Device for determining deterioration of a catalytic converter for an engine

A device for determining a deterioration of the catalytic converter for an engine equipped with a catalytic converter disposed in the exhaust passage and upstream and downstream air-fuel ratio sensors disposed in the exhaust passage upstream and downstream of the catalytic converter, respectively. The device also determines whether the three-way catalyst in the catalytic converter has deteriorated based on the output signal of the downstream air-fuel ratio sensor when the air-fuel ratio of the engine is feedback controlled by the output of the upstream air-fuel ratio sensor, wherein the execution of the determining operation of catalyst deterioration is prohibited when the period of the cycle of the air-fuel ratio feedback control becomes longer than a predetermined value, thereby preventing errors from accuracy in the determination.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an air-fuel ratio control device for an 
engine that controls an air-fuel ratio of the engine based on at least an 
output of an air-fuel ratio sensor disposed in the exhaust passage 
upstream of a three-way catalyst. More specifically, the present invention 
relates to such an air-fuel control device that is able to detect the 
deterioration of the three-way catalyst based on at least an output of an 
air-fuel ratio sensor disposed in the exhaust passage downstream of the 
three-way catalyst. 
2. Description of the Related Art 
An air-fuel ratio control device for controlling an air-fuel ratio of an 
engine by a feedback control based on an output of one air-fuel ratio 
sensor (O.sub.2 sensor) disposed in an exhaust passage upstream of a 
catalytic converter is known as a single O.sub.2 sensor system. The single 
O.sub.2 sensor system is used to control the air-fuel ratio of the engine 
at a stoichiometric air-fuel ratio to improve the condition of exhaust 
emissions by utilizing the ability of the three-way catalytic converter to 
a maximum degree. 
Also, to compensate for the individual difference among cylinders or 
changes due to aging of the upstream O.sub.2 sensor, a double O.sub.2 
sensor system using two O.sub.2 sensors has been developed (U.S. Pat. No. 
4,739,614). In the double O.sub.2 sensor system, O.sub.2 sensors are 
disposed upstream and downstream of the catalytic converter in the exhaust 
passage, and the air-fuel ratio control is carried out based on the output 
of the downstream O.sub.2 sensor as well as the output of the upstream 
O.sub.2 sensor. 
Nevertheless, even in the double O.sub.2 sensor system, if the catalyst in 
the catalyst converter deteriorates, the condition of the exhaust 
emissions such as HC, CO, NO.sub.x deteriorates. Therefore, it is 
necessary to detect the deterioration of the catalyst accurately. 
To detect the deterioration of the catalyst in the catalytic converter, 
various methods and devices have been proposed. 
For example, Japanese Unexamined Patent Publication No. 63-97852 discloses 
a method for detecting the deterioration of the catalyst based on the 
interval of reversals of the output of the downstream O.sub.2 sensor 
(i.e., the period of changes of the output signal of the downstream O 
sensor from a rich side air-fuel ratio to a lean side air-fuel ratio, or 
vice versa ) during air-fuel ratio feedback control based on the output of 
the upstream O.sub.2 sensor. 
It is known that the interval of reversals of the output of the downstream 
O.sub.2 sensor during the air-fuel ratio feedback control becomes shorter 
when the catalyst in the catalytic converter has deteriorated. The method 
disclosed in Japanese Unexamined Patent Publication No. 63-97852 utilizes 
this phenomenon to detect the deterioration of the catalyst by counting 
the number of reversals of the output of the downstream O.sub.2 sensor 
over a predetermined time period when the air-fuel ratio of the engine is 
feedback controlled in accordance with the output of the upstream O.sub.2 
sensor under predetermined operating conditions of the engine. 
If the number of reversals is larger than a predetermined value (i.e., if 
the intervals of the output of the downstream O.sub.2 sensor becomes 
shorter), it is determined that the catalyst has deteriorated. 
In the above method, the deterioration of the catalyst is determined by 
detecting a reduction in an storage effect of the catalyst. That is, the 
catalyst has an ability to adsorb oxygen in the exhaust gas when the 
air-fuel ratio is in a rich side compared to the stoichiometric air-fuel 
ratio (i.e., the air-fuel ratio of the exhaust gas is lower than the 
stoichiometric air-fuel ratio), and to release the oxygen when the 
air-fuel ratio is in a lean side compared with the stoichiometric air-fuel 
ratio (i.e., the air-fuel ratio of the exhaust gas is higher than the 
stoichiometric air-fuel ratio). This ability, i.e., the O.sub.2 storage 
effect of the catalyst, becomes lower as deterioration of the catalyst 
proceeds. In the above method, the reduction in the O.sub.2 storage effect 
is detected by counting the number of reversals of the output of the 
downstream O.sub.2 sensor. 
The deterioration of the catalyst can be detected accurately by utilizing 
the O.sub.2 storage effect of the catalyst provided that a period of a 
cycle of the air-fuel ratio feedback control is relatively short. (In this 
specification, the term "period of a cycle of the air-fuel ratio feedback 
control" means a period of oscillation of the air-fuel ratio between a 
rich side air-fuel ratio and a lean side air-fuel ratio when the air-fuel 
ratio is feedback controlled, i.e., the period represented by "T" in FIG. 
1A. ) 
However, if the period of the cycle of the air-fuel ratio becomes 
relatively longer, it is difficult to determine the deterioration of the 
catalyst accurately by utilizing the O.sub.2 storage effect. 
This problem is explained in detail with reference to FIGS. 1A to 1G. 
FIG. 1A shows a typical response of the air-fuel ratio of the exhaust gas 
upstream of the catalytic converter when the air-fuel ratio feedback 
control is carried out. As shown in FIG. 1A, the air-fuel ratio of the 
exhaust gas oscillates periodically between a rich side air-fuel ratio and 
a lean side air-fuel ratio so that the central value of the oscillation 
coincides with the stoichiometric air-fuel ratio. The period of the cycle 
of the air-fuel ratio feedback control, which is indicated by T in FIG. 
