Patent Publication Number: US-6668813-B2

Title: Air-fuel ratio control device for internal combustion engine

Description:
This application is based on Application No. 2001-265664, filed in Japan on Sep. 3, 2001, the contents of which are hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an air-fuel ratio control device for an internal combustion engine and particularly concerns an air-fuel ratio control device for an internal combustion engine, by which an air-fuel ratio of air-fuel mixture supplied to the internal combustion engine is controlled so as to efficiently obtain the purifying performance of a catalytic converter. 
     2. Description of the Related Art 
     Conventionally, as one of air-fuel ratio control devices of an internal combustion engine, JP-A-H5-39741 discloses the following control device: in an internal combustion engine having a catalytic converter, an air-fuel ratio sensor is provided upstream of the catalytic converter and an O 2  sensor is provided downstream of the catalytic converter, an air-fuel ratio on the upstream side is synchronized with the rotation of the internal combustion engine, a forcible oscillation value is reversed to a positive or negative value, a correction coefficient is updated such that a mean air-fuel ratio on the upstream side of the catalytic converter is set at a target air-fuel ratio, the median air-fuel ratio being detected by the air-fuel ratio sensor, when an air-fuel ratio on the downstream side of the catalytic converter is biased to a rich or lean side by the O 2  sensor provided downstream of the catalytic converter, a target air-fuel ratio on the upstream side is corrected in a direction of canceling the bias to improve the purifying performance of the catalytic converter, during transient driving such as acceleration and deceleration, in which an irregular air-fuel ratio appears transiently, application of a forcible oscillation signal is prohibited, and degradation in exhausting characteristics is prevented. 
     However, in a conventional air-fuel ratio control device, forcible oscillation is prohibited only in transient driving, and in the other states forcible oscillation is always applied. Even in a relatively stable condition, an air-fuel ratio after the catalytic converter is biased due to interference such as introduction of purge. In this case (e.g., when being biased to a rich side), when application of forcible oscillation continues, a rich state other than a lean state exists. The lean state is a demanded air-fuel ratio from the state of the catalytic converter. Consequently, optimizing the state of the catalytic converter is interfered, resulting in deterioration in control response. In some cases, exhaust gas may be deteriorated in a rich state of forcible oscillation. 
     Further, immediately after returning from a fuel cutting state, the catalyst converter enters a state of excessive oxygen, and a purification factor of NOx is considerably reduced relative to a lean state provided upstream of the catalyst converter. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention is devised to solve the above problems and has as its object the provision of an air-fuel ratio control device for an internal combustion engine, by which even in a state other than a transient state, when an O 2  sensor provided downstream of a catalyst converter is in a rich state from a first predetermined value or in a lean state from a second predetermined value, periodic forcible oscillation is suspended, and a state for offsetting the biased state of the O 2  sensor provided downstream of the catalyst converter is continued until the biased state is ended (until a lean state from the first predetermined value or a rich state from the second predetermined value is provided), so that control can be exercised only in a state required for optimizing the state of the catalyst converter, thereby improving response in control and eliminating the possibility of deteriorating exhaust gas. 
     Besides, the object of the present invention is to provide an air-fuel ratio control device for an internal combustion engine, by which forcible oscillation after returning to fuel cutting is controlled such that first rich side control time is corrected in an extending direction according to fuel cutting time, so that oxygen of a catalytic converter is consumed and a catalytic converter is immediately brought into a state of a good purification factor. 
