sub.G ="1"), thereby carrying out a learning control. Thus, when the change .DELTA.FAF2AVX is large, which means that the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is unstable, the learning control is prohibited, while when the change .DELTA.FAF2AVX is small, which means that the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is stable, the learning control as well as the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is carried out.

At step 710, the counter C is reset, and at step 711,

in order to prepare the next operation. Also, at step 712,

Then, this routine is completed by step 713.

Note that a change of the mean value FAF2 can be used instead of the change .DELTA.FAF2AVX of the blunt value FAF2AVX.

In FIG. 8A, which is a modification of FIG. 6, steps 801 and 802 are added to FIG. 6. That is, when the learning control operation is carried out (F.sub.G ="1"), the air-fuel ratio feedback control by the downstreamside O.sub.2 sensor 15 is prohibited. In this case, since the first air-fuel ratio correction coefficient FAF1 is changed symmetrically with respect to the mean value thereof, an accurate learning control operation is carried out.

In FIG. 8B, which is a modification of FIG. 7, steps 803 and 804 are added to FIG. 7. That is, at step 803, the intake air amount data Q is read out of the RAM 105, and it is determined whether Q is smaller than a definite value Q.sub.0. If Q.gtoreq.Q.sub.0, the control proceeds to step 804, which sets the learning control execution flag F.sub.G, thereby prohibiting a learning control operation. Otherwise, the control proceeds to step 701. Note that if the intake air amount Q is large, the learning correction amount FGHAC may be erroneously calculated because of evaporation or the like. Such an erroneous learning control is avoided by the routine of FIG. 8B.

Note that, in FIG. 8B, other load parameters such as intake air amount per one revolution, the intake air pressure, or the throttle opening of the engine can be used instead of the intake air amount Q.

FIG. 9 is a routine for calculating a fuel injection amount TAU executed at every predetermined crank angle such as 360.degree. CA. At step 901, 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,

where K is a constant. Then, at step 902, a warming-up incremental amount FWL is calculated from a one-dimensional map stored in the ROM 104 by using the coolant temperature data THW stored in the RAM 105. Note that the warming-up incremental amount FWL decreases when the coolant temperature THW increases. At step 903, a final fuel injection amount TAU is calculated by

Where .alpha. 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 903, the final fuel injection amount TAU is set in the down counter 107, and in addition, the flip-flop 108 is set initiate the activation of the fuel injection valve 7. Then, this routine is completed by step 904. Note that, as explained above, when a time period corresponding to the amount TAU passes, 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. 10A through 10H are timing diagrams for explaining the two air-fuel ratio correction amounts FAF1 and FAF2 obtained by the flow charts of FIGS. 3, 4, 6, 7, 8A, 8B, and 9. In this case, the engine is in a closed-loop control state for the two O.sub.2 sensors 13 and 15. When the output of the upstream-side O.sub.2 sensor 13 is changed as illustrated in FIG. 10A, the determination at step 303 of FIG. 3 is shown in FIG. 10B, and a delayed determination thereof corresponding to the first air-fuel ratio flag F1 is shown in FIG. 10C. As a result, as shown in FIG. 10D, every time the delayed determination is changed from the rich side to the lean side, or vice versa, the first air-fuel ratio correction amount FAF1 is skipped by the amount RSR or RSL. On the other hand, when the output of the downstream-side O.sub.2 sensor 15 is changed as illustrated in FIG. 10E, the determination at step 603 of FIG. 6 is shown in FIG. 10F, and the delayed determination thereof corresponding to the second air-fuel ratio flag F2 is shown in FIG. 10G. As a result, as shown in FIG. 10H, every time the delayed determination is changed from the rich side to the lean side, or vice versa, the second air-fuel ratio correction amount FAF2 is skipped by the skip amount RS2.

FIGS. 11A, 11B, and 11C are timing diagrams for explaining the learning correction amount FGHAC obtained by the routines of FIGS. 3, 4, 6, 7, 8A, 8B, and 9. In this case, the routines of FIGS. 6 and 7 are modified by FIGS. 8A and 8B, respectively. When the intake air amount Q is changed as shown in FIG. 11A, and, in addition, the second air-fuel ratio correction coefficient FAF2 is changed as shown in FIG. 11B, the learning correction amount FGHAC is renewed from t.sub.1 to time t.sub.2 and from time t.sub.5 to time t.sub.6 as shown in FIG. 11C. In this case, the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is prohibited (FAF2=1.0), and in addition, the first air-fuel ratio correction coefficient FAF (not shown) is changed symmetrically with respect to the mean value thereof, since RSR=RSL and KIR=KIL. On the other hand, from time t.sub.3 to time t.sub.4, although the intake air amount Q is small, the change of the second air-fuel ratio correction coefficient FAF2 is large, so that a learning control is prohibited and the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is carried out.