1A, is normally relatively short (for example, approximately 0.5 seconds). 
FIG. 1B shows the response curve of the output signal VOM of the upstream 
O.sub.2 sensor when the air-fuel ratio is oscillating, as shown in FIG. 
1A. The output signal VOM also oscillates between a rich side and a lean 
side, and the interval of the reversal of the output signal VOM is same as 
the period of the cycle of the air-fuel ratio feedback control (i.e., T in 
FIG. 1A). 
FIGS. 1C and 1D show the response curves of the output signal VOS of the 
downstream O.sub.2 sensor in this case. FIG. 1C shows the response curve 
when the catalyst is normal, and FIG. 1D shows the same when the catalyst 
has deteriorated. 
If the catalyst is normal, the catalyst adsorbs surplus oxygen in the 
exhaust gas when the air-fuel ratio of the exhaust gas is in the lean side 
compared with the stoichiometric air-fuel ratio, and releases the adsorbed 
oxygen when the air-fuel ratio of the exhaust gas is in the rich side 
compared with the stoichiometric air-fuel ratio. Therefore, the air-fuel 
ratio of the exhaust gas downstream of the catalyst is maintained nearly 
constant at the mean value of the oscillation of the air-fuel ratio of the 
exhaust gas upstream of the catalyst (i.e., stoichiometric air-fuel ratio) 
though the air-fuel ratio of the exhaust gas upstream of the catalyst is 
oscillating. Accordingly, the output signal VOS of the downstream O.sub.2 
sensor reverses at a relatively longer interval as shown in FIG. 1C. 
On the other hand, if the catalyst is deteriorated, since the O.sub.2 
storage effect of the catalyst also becomes lower, the amount of the 
oxygen which is adsorbed and released from the catalyst decreases. This 
causes the output signal VOS to oscillate at a short interval of reversals 
in the same manner as the output VOM of the upstream O.sub.2 sensor (see 
FIG. 1D). Therefore, it is possible to detect the deterioration of the 
catalyst easily by monitoring the interval of reversals of the output 
signal VOS of the downstream O.sub.2 sensor. 
However, if the period of the cycle of the air-fuel ratio feedback control 
becomes longer as shown in FIG. 1E for some reason, the time period in 
which the air-fuel ratio of the exhaust gas upstream of the catalyst stays 
in the rich side or the lean side also becomes longer. 
If the upstream air-fuel ratio continues to stay in the lean side after the 
catalyst has adsorbed the oxygen to the maximum adsorbing capacity, the 
catalyst does not adsorb the surplus oxygen in the exhaust gas. This 
causes the air-fuel ratio of the exhaust gas down stream of the catalyst 
to also be in lean side since the surplus oxygen is no longer adsorbed by 
the catalyst. Similarly, if the upstream air-fuel ratio continues to stay 
in the rich side still after the catalyst has released all the adsorbed 
oxygen, the air-fuel ratio of the exhaust gas turns to the rich side since 
the oxygen is no longer released from the catalyst. 
Therefore, when the period of the cycle of the air-fuel ratio feedback 
control becomes longer (as shown in FIG. 1E), the air-fuel ratio 
downstream of the catalyst oscillates in a similar manner as the air-fuel 
ratio upstream of the catalyst, thereby causing the output VOS of the 
downstream O.sub.2 sensor to oscillate at relatively short interval of 
reversals in the similar manner as the output VOM of the upstream O.sub.2 
sensor regardless of the deterioration of the catalyst (see FIGS. 1F and 
1G). In such cases, if the determination of the deterioration of the 
catalyst is carried out, a normal catalyst can be erroneously determined 
as being deteriorated. 
There are cases in which the period of the cycle of the air-fuel ratio 
feedback control becomes longer. For example, when the upstream O.sub.2 
sensor has deteriorated, the period of the cycle of the air-fuel ratio 
feedback control becomes longer since the response of the upstream O.sub.2 
sensor becomes lower. U.S. Pat. No. 5,134,847 discloses a device for 
determining the deterioration of the catalyst that can prevent the above 
mistake in determination due to the deterioration of the upstream O.sub.2 
sensor. The device in U.S. Pat. No. 5,134,847 monitors the condition of 
the upstream O.sub.2 sensor, and prohibits the determining operation when 
the upstream O.sub.2 sensor is determined as being deteriorated. The 
upstream O.sub.2 sensor is determined as being deteriorated when the 
response of the upstream O.sub.2 sensor becomes lower (e.g. when the 
period of the cycle of the oscillation of the output of the upstream 
O.sub.2 sensor becomes longer than a predetermined value). 
However, even though the upstream O.sub.2 sensor has not deteriorated, the 
period of the cycle of the air-fuel ratio feedback control can be longer 
in some cases. For example, in a transition period of the sudden change in 
the operating conditions of the engine, such as in a sudden acceleration 
or a deceleration, the period of the cycle of the air-fuel ratio can be 
longer even though the response of the upstream O.sub.2 sensor is normal. 
In such a transition period, the output signal VOM of the upstream O.sub.2 
sensor may oscillate in the rich air-fuel ratio side or the lean air-fuel 
ratio side only, but does not oscillate between the rich air-fuel ratio 
side and the lean air-fuel ratio side (See FIG. 1H). Therefore the period 
of the cycle of the air-fuel ratio feedback control becomes longer even 
though the period of the cycle of the oscillation (T.sub.U in FIG. 1H) of 
the output signal of the upstream O.sub.2 sensor is still short. 
Also, when the engine is operated under conditions in which the velocity of 
the exhaust gas flow in the exhaust passage becomes low, the period of the 
cycle of the air-fuel ratio feedback control becomes longer since the time 
required for exhaust gas to flow over the distance between the engine and 
the position of the upstream O.sub.2 sensor increases. 