     An air-fuel ratio control device for an internal combustion engine is provided with an air-fuel ratio sensor which is provided upstream of a catalytic converter provided in an exhaust system of the internal combustion engine and detects an air-fuel ratio of the internal combustion engine, an O 2  sensor which is provided downstream of the catalytic converter and detects a concentration of oxygen after the catalytic converter, a reference air-fuel ratio target value setting means for setting a reference air-fuel ratio target value based on the number of revolutions and filling efficiency of the internal combustion engine, an O 2  voltage target setting means for setting a target value of an output voltage of the O 2  sensor based on the number of revolutions and filling efficiency of the internal combustion engine, an air-fuel ratio target value correcting means for obtaining an air-fuel ratio target value correction value based on an output voltage of the O 2  sensor and a target value set by the O 2  voltage target setting means, a forcible air-fuel ratio oscillation width target value correcting means for obtaining a forcible air-fuel ratio oscillation width target value based on the number of revolutions and filling efficiency of the internal combustion engine, an air-fuel ratio computing means for computing an air-fuel ratio target value based on outputs of the reference air-fuel ratio target value setting means, the air-fuel ratio target value correcting means, and the forcible air-fuel ratio oscillation width target value correcting means, an air-fuel ratio correction value computing means for computing a correction value based on an air-fuel ratio target value computed by the air-fuel ratio target value computing means and an output of the air-fuel ratio sensor, an injector driving time correction value computing means for obtaining a forcible air-fuel ratio oscillation width injector driving time correction value based on the number of revolutions and filling efficiency of the internal combustion engine, and an injector driving time setting means for setting time for driving an injector based on a correction value from the air-fuel ratio correction value computing means and a correction value from the injector driving time correction value computing means. 
     According to the above configuration, it is possible to exercise control simply by using a state required for optimizing a state of the catalytic converter, improve responsiveness of control, eliminate possibility of deteriorating exhaust gas, and immediately optimize the state of the catalytic converter even in a relatively stable condition. 
     An air-fuel ratio control device for an internal combustion engine may be characterized in that the forcible air-fuel ratio oscillation width target value correcting means forcibly varies the reference air-fuel ratio target value and the air-fuel ratio target value correction value to a rich side and a lean side in an alternate manner with predetermined widths in synchronization with the rotation of the internal combustion engine. 
     An air-fuel ratio control device for an internal combustion engine may be characterized in that for the forcible air-fuel ratio oscillation width target value correcting means, a forcible air-fuel ratio oscillation period setting means is provided which sets an air-fuel ratio oscillation period based on the number of revolutions of the internal combustion engine. 
     An air-fuel ratio control device for an internal combustion engine may be characterized in that for the forcible air-fuel ratio oscillation width target value correcting means, a forcible air-fuel ratio oscillation prohibiting means is provided which prohibits periodic forcible air-fuel ratio oscillation according to an output voltage of the O 2  sensor. The forcible air-fuel ratio oscillation prohibiting means prohibits periodic forcible air-fuel ratio oscillation and continues a state for offsetting a detection state of an output voltage of the O 2  sensor when an output voltage of the O 2  sensor is at a first predetermined value or more or at a second predetermined value or less. 
     According to the above configuration, it is possible to improve accuracy of control and prevent deterioration of exhust gas. 
     An air-fuel ratio control device for an internal combustion engine may be characterized in that regarding forcible air-fuel ratio oscillation correction performed after returning to fuel cutting, correcting time of an initial rich side is corrected to an extending side according to fuel cutting time, in the forcible air-fuel ratio oscillation width target value correcting means. 
     According to the above configuration, it is possible to consume oxygen of the catalytic converter, bring the catalytic converter immediately into a state of a good purification factor, and immediately optimize the state of the catalytic converter. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram showing Embodiment 1 of the present invention; 
     FIG. 2 is a functional block diagram showing Embodiment 1 of the present invention; 
     FIG. 3 is a flowchart for forcibly oscillating a target value of Embodiment 1 of the present invention; 
     FIG. 4 is a flowchart for forcibly oscillating INJ driving time that is performed simultaneously with the forceful oscillation of a target value of FIG. 3; 
     FIG. 5 is a flowchart for correcting a reference air-fuel ratio target value according to Embodiment 1 of the present invention; 
     FIG. 6 is a graph showing an integral gain and a proportional correction value that are obtained for computing a correction value of a reference air-fuel ratio target value according to Embodiment 1 of the present invention; 
     FIG. 7 is a divided table showing a reference air-fuel ratio target value, a forcible air-fuel ratio oscillation width target value, and a forcible air-fuel ratio oscillation width INJ driving time correction value according to Embodiment 1 of the present invention; 
     FIG. 8 is a diagram showing tables of a reference air-fuel ratio target value, a forcible air-fuel ratio oscillation width target value, a forcible air-fuel ratio oscillation width INJ driving time correction value, and a forcible air-fuel ratio oscillation period according to Embodiment 1 of the present invention; 
     FIG. 9 is a flowchart for forcibly oscillating a target value that includes a rich-side continuous operation of forcible air-fuel ratio oscillation after cutting fuel according to Embodiment 2 of the present invention; 
     FIG. 10 is a flowchart for forcibly oscillating INJ driving time that is performed simultaneously with forceful oscillation of a target value of FIG. 8; 
     FIG. 11 is a flowchart showing a computation of a forcible air-fuel ratio oscillation rich-period fuel cutting post-extension counter according to Embodiment 2 of the present invention; and 
     FIG. 12 is a graph showing the relationship between fuel cutting duration and a post-fuel cutting rich period extension counter according to Embodiment 2 of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, embodiments of the present invention will be described in accordance with the accompanied drawings. 