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. 12, 13, 14A, 14B, and 15. In this case, the skip amounts RSR and RSL as the air-fuel ratio feedback control parameters are variable.

FIG. 12 is a routine for calculating the skip amounts RSR and RSL in accordance with the output of the downstream-side O.sub.2 sensor 15 executed at every predetermined time period such as 1 s.

Steps 1201 through 1215 are the same as steps 601 through 615 of FIG. 6. That is, if one or more of the feedback control conditions is not satisfied, the control proceeds to steps 1233 and 1234, thereby carrying out an open-loop control operation. That is, at step 1233, the rich skip amount RSR and the lean skip amount RSL are both made a definite value RS1, i.e., RSR=RSL=RS1. Further, at step 1234, the rich integration amount KIR and the lean integration amount KIL are both made a definite value KI1, i.e., KIR=KIL=KI1. As a result, in the same way as in steps 632 and 633, the air-fuel ratio feedback control by the upstream-side O.sub.2 sensor 13 makes it possible for the first air-fuel ratio correction coefficient FAF1 to be changed symmetrically with respect to the mean value thereof, so that, if the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is opened, the mean value FAF1 calculated at step 401 of FIG. 4 exactly indicates a mean value of the first air-fuel ratio correction coefficient FAF1. Thus, erroneous calculation of the learning correction amount FGHAC can be prevented.

Contrary to the above, if all of the feedback control conditions are satisfied, the second air-fuel ratio flag F2 is determined by the routine of steps 1202 through 1215.

At step 1216, it is determined whether or not the second air-fuel ratio flag F2 is reversed, i.e., whether or not the delayed air-fuel ratio detected by the downstream-side O.sub.2 sensor 15 is reversed. Only if the second air-fuel ratio flag F2 is reversed, the control proceeds to step 1217 which carries out a learning control determination which will be later explained with reference to FIG. 13.

At step 1218, it is determined whether or not the second air-fuel ratio F2 is "0". If F2="0", which means that the air-fuel ratio is lean, the control proceeds to steps 1219 through 1224, and if F2="1", which means that the air-fuel ratio is rich, the control proceeds to steps 1225 through 1230.

At step 1219, a rich skip amount RSR.sub.i during an air-fuel ratio feedback control is increased by a definite value .DELTA.RS which is, for example, 0.08, to move the air-fuel ratio to the rich side. At steps 1220 and 1221, the rich skip amount RSR.sub.i is guarded by a maximum value MAX which is, for example, 6.2%. Further, at step 1222, a lean skip amount RSL.sub.i during an air-fuel ratio feedback control is decreased by the definite value .DELTA.RS to move the air-fuel ratio to the lean side. At steps 1223 and 1224, the lean skip amount RSL.sub.i is guarded by a minimum value MIN which is, for example 2.5%.

On the other hand, at step 1225, the rich skip amount RSR.sub.i is decreased by the definite value .DELTA.RS to move the air-fuel ratio to the lean side. At steps 1226 and 1227, the rich skip amount RSR.sub.i is guarded by the minimum value MIN. Further, at step 1228, the lean skip amount RSL.sub.i is decreased by the definite value .DELTA.RS to move the air-fuel ratio to the rich side. At steps 1229 and 1230, the lean skip amount RSL.sub.i is guarded by the maximum value MAX.

At step 1231,

Note that, in this case, the rich skip amount RSR is different from the lean skip amount RSL, since the amounts RSR.sub.i and RSL.sub.i are variable. Then, at step 1232, the rich integration amount KIR and the lean integration amount KIL are made definite values KIR.sub.1 and KIL.sub.1 (KIR.sub.1 .noteq.KIL.sub.1), respectively. Note that the values KIR.sub.1 and KIL.sub.1 are determined in view of the characteristics of the engine parts.

The values RSR, RSL, KIR, and KIL are then stored in the RAM 105, thus completing this routine of FIG. 12 at step 1235.

Thus, according to the routine of FIG. 12, when the delayed output of the second O.sub.2 sensor 15 is lean, the rich skip amount RSR is gradually increased, and the lean skip amount RSL is gradually decreased, thereby moving the air-fuel ratio to the rich side. Contrary to this, when the delayed output of the second O.sub.2 sensor 15 is rich, the rich skip amount RSR is gradually decreased, and the lean skip amount RSL is gradually increased, thereby moving the air-fuel ratio to the lean side.