Therefore, according to the device in U.S. Pat. No. 5,134,847, a normal 
catalyst can be determined as being deteriorated under such conditions. 
SUMMARY OF THE INVENTION 
Therefore, in view of the problems of the related art, the object of the 
present invention is to provide a device for accurately determining the 
deterioration of a three-way catalyst in a catalytic converter used in a 
double O.sub.2 sensor system. 
According to the present invention, there is provided a device for 
determining the deterioration of a three-way catalyst disposed in an 
exhaust passage of an internal combustion engine equipped with an upstream 
air-fuel ratio sensor disposed in the exhaust passage upstream of the 
three-way catalyst for detecting an air-fuel ratio of the exhaust gas 
upstream of the three-way catalyst, a downstream air-fuel ratio sensor 
disposed in the exhaust passage downstream of the three-way catalyst for 
detecting the air-fuel ratio of the exhaust gas downstream of the 
three-way catalyst, and a feedback control means for controlling the 
air-fuel ratio of the engine by a feedback control based on, at least, the 
output of the upstream air-fuel ratio sensor. 
The device comprises a determining means for determining whether the 
three-way catalyst has deteriorated based on, at least, the output of the 
downstream air-fuel ratio sensor when the air-fuel ratio of the engine is 
controlled by the feedback control means, a condition determining means 
for determining that the engine operating conditions are not appropriate 
for the determination of the deterioration of the three-way catalyst in 
which the length of a period of a cycle of the feedback control of the 
air-fuel ratio by the feedback control means becomes larger than a value 
appropriate for the determination of the deterioration of the three-way 
catalyst, and a means for prohibiting the determination of the 
deterioration of the three-way catalyst when the condition detecting means 
determines that the engine operating conditions are not appropriate for 
the determination of the deterioration of the three-way catalyst.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIG. 2 schematically illustrates an embodiment of the device for 
determining the deterioration of the catalyst according to the present 
invention. 
In FIG. 2, reference numeral 1 represents an internal combustion engine for 
an automobile. An air intake passage 2 of the engine 1 is provided with a 
potentiometer-type airflow meter 3 for detecting an amount of air drawn 
into the engine 1, and generates an analog voltage signal proportional to 
the amount of air flowing therethrough. The signal from the airflow meter 
3 is transmitted to a multiplexer-incorporating analog-to-digital (A/D) 
converter 101 of the control circuit 10. 
Crank angle sensors 5 and 6, for detecting the angle of the crankshaft (not 
shown) of the engine 1, are disposed at a distributor 4. 
In this embodiment, the crank angle sensor 5 generates a pulse signal at 
every 720.degree. crank angle (CA) and the crank angle sensor 6 generates 
a pulse signal at every 30.degree. CA. The pulse signals from the crank 
angle sensors 5 and 6 are supplied to an input/output (I/O) interface 102 
of the control circuit 10. Further, the pulse signal of the crank angle 
sensor 6 is then supplied to an interruption terminal of a central 
processing unit (CPU) 103. 
In the intake passage 2, a fuel injection valve 7 is provided at an inlet 
port of each cylinder of the engine 1, for supplying pressurized fuel from 
the fuel system to the cylinders of the engine. 
A coolant temperature sensor 9 for detecting the temperature of the coolant 
is disposed in a water jacket of a cylinder block 8 of the engine 1. The 
coolant temperature sensor 9 generates an analog voltage signal in 
response to the temperature THW of the coolant, and transmits this signal 
to the A/D converter 101 of the control circuit 10. 
In the exhaust system, a three-way reducing and oxidizing catalytic 
converter 12 is disposed in the exhaust passage downstream of the exhaust 
manifold 11. The catalytic converter 12 has the O.sub.2 storage effect and 
is capable of removing three pollutants in the exhaust gas, i.e., CO, HC 
and NO.sub.x, simultaneously. 
An upstream O.sub.2 sensor 13 is provided at the exhaust manifold 11, i.e., 
upstream of the catalytic converter 12. 
A downstream O.sub.2 sensor 15 is disposed at an exhaust pipe 14 downstream 
of the catalytic converter 12. 
The upstream O.sub.2 sensor 13 and the downstream O.sub.2 sensor 15 
generate output signals corresponding to the concentration of the oxygen 
component in the exhaust gas. 
More specifically, the O.sub.2 sensors 13 and 15 generate output voltage 
signals that are changed in accordance with whether the air-fuel ratio of 
the exhaust gas is rich or lean, compared to the stoichiometric air-fuel 
ratio. The signals output by the O.sub.2 sensors 13 and 15 are transmitted 
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 and interrupt routines such as a fuel 
injection routine, and an ignition timing routine and constants, etc., a 
random-access-memory (RAM) 105 for storing temporary data, a backup RAM 
106, and a clock generator 107 for generating various clock signals. The 
backup RAM 106 is directly connected to a battery (not shown), and 
therefore, the content of the backup RAM 106 is preserved even when the 
ignition switch (not shown) is turned off. 
A throttle valve 16 operated by a vehicle driver, is provided in the intake 
air passage 2, together with an idle switch 17 for detecting the opening 
of the throttle valve and generating a signal ("LL signal") when the 
throttle valve 16 is fully closed. This LL signal is supplied to the I/O 
interface 102 of the control circuit 10. 
Reference 18 designates a secondary air supply valve for introducing 
secondary air to the exhaust manifold 11, thereby reducing the emission of 
HC and CO during a deceleration or an idling operation of the engine. 
Reference 19 designates an alarm that is activated when the catalytic 
converter 12 is determined as being deteriorated. 
A down counter 108, a flip-flop 109, and a drive circuit 110 are provided 
in the control circuit 10 for controlling the fuel injection valve 7. 