     Embodiment 1 
     FIG. 1 is a block diagram showing Embodiment 1 of the present invention. 
     In FIG. 1, as for intake from an air cleaner  1 , an intake air quantity Qa is measured by an air flow sensor  2 , an intake quantity is controlled by a throttle valve  3  according to a load, and the air is sucked to each cylinder of an engine  6  via a surge tank  4  and an intake pipe  5 . Meanwhile, fuel is injected into the intake pipe  5  via an injector  7 . 
     Further, an engine control unit  20  for exercising controls such as air-fuel ratio control and ignition timing control is constituted by a micro computer including a CPU  21 , a ROM  22 , and a RAM  23 , and the engine control unit  20  receives an intake air quantity Qa, which is measured by the air flow sensor  2  via an input/output interface  24 , a throttle opening ø detected by the throttle sensor  12 , a signal of an idle switch  13 , which is turned on during idling opening, an engine cooling water temperature WT detected by a water temperature sensor  14 , an air-fuel ratio feedback signal O 2  transmitted from an air-fuel ratio sensor  16  provided on an exhaust pipe  15 , the number of revolutions Ne of an engine that is detected by a crank angle sensor  17 , and so on. 
     And then, the CPU  21  performs an air-fuel ratio feedback control computation based on control programs and a variety of maps stored in the ROM  22 , and drives the injector  7  via a driving circuit  25 . 
     Moreover, catalytic converters  27  and  28  are provided in an exhaust system of the internal combustion engine, and an O 2  sensor (hereinafter, referred to as a rear O 2  sensor)  26  is provided which is provided downstream of the catalytic converter  27  and detects a concentration of oxygen after the catalytic converter. 
     FIG. 2 is a block diagram showing the configuration of functions according to Embodiment 1 of the present invention. 
     In FIG. 2, reference numeral  30  denotes a reference air-fuel ratio target value setting means that obtains a reference air-fuel ratio target value based on the number of revolutions of an engine (ENG) and filling efficiency. The reference air-fuel ratio target value will be discussed in FIG.  8 ( a ). Reference numeral  31  denotes a rear O 2  voltage target value setting means that obtains a rear O 2  voltage target value based on the number of ENG revolutions and filling efficiency. Reference numeral  32  denotes an air-fuel ratio target value correcting means that obtains an air-fuel ratio target value correction value (air-fuel ratio target value integral correction value, air-fuel ratio target value proportional correction value) based on a rear O 2  sensor output voltage and a rear O 2  voltage target value, which is set by the rear O 2  voltage target value setting means  31 . 
     Next, as a means for forcibly oscillating an air-fuel ratio, reference numeral  36  denotes a forcible air-fuel ratio oscillation period setting means that obtains a period of air-fuel ratio oscillation based on the number of ENG revolutions, and reference numeral  38  denotes a forcible air-fuel ratio oscillation width target value correcting means that obtains a forcible air-fuel ratio oscillation width target value based on the number of ENG revolutions and filling efficiency. As will be discussed later, a forcible air-fuel ratio oscillation prohibiting means  37  may be provided for prohibiting periodic forcible air-fuel ratio oscillation in accordance with the state of rear O 2 . An air-fuel ratio target value is computed by an air-fuel ratio target value computing means  33  based on the outputs of the reference air-fuel ratio target value setting means  30 , the air-fuel ratio target value correcting means  32 , and the forcible air-fuel ratio oscillation width target value correcting means  38 . 