The learning control determination step 1217 of FIG. 12 will be explained below with reference to FIG. 13. Note that, as explained above, the routine of FIG. 13 is carried out at every switching of the delayed output the second air-fuel ratio flag F2 of the downstream-side O.sub.2 sensor 15, i.e., at every switching of the skip amount RSR (RSL). At step 1301, a mean value RSR of the rich skip amount RSR is calculated by

where RSR0 is a value of the rich skip amount RSR immediately before a previous switching of the second air-fuel ratio flag F2.

At step 1302, a blunt value RSRAVX of the mean value RSR is calculated by ##EQU2## At step 1303, a counter C is counted up by 1 in order to measure the number of switchings of the second air-fuel ratio flag F2, and at step 1304, it is determined whether or not the counter C exceeds a predetermined value C.sub.0. If C>C.sub.0, the control proceeds to step 1305, and if C.ltoreq.C.sub.0, the control directly proceeds to step 1312.

At step 1305, a change .DELTA.RSRAVX of the blunt value RSRAVX is calculated by

where RSRAVX0 is a value of the blunt value RSRAVX at a previous execution of this step 1305. At step 1306, it is determined whether or not the change .DELTA.RSRAVX is larger than a definite value B. As a result, it .DELTA.RSRAVX>B, the control proceeds to step 1307 which resets the learning control execution flag F.sub.G (F.sub.G ="0"), thereby prohibiting a learning control. Otherwise, the control proceeds to step 1308 which determines whether or not the other learning control conditions are satisfied. The other learning control conditions are as follows:

(i) the coolant temperature THW is higher than 70.degree. C. and lower than 90.degree. C.; and

(ii) the deviation .DELTA.Q of the intake air amount is smaller than a predetermined value.

Of course, other learning control conditions are also introduced as occasion demands. If one or more of the learning control conditions are not satisfied, the control proceeds to step 1307, and if all the learning control conditions are satisfied, the control proceeds to step 1309 which sets the learning control execution flag F.sub.G (F.sub.G ="1"), thereby carrying out a learning control. Thus, when the change .DELTA.RSRAVX is large, which means that the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is unstable, the learning control is prohibited, while when the change .DELTA.RSRAVX is small, which means that the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is stable, the learning control as well as the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is carried out.

At step 1310, the counter C is reset, and at step 1311,

in order to prepare the next operation. Also, at step 1312,

Then, this routine is completed by step 1313.

Note that a change of the mean value RSR can be used instead of the change .DELTA.RSRAVX of the blunt value RSRAVX. Similarly, a change of a blunt or mean value of the lean skip amount RSL is also possible.

In FIG. 14A, which is a modification of FIG. 12, step 1401 is added to FIG. 12. That is, when the learning control operation is carried out (F.sub.G ="1"), the air-fuel ratio feedback control by the downstreamside O.sub.2 sensor 15 is prohibited. In this case, since the first air-fuel ratio correction coefficient FAF1 is changed symmetrically with respect to the means value thereof, an accurate learning control operation is carried out.

In FIG. 14B, which is a modification of FIG. 13, steps 1402 and 1403 are added to FIG. 13. Steps 1402 and 1403 are the same as step 803 and 804 of FIG. 8, respectively, and therefore, a detailed explanation thereof is omitted.

FIG. 15 is a routine for calculating a fuel injection amount TAU executed at every predetermined crank angle such as 360.degree. CA. At step 1501, 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,

where K is a constant. Then at step 1502, 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 decreases when the coolant temperature THW increases. At step 1503, a final fuel injection amount TAU is calculated by

where .alpha. 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 1504, the final fuel injection amount TAU is set in the down counter 108, and in addition, the flip-flip 109 is set to initiate the activation of the fuel injection valve 7. Then, this routine is completed by step 1505. 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. 16A through 16I are timing diagrams for explaining the air-fuel ratio correction amount FAF1 and the skip amounts RSR and RSL obtained by the flow charts of FIGS. 3, 4, 12, 13, 14A, 14B, and 15. FIGS. 16A through 16G are the same as FIGS. 10A through 10G, respectively. As shown in FIGS. 16H and 16I, when the delayed determination F2 is lean, the rich skip amount RSR is increased and the lean skip amount RSR is increased and the lean skip amount RSL is decreased, and when the delayed determination F2 is rich, the rich skip amount RSR is decreased and the lean skip amount RSL is increased. In this case, the skip amounts RSR and RSL are changed within a range from MAX to MIN.