When a fuel injection amount TAU is calculated in a routine, as explained 
later, the amount TAU is preset in the down counter 108, and 
simultaneously, the flip-flop 109 is set, and as a result, the drive 
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, a logic "1" signal is generated from the 
terminal of the down counter 108, to reset the flip-flop 109, so that the 
drive circuit 110 stops the activation of the fuel injection valve 7, 
whereby an amount of fuel corresponding to the fuel injection amount TAU 
is supplied to the cylinders. 
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 from the airflow meter 3 and the coolant 
temperature data THW from the coolant sensor 9 are fetched by an A/D 
conversion routine(s) executed at predetermined intervals, and then stored 
in the RAM 105; i.e., the data Q and THW in the RAM 105 are updated at 
predetermined intervals. The engine speed Ne is calculated by an 
interruption routine executed at 30.degree. CA, i.e., at every pulse 
signal of the crank angle sensor 6, and is stored in the RAM 105. 
The operation of the control circuit 10 of FIG. 2 is now explained. 
FIGS. 3A and 3B show a routine for a feedback control of the air-fuel 
ratio. This routine calculates an air-fuel ratio correction factor FAF in 
accordance with the output VOM of the upstream O.sub.2 sensor 13, and is 
executed at predetermined intervals of, e.g., 4 ms. 
At step 301 in FIG. 3A, it is determined whether or not all conditions for 
air-fuel ratio feedback control are satisfied. The conditions for a 
feedback control are, for example, 
the engine is not being started, 
the coolant temperature is higher than a predetermined value, 
the fuel increments, such as a start-up fuel increment, a warming-up fuel 
increment, a power fuel increment, or an OTP fuel increment for preventing 
an excess rise in the temperature of the catalytic converters, are not 
being carried out, 
the outputs of the upstream O.sub.2 sensor 13 have been reversed (i.e., 
changed from a rich air-fuel ratio output signal to a lean air-fuel ratio 
output signal or vice versa) at least once, 
a fuel cut operation is not being carried out. 
If any one of these conditions is not satisfied, the routine proceeds to 
step 328 in FIG. 3B, which causes an air-fuel ratio feedback control flag 
XMFB to be "0" and the routine terminates at step 329 in FIG. 3B. 
If all of the conditions for the air-fuel ratio feedback control are 
satisfied at step 301, the routine proceeds to step 302. 
At step 302, an A/D conversion is performed upon receiving the output 
voltage VOM of the upstream 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 VOM is compared with a reference voltage V.sub.R1 to thereby 
determine whether the current air-fuel ratio detected by the upstream 
O.sub.2 sensor 13 is on the rich side or on the lean side with respect to 
the stoichiometric air-fuel ratio. The reference voltage V.sub.R1 is 
usually set at or near the central value of the maximum amplitude of the 
output of the O.sub.2 sensor and, in this embodiment, V.sub.R1 is set at 
0.45 V. 
If VOM.ltoreq.V.sub.R1, which means that the current air-fuel ratio is 
lean, the control proceeds to step 304, at which it is determined whether 
the value of a delay counter CDLY is positive. If CDLY&gt;0, the control 
proceeds to step 305, which clears the delay counter CDLY, and then 
proceeds to step 306. At step 306, the delay counter CDLY is counted down 
by 1, and at step 307, it is determined whether or not CDLY&lt;TDL. Note that 
TDL is a lean delay time for which a rich state is maintained even after 
the output of the upstream 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 CDLY&lt;TDL does the control proceed to step 308, which causes 
CDLY to be TDL, and then to step 309, which causes an air-fuel ratio flag 
F1 to be "0" (lean state). On the other hand, if VOM&gt;V.sub.R1, which means 
current air-fuel ratio is rich, the control proceeds to step 310, which 
determines whether or not the value of the delay counter CDLY is negative. 
If CDLY&lt;0, the control proceeds to step 311, which clears the delay 
counter CDLY, and then proceeds to step 312. If CDLY.gtoreq.0, the control 
directly proceeds to step 312. At step 312, the delay counter CDLY is 
counted up by 1, and at step 313, it is determined whether or not 
CDLY&gt;TDR. Note that TDR is a rich delay time for which a lean state is 
maintained even after the output of the upstream 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 CDLY&gt;TDR does the control proceed 
to step 314, which causes CDLY to be TDR, and then proceeds to step 315, 
which causes an air-fuel ratio flag F1 to be "1" (rich state). 
Then at step 316, a counter CTF is counted up by 1. As explained later, the 
counter CTF is used for measuring the period TF of the cycle of the 
air-fuel ratio feedback control, and counted up by 1 at every execution of 
the routine. 
Next, at step 317 in FIG. 3B, it is determined whether the air-fuel ratio 
flag F1 is reversed, i.e., whether the delayed air-fuel ratio detected by 
the upstream O.sub.2 sensor 13 is reversed. If the air-fuel ratio flag F1 
is reversed, the control proceeds to steps 318 to 320, and a skip 
operation is carried out. That is, the flag F1 is "0" (lean) at step 318, 
the control proceeds to step 319, which increases the correction factor 
FAF by a skip amount RSR. 
If the flag F1 is "1" (rich) at step 318, the control proceeds to step 320, 
which reduces the correction factor FAF by a skip amount RSL. In this 
case, also steps 324 and 325 are executed, which stores the value of the 
counter CTF in the RAM 105 as the value TF at step 324, and clears the 
counter CTF at step 325. Thereby, the value corresponding to the time 
lapsed from the time when the flag F1 was last reversed from "0" to "1" to 
the time when the flag F1 was reversed from "0" to "1" this time, i.e., 
the value of the period of the cycle of the air-fuel ratio feedback 
control is always updated and stored in the RAM 105 as TF. 
If the air-fuel ratio flag F1 is not reversed at step 317, the control 
proceeds to steps 321 to 323, which carry out an integration operation. 
That is, if the flag F1 is "0" (lean) at step 321, the control proceeds to 
step 322, which gradually increases the correction factor FAF by a rich 
integration amount KIR. Also, if the flag F1 is "1" (rich) at step 321, 
the control proceeds to step 323, which gradually decreases the correction 
factor FAF by a lean integration amount KIL. 
Then, at step 326, the air-fuel ratio correction factor FAF is guarded, for 
example, by a minimum value of 0.8 and by a maximum value of 1.2, thereby 
preventing the controlled air-fuel ratio from becoming overrich or 
overlean. 
The correction factor FAF is then Stored in the RAM 105 and the control 
proceeds to step 327, which causes the air fuel ratio feedback control 
flag XMFB to be "1", and the routine then terminates at step 326. 
The control operation by the flowcharts of FIGS. 3A and 3B are further 
explained with reference to FIGS. 4, A through D. As illustrated in FIG. 
4A, when the air-fuel ratio signal A/F is obtained by the output of the 
upstream O.sub.2 sensor 13, the delay counter CDLY is counted up when in a 
rich state, and is counted down when in a lean state, as illustrated in 
FIG. 4B. As a result, a delayed air-fuel ratio corresponding to the 
air-fuel ratio flag F1 is obtained as illustrated in FIG. 4C. 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 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 A/F' (F1) is changed at time t.sub.4 
after the lean delay time TDL. At time t.sub.5, t.sub.6, or t.sub.7, 
however, when the air-fuel ratio A/F is reversed in a shorter time than 
the rich delay time TDR or the lean delay time TDL, the delayed air-fuel 
ratio F1 is reversed at time t.sub.8. That is, the delayed air-fuel ratio 
A/F' (F1) 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 F1 
from the rich side to the lean side, or vice versa, the correction factor 
FAF is skipped by the skip amount RSR or RSL, and the correction factor 
FAF is gradually increased or reduced in accordance with the delayed 
air-fuel ratio F1. 
In this embodiment, the above-explained period TF (the period of the cycle 
of the air-fuel ratio feedback control) is equal to the interval of 
executions of the RSL skip operation. 
Next, the air-fuel ratio feedback control of the double O.sub.2 sensor 
system, in which the air-fuel ratio is controlled based on the output of 
the downstream O.sub.2 sensor 15 as well as the output of the upstream 
O.sub.2 sensor 13, is explained. 
Generally, three types of air-fuel ratio feedback control operations by the 
downstream O.sub.2 sensor 15 are used, i.e., the operation type in which 
one or more of the parameters such as the skip amounts RSR, RSL, 
integration amounts KIR, KIL and delay times TDR, TDL are variable, and 
the operation type in which the reference voltage V.sub.R1 of the outputs 
VOM of the upstream O.sub.2 sensor is variable, or, the operation type in 
which a second air-fuel ratio correction factor FAF2 calculated in 
accordance with the output of the downstream O.sub.2 sensor 15 is 
introduced. 
For example, 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 
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 O.sub.2 sensor 15. 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 O.sub.2 sensor 15. 
Also, if the rich delay time becomes longer than the lean delay time (i.e., 
TDR&gt;TDL), the controlled air-fuel ratio becomes richer, and if the lean 
delay time becomes longer than the rich delay time (i.e., TDL TDR), the 
controlled air-fuel ratio becomes leaner. Thus, the air-fuel ratio can be 
controlled by changing the rich delay time TDR and the lean delay time TDL 
in accordance with the output of the downstream O.sub.2 sensor 15. 
These types of air-fuel ratio control operations have respective 
advantages. For example, if the delay times TDR, TDL are variable, a 
precise control of the air-fuel ratio can be obtained, and if the skip 
amounts RSR, RSL are variable, the response of the control is improved. 
Naturally, two or more of these types of operation can be used at the same 
time. 
FIGS. 5A and 5B show a flow chart of the control operation of the double 
O.sub.2 sensor system in which the skip amounts RSR, RSL are varied in 
accordance with the output VOS of the downstream O.sub.2 sensor 15. This 
routine is executed at predetermined intervals of, e.g., 512 ms. 
The steps from 501 to 506 of FIG. 5A show the operation for determining 
whether the conditions for executing the feedback control based on the 
output of the downstream O.sub.2 sensor 15 are satisfied. 
These conditions are, 
the conditions for executing the air-fuel ratio feedback control based on 
the output of the upstream O.sub.2 sensor 13 are satisfied (the air-fuel 
ratio feedback control flag XMFB="1" at step 501), 
the temperature THW of the coolant is higher than a predetermined value 
(e.g., 70.degree. C.), (step 502), 
the throttle valve 16 is not fully closed (i.e., the signal LL is not ON), 
(step 503), 
the secondary air AS is not introduced into the exhaust manifold, (step 
504), 
the load of the engine represented by Q/Ne is more than a predetermined 
value X.sub.1 (i.e., Q/Ne.gtoreq.X.sub.1), (step 505), 
the downstream O.sub.2 sensor 15 is activated (step 506). 
If any one of these conditions are not satisfied, the routine proceeds to 
step 519 in which an air-fuel ratio feedback control flag XFSB is reset 
(="0"). 
If all of the conditions of steps 501 to 506 are satisfied, the flag XSFB 
is set (="1") at step 508, and the routine proceeds to step 509 of FIG. 
5B. 
The steps 509 through 518 illustrate the operation for calculating the skip 
amounts RSR or RSL in accordance with the output VOS of the downstream 
O.sub.2 sensor 15. 
At step 509, an A/D conversion is performed on the output voltage VOS of 
the downstream O.sub.2 sensor 15, and the A/D converted value thereof is 
then fetched from the A/D converter 101. Then at step 510, the voltage VOS 
is compared with a reference voltage V.sub.R2 such as 0.55 v, to determine 
whether the current air-fuel ratio detected by the downstream 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 
catalytic converter and the O.sub.2 sensor 15 downstream of the catalytic 
converter. 