FIG. 17A, 17B, and 17C are timing diagrams for explaining the learning correction amount FGHAC obtained by the routines of FIGS. 3, 4, 12, 13, 14A, 14B, and 15. In this case, the routines of FIGS. 12 and 13 are modified by FIGS. 14A and 14B, respectively. When the intake air amount Q is changed as shown in FIG. 17A, and in addition, the skip amounts RSR and RSL are changed as shown in FIG. 17B, the learning correction amount FGHAC is renewed from t.sub.1 to time t.sub.2 and from time t.sub.5 to time t.sub.6 as shown in FIG. 17C. In this case, the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is prohibited (RSR=RSL=RS1=0.05), and in addition, the first air-fuel ratio correction coefficient FAF (not shown) is changed symmetrically with respect to its mean value since RSR=RSL and KIR=KIL. On the other hand, from time t.sub.3 to time t.sub.4, although the intake air amount Q is small, the change of the skip amount RSR (RSL) is large, so that a learning control is prohibited and the air-fuel ratio feedback control by the downstream-side O.sub.2 sensor 15 is carried out.

In FIG. 18, which is a modification of FIG. 3, a delay operation different from the of FIG. 3 is carried out. That is, at step 1801, if V.sub.1 .ltoreq.V.sub.R1, which means that the current air-fuel ratio is lean, the control proceeds to steps 1802 which decreases a first delay counter CDLY1 by 1. Then, at steps 1803 and 1804, the first delay counter CDLY1 is guarded by a minimum value TDR1. Note that TDR1 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 negative value.

Note that, in this case, if CDLY1>0, then the delayed air-fuel ratio is rich, and if CDLY.ltoreq.0, then the delayed air-fuel ratio is lean.

Therefore, at step 1805, it is determined whether or not CDLY.ltoreq.0 is satisfied. As a result, if CDLY1<0, at step 1806, the first air-fuel ratio flag F1 is caused to be "0" (lean). Otherwise, the first air-fuel ratio flag F1 is unchanged, that is, the flag F1 remains at "1".

On the other hand, if V.sub.1 >V.sub.R1, which means that the current air-fuel ratio is rich, the control proceeds to step 1808 which increases the first delay counter CDLY1 by 1. Then, at steps 1809 and 1810, the first delay counter CDLY1 is guarded by a maximum value TDL1. Note that TDL1 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 positive value.

Then, at step 1811, it is determined whether or not CDLY>0 is satisfied. As a result, if CDLY>0, at step 1812, the first air-fuel ratio flag F1 is caused to be "1" (rich). Otherwise, the first air-fuel ratio flag F1 is unchanged, that is, the flag F1 remains at "0".

The operation by the flow chart of FIG. 18 will be further explained with reference to FIGS. 19A through 19D. As illustrated in FIGS. 19A, when the air-fuel ratio A/F1 is obtained by the output of the upstream-side O.sub.2 sensor 13, the first delay counter CDLY1 is counted up during a rich state, and is counted down during a lean state, as illustrated in FIG. 19B. As a result, the delayed air-fuel ratio A/F1' is obtained as illustrated in FIG. 19C. For example, at time t.sub.1, even when the air-fuel ratio A/F1 is changed from the lean side to the rich side, the delayed air-fuel ratio A/F1 is changed at time t.sub.2 after the rich delay time period TDR1. similarly, at time t.sub.3, even when the air-fuel ratio A/F1 is changed from the rich side to the lean side, the delayed air-fuel ratio A/F1' is changed at time t.sub.4 after the lean delay time period TDL1. However, at time t.sub.5, t.sub.6, or t.sub.7, when the air-fuel ratio A/F is reversed within a smaller time period than the rich delay time period TDR1 or the lean delay time period TDL1, the delayed air-fuel ratio A/F1' 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/F1. Further, as illustrated in FIG. 19D, at every change of the delayed air-fuel ratio A/F1' from the rich side to the lean side, or vice versa, the correction amount FAF1 is skipped by the skip amount RSR or RSL, and also, the correction amount FAF1 is gradually increased or decreased in accordance with the delayed air-fuel ratio A/F1'.

Note that, in this case, during an open-control mode, the rich delay time period TDR1 is, for example, -12 (48 ms), and the lean delay time period TDL1 is, for example, 6 (24 ms).

In FIG. 20, which is a modification of FIG. 12, the same delay operation as in FIG. 18 is carried out, and therefore, a detailed explanation thereof is omitted.

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 TDR1 and TDL1, 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 901 of FIG. 9 or at step 1501 of FIG. 15 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 903 of FIG. 9 or at step 1503 of FIG. 15.

Further, a CO sensor, a lean-mixture sensor or the like can be also used instead of the O.sub.2 sensor.

As explained above, according to the present invention, when the air-fuel ratio feedback control by the downstream-side air-fuel ratio sensor is unstable, a leaning control operation is prohibited so that the air-fuel ratio feedback control by the downstream-side air-fuel ratio sensor is prominently carried out. In other words, when the air-fuel ratio feedback control by the downstream-side air-fuel ratio sensor is stable, and a change occurs in the intake air density, a learning control operation is carried out, thereby improving the fuel consumption, the drivability, and the emission characteristics.