If VOS.ltoreq.V.sub.R2 (lean state) at step 510, then the routine proceeds 
to steps 511 to 513, and if VOS&gt;V.sub.R2 (rich state), the routine 
proceeds to steps 514 to 516. Namely, at step 511, the rich skip amount 
RSR is increased by .DELTA.RS (constant value), thereby shifting the 
air-fuel ratio to the rich side. Then, at steps 512 and 513, the rich skip 
amount RSR is guarded by a maximum value MAX (e.g., approximately 7.5%). 
On the other hand, at step 514, the rich skip amount is decreased by 
.DELTA.RS, thereby shifting the air-fuel ratio to the lean side. Then, at 
steps 515 and 516, the rich skip amount RSR is guarded by a minimum value 
MIN (e.g., approximately 2.5%). The maximum value MAX is selected so that 
the amount of change of the air-fuel ratio is maintained within a range 
that does not deteriorate driveability, and the minimum value MIN is 
selected so that the response of the control in a transient condition is 
not lowered. 
At step 517, the lean skip amount RSL is calculated by 
EQU RSL.rarw.10%-RSR. 
Namely, a sum of RSR and RSL is maintained at 10. Then at step 518, the 
skip amounts RSR and RSL are stored in the backup RAM 106, and the routine 
terminates at step 520 in FIG. 5A. 
FIG. 6 shows a routine for calculating the fuel injection amount using the 
air-fuel ratio correction factor FAF calculated by the routine of FIGS. 3A 
and 3B. 
At step 601, a basic fuel injection amount TAUP is calculated in accordance 
with the amount of the inlet air per one revolution of the engine, Q/Ne, 
by 
EQU TAUP.rarw..alpha..multidot.Q/Ne 
where, TAUP is the fuel injection amount required to obtain the 
stoichiometric air-fuel ratio and .alpha. is a predetermined constant. 
Then, at step 602, a fuel injection amount TAU is calculated by 
EQU TAU.rarw.TAUP.multidot.FAF.multidot..beta.+.gamma. 
where, .beta. and .gamma. are correction factors determined by operating 
conditions of the engine. The calculated TAU is set to the down counter 
108 and a flip-flop 109 is set at step 603, whereby fuel injection is 
started. 
As stated before, when the time corresponding to TAU has lapsed, the 
flip-flop 109 is reset by the signal from the down counter 108, whereby 
the fuel injection is terminated. 
FIGS. 7A and 7B show the routine for determining whether the catalytic 
converter 12 has deteriorated. This routine is executed by the control 
circuit 10 at a predetermined intervals such as 4 ms. 
When the routine is started, it is determined at step 701 in FIG. 7A, 
whether the air-fuel ratio feedback control based on the output VOM of the 
upstream O.sub.2 sensor 13 is being carried out, from the value of the 
flag XMFB. If the feedback control is being carried out (i.e., XMFB="1" at 
step 701), it is determined whether a lean side condition or a rich side 
condition of the output VOM of the upstream O.sub.2 sensor 13 is being 
maintained at more than a predetermined time by a lean monitor at step 702 
and a rich monitor at step 703. And at step 704, it is determined whether 
the air-fuel ratio feedback control based on the output VOS of the 
downstream O.sub.2 sensor 15 is being carried out, from the value of the 
flag XSFB. 
The routine proceeds to step 710 in FIG. 7B only when the air-fuel ratio 
feedback control based on both VOM and VOS is carried out (XMFB="1" at 
step 701 and XSFB="1" at step 704), and the output VOM of the upstream 
O.sub.2 sensor 13 does not stay at the lean side nor the rich side for 
more than a predetermined time (step 702 and 703). 
At step 710, it is determined whether the execution of the determining 
operation of the catalyst deterioration is allowed based on the period TF 
of the cycle of the air-fuel ratio feedback control. 
As explained before, errors in the determination of the deterioration of 
the catalyst may occur when the period TF of the cycle of the air-fuel 
ratio feedback control becomes longer. Therefore, in this embodiment, the 
execution of the determining operation of the deterioration of the 
catalyst is allowed only when said period TF, which is stored in the RAM 
105 at step 324 in FIG. 3B, is smaller than a predetermined value 
TF.sub.0. In this embodiment, the value TF.sub.0 is set at the value 
corresponding to approximately 2 seconds, however, it is preferable to 
determine an appropriate value of TF.sub.0 by experiments, since the 
suitable value of TF.sub.0 varies according to the type of the vehicle and 
the engine, etc. 
If the period of the cycle of the air-fuel ratio feedback control is longer 
than the predetermined time, i.e., if TF&gt;TF.sub.0 at step 710, the 
execution of the determining operation of the catalyst deterioration is 
prohibited even if all of the conditions of steps 701 through 704 are 
satisfied. In this case, the routine proceeds to step 712, which clears a 
counter CT.sub.1 and other parameters used for determining operation of 
the catalyst deterioration (CS, VOM.sub.i-1, VOS.sub.i-1, etc.). The 
routine then terminates at step 713. 
If TF.ltoreq.TF.sub.0 at step 710, the routine then proceeds to step 711, 
at which a subroutine for determining the deterioration of the catalyst is 
executed. 
In the subroutine of step 711, various methods can be used to determine the 
deterioration of the catalyst. Hereinafter, three typical methods, i.e., a 
method using the number of reversals of the output signal of the 
downstream O.sub.2 sensor, a method using the lengths of the output signal 
response curves both of the O.sub.2 sensors, and a method using the 
lengths and areas of the output signal response curves are explained with 
reference to FIGS. 8 through 11. 
FIG. 8 shows an embodiment of the subroutine for determining the 
deterioration of the catalyst using the number of reversals of the output 
signal of the downstream O.sub.2 sensor 15. 
In FIG. 8, when the subroutine starts, a counter CT.sub.1 is counted up by 
1 at step 801. Then, at step 802, it is determined whether or not the 
value of the counter CT.sub.1 after count up is larger than T.sub.1, where 
T.sub.1 is the value corresponding to a predetermined time period for the 
execution of the determining operation. 
If CT.sub.1 &lt;T.sub.1 at step 802 (i.e., the time period T.sub.1 has not yet 
lapsed), the routine proceeds to step 803, which determines whether the 
output VOS of the downstream O.sub.2 sensor 15 has reversed (i.e., changed 
from the rich air-fuel ratio state signal (VOS.gtoreq.V.sub.R2) to the 
lean air-fuel ratio state signal (VOS&lt;V.sub.R2), or vice-versa.) compared 
with the value of VOS when the subroutine was last executed, and if the 
output VOS has reversed, a counter CS is counted up by 1 at step 804. 
Where, the counter CS represents the number of reversals of the output VOS 
during a predetermined time period T.sub.1. 
If the time period T.sub.1 has lapsed (i.e., CT.sub.1 .gtoreq.T.sub.1 at 
step 802), the routine proceeds to step 805, which determines whether the 
catalyst has deteriorated by comparing the value of the counter CS with a 
predetermined value CS.sub.0. 
If CS.gtoreq.CS.sub.0, which means the number of reversals of the output 
signal VOS of the downstream O.sub.2 sensor over the predetermined time 
period T.sub.1 is larger than a predetermined value, it can be considered 
that the condition of the output VOS is similar to the condition as shown 
in FIG. 1D (i.e., the catalyst has deteriorated). The routine then 
proceeds to step 806, which sets (="1") an alarm flag ALM, and to step 
807, which activates the alarm 19, thereby warning the driver of catalyst 
deterioration. 
If CS&lt;CS.sub.0 at step 805, it can be considered that the output VOS is in 
a similar condition as in FIG. 1C (i.e., the catalyst is not 
deteriorated). The routine then proceeds to steps 808 and 809, which 
resets (="0") the alarm flag ALM, and deactivates the alarm 19. 
After executing the above steps, the alarm flag ALM is stored in the backup 
RAM 106 at step 810, and the counters CT.sub.1 and CS are cleared at step 
811. The subroutine is then terminated. 
In the above subroutine, also the number of reversals of the output signal 
of the upstream O.sub.2 sensor can be used in addition to the number of 
reversals of the output signal of the downstream O.sub.2 sensor. In this 
case, the number of reversals of the output signal VOM of the upstream 
O.sub.2 sensor is counted by another counter CM, and the catalyst is 
determined as being deteriorated if a ratio CS/CM is larger than a 
predetermined value. 
FIGS. 9A and 9B show an embodiment of a subroutine for determining the 
deterioration of the catalyst based on the lengths of the output signal 
response curves of the upstream O.sub.2 sensor 13 and the downstream 
O.sub.2 sensor 15. 
As illustrated in FIGS. 1C and 1D, if the air-fuel ratio is feedback 
controlled at a relatively short period of the control cycle, the 
amplitude of the oscillation of the output response curve of the 
downstream O.sub.2 sensor 15 becomes larger and the period of the cycle of 
the oscillation becomes shorter when the catalyst has deteriorated, which 
causes the length of the output signal curve of the downstream O.sub.2 
sensor 15 to become larger (FIG. 1D) when the catalyst has deteriorated, 
compared to the same when the catalyst is normal (FIG. 1C). Therefore, the 
deterioration of the catalyst can be determined by monitoring the length 
of the output signal response curve of the downstream O.sub.2 sensor 15. 
In this embodiment, the lengths of the output response signal curves LVOS 
and LVOM of the downstream O.sub.2 sensor 15 and the upstream O.sub.2 
sensor 13, respectively, are calculated, and the catalyst is determined as 
being deteriorated when the ratio (LVOS/LVOM) becomes larger than a 
predetermined value.degree. 
In FIG. 9A, when the subroutine is started, at step 901, the length LVOM of 
the output signal response curve of the output VOM of the upstream O.sub.2 
sensor is calculated approximately by 
EQU LVOM.rarw.LVOM+.vertline.VOM-VOM.sub.i-1 .vertline. 
where, VOM.sub.i-1 is the value of the output VOM when the routine was last 
executed (see FIG. 12). The routine then proceeds to step 902 at which the 
value of VOM.sub.i-1 is updated to prepare for the next execution of the 
routine. 
At steps 903 and 904, the calculation of the length LVOS of the output 
signal response curve of the output VOS of the downstream O.sub.2 sensor 
and the updating of the value of VOS.sub.i-1 are carried out. 
The routine then proceeds to steps 905 in FIG. 9B, which counts up the 
counter CT.sub.1 by 1, and 906, which determines from the value of 
CT.sub.1 whether the predetermined time period T.sub.1 for executing the 
determining operation has lapsed. If the time period T.sub.1 has lapsed 
(i.e., CT.sub.1 &gt;T.sub.1 at step 906), it is determined whether or not the 
ratio LVOS/LVOM is larger than a predetermined value K at step 907. 
If the ratio LVOS/LVOM is larger than or equal to the value K, it is 
determined that the catalyst has deteriorated, and the routine proceeds to 
steps 908, which sets (="1") the alarm flag ALM, and 909, which activates 
the alarm 19. 
If the ratio LVOS/LVOM is smaller than the value K, then the flag ALM is 
reset (="0") at step 910, and the alarm 19 is deactivated at step 911. 
After completing the above steps, the value of the alarm flag ALM is stored 
in the backup RAM 106 (step 913), and the parameters used for the 
determining operation are cleared (step 914). 
In this embodiment, though both lengths LVOM and LVOS are used for 
determining the deterioration of the catalyst, the determination of the 
catalyst deterioration may be carried out using only the length LVOS of 
the response curve of the output VOS of the downstream O.sub.2 sensor 15. 
FIGS. 10A and 10B show an embodiment of the subroutine for determining the 
deterioration of the catalyst based on the lengths and areas of the output 
response curves of the downstream O.sub.2 sensor 15 and the upstream 
O.sub.2 sensor 13. 
In this embodiment, the areas (AVOS and AVOM) surrounded by the response 
curves of the output (VOS and VOM) of the upstream and the downstream 
O.sub.2 sensors and the reference voltage line (V.sub.R2 and V.sub.R1) 
thereof are used as well as the lengths LVOS and LVOM of the output signal 
response curves to increase the accuracy of the determination. 
As illustrated in FIG. 1C, when the catalyst is not deteriorated, the area 
AVOS surrounded by the output response curve of the downstream O.sub.2 
sensor and the reference voltage line V.sub.R2 is relatively large 
although the length LVOS of the output signal response curve is relatively 
small. On the other hand, as illustrated in FIG. 1D, the area AVOS becomes 
relatively small although the length LVOS becomes relatively large when 
the catalyst has deteriorated. Therefore, the deterioration of the 
catalyst can be determined more accurately by monitoring the area AVOS as 
well as the length LVOS of the downstream O.sub.2 sensor. Such a method 
for determining the catalyst deterioration based on the lengths and the 
areas of the O.sub.2 sensors is disclosed in the co-pending U.S. 
application Ser. No. 957,041 in detail and the disclosure thereof is 
incorporated into the present specification by reference thereto. 
In this embodiment, the lengths LVOS, LVOM and the areas AVOS, AVOM of the 
output response signal curves VOS, and VOM of the downstream O.sub.2 
sensor 15 and the upstream O.sub.2 sensor 13, respectively, are 
calculated, and the catalyst deterioration is determined based on the 
ratios (LVOS/LVOM) and (AVOS/AVOM) using one of the maps illustrated in 
FIGS. 11A through 11C. 
In FIG. 10A, when the subroutine starts, the length LVOM and the area AVOM 
of the output response curve VOM of the upstream O.sub.2 sensor 13 are 
calculated at step 1001, and the length LVOS and the area AVOS of the 
output response curve of the downstream O.sub.2 15 sensor are calculated 
at step 1002. The lengths LVOM and LVOS are calculated by the same formula 
as in steps 901 and 902 in FIG. 9A. The areas AVOM and AVOS are calculated 
approximately by, 
EQU AVOM.rarw.AVOM+.vertline.VOM-V.sub.R1 .vertline. 
EQU AVOS.rarw.AVOS+.vertline.VOS-V.sub.R2 .vertline. 
where, V.sub.R1 and V.sub.R2 are the reference voltages of the upstream 
O.sub.2 sensor 13 and the downstream O.sub.2 sensor 15 respectively. Then, 
after the values of VOM.sub.i-1 and VOS.sub.i-1 are updated at step 1003, 
the routine proceeds to step 1004 in FIG. 10B. 
At step 1004, the counter CT.sub.1 is counted up by 1, and at step 1005, it 
is determined from the value of CT.sub.1 whether the predetermined time 
period T.sub.1 for the execution of the determining operation has lapsed. 
If the time period T.sub.1 has lapsed (i.e., CT.sub.1 &gt;T.sub.1 at step 
1005), a ratio of the lenth (LVOS/LVOM) and a ratio of the areas 
(AVOS/AVOM) are calculated at step 1007, and the deterioration of the 
catalyst is determined by any one of the maps in FIGS. 11A through 11C. 
After the determination of catalyst deterioration is carried out at step 
1007, the alarm flag ALM is set or reset, and the alarm 19 is activated or 
deactivated at steps 1008 to 1011 in accordance with the result of the 
above determination. The value of the alarm flag ALM is then stored in the 
backup RAM 106 (step 1013), and the parameters are cleared (step 1014). 
In the above embodiment, operating conditions that cause errors in the 
determination of catalyst deterioration are detected by monitoring the 
period of the cycle of the air-fuel ratio feedback control (FIG. 7B, step 
710). However, the detection of such operating conditions can be carried 
out by monitoring other parameters representing the engine operating 
condition. 
FIG. 13 is a flow chart that can be used in lieu of FIG. 7B, showing an 
embodiment in which the amount of the inlet air flow of the engine is used 
for detecting such operating conditions. 
As explained before, when the velocity of the exhaust gas flow in the 
exhaust passage is low, the period of the cycle of the air-fuel ratio 
feedback control becomes longer, and since the velocity of the exhaust gas 
flow increases or decreases in accordance with the amount of the inlet air 
flow of the engine, the operating conditions causing errors in the 
determination of catalyst deterioration can be detected by monitoring the 
amount of the inlet air flow of the engine. 
In FIG. 13, it is determined that the engine is operated under conditions 
in which errors may occur in the determination of catalyst deterioration 
when the amount of inlet air flow of the engine Q is lower than a 
predetermined value Q0 (step 1310), and the execution of the subroutine 
for determining catalyst deterioration is prohibited in such a case (steps 
1312, 1313). Q.sub.0 is set at a value corresponding to the amount of 
inlet air flow when the engine is operated under low load conditions. 
Since the value of Q.sub.0 varies according to the type of engine and 
vehicle, it is preferable to determine the appropriate value for Q.sub.0 
experimentally. 
According to the embodiments explained above, the error in the 
determination of catalyst deterioration due to changes in the operating 
conditions of the engine or the deterioration of the upstream O.sub.2 
sensor can be eliminated. 
Although the invention has been described with reference to specific 
embodiments chosen for the purpose of illustration, it should be 
understood that numerous modifications could be applicable by those 
skilled in the art without departing from the basic concept and scope of 
the invention.