     Subsequently, a correction value is computed by an air-fuel ratio correction value computing means  34  such that an air-fuel ratio target value from the air-fuel ratio target value computing means  33  and an output from a front air-fuel ratio sensor, that is, the air-fuel ratio sensor  16  may coincide. Driving time for driving the injector  7  is set by an INJ driving time setting means  35  based on the correction value and a forcible air-fuel ratio oscillation width INJ driving time correction value  39 , which is obtained from the number of ENG revolutions and filling efficiency. 
     Next, the operations will be discussed. 
     FIG. 3 is a flowchart for setting a forcible air-fuel ratio oscillation width target value. Referring to FIG. 3, the following will discuss setting of a forcible air-fuel ratio oscillation width target value. 
     First, in step S 110 , determination is made if a mode is an O 2 FB (feedback) mode or not. When a mode is not the O 2 FB mode, the flow goes to EXIT, and when a mode is the O 2 FB mode, the flow goes to step S 111 . In step S 111 , determination is made if a condition of DualO 2  control is established or not. 
     Here, the DualO 2  control refers to a part constituted by the air-fuel ratio sensor  16 , which is provided upstream of the catalyst converter  27  provided in the exhaust system of the internal combustion engine and detects an air-fuel ratio of the internal combustion engine, the O 2  sensor (hereinafter, referred to as a rear O 2  sensor)  26 , which is provided downstream of the catalytic converter  27  and detects a concentration of oxygen after the catalytic converter, the reference air-fuel ratio target value setting means  30  for setting a target value of an air-fuel ratio of the internal combustion engine, the rear O 2  voltage target setting means  31  for setting a target of an output voltage of the rear O 2  sensor  26 , and the air-fuel ratio target value correcting means  32  which obtains an air-fuel ratio target value correction value for correcting a reference air-fuel ratio target value such that a rear O 2  sensor voltage is equal to a rear O 2  voltage target value. 
     Further, reference characters of the flowchart denote as follows: 
     L: air-fuel ratio target value 
     L 0 : reference air-fuel ratio target value 
     Li: air-fuel ratio target value integral correction value (part of output of the air-fuel ratio target value correcting means) 
     LR: air-fuel ratio target value proportional correction value (part of output of the air-fuel ratio target value correcting means) 
     TRVO 2 : rear O 2  voltage target value 
     In step S 111 , when Dual O 2  control is not established, an air-fuel ratio target value L is set at L 0 +Li in step S 124  and the flow proceeds to EXIT. Moreover, when the condition is established, the flow proceeds to step S 112  and mapping is performed on a rich side forcible air-fuel ratio oscillation period Rn, a lean side forcible air-fuel ratio oscillation period Ln, and a rear O 2  target voltage TRVO 2  based on the number of revolutions of the engine and filling efficiency. 
     Subsequently, the flow proceeds to step S 113 , and a rear O 2  voltage and a rear O 2  voltage target value are compared with each other. When a rear O 2  voltage is larger than a target voltage (rich state), the flow proceeds to the step S 114 . 
     Next, in step S 114 , mapping is performed on L 0  and a forcible air-fuel ratio oscillation width target value DAF, and the flow proceeds to the next step S 115 . In step S 115 , Li and LR are computed based on the computation of Li and LR, that will be discussed later. In the next step S 116 , an air-fuel ratio target value L is computed, which is biased to a lean state by DAF from ordinary control, based on L 0  and DAF mapped in step S 114  and Li and LR computed in step S 115 . In the next step S 117 , a lean side forcible air-fuel ratio oscillation period counter is subtracted by 1. 
     In the next steps S 118  and S 119 , confirmation is made again if a mode is an O 2 FB mode or if DualO 2  control is established. When the condition is not established, the same operations are performed as steps S 100  and S 111 . Meanwhile, when the condition is established, a rear O 2  voltage and a rear O 2  lean state determining voltage DIZL (first predetermined value) are compared with each other instep S 120 . When a rear O 2  voltage is DIZL or more, the flow proceeds to step S 122  and comparison is made if a counter Ln is 0 or not. When the counter Ln is not 0, the flow returns to step S 114  and the above-mentioned operations are performed again and are repeated until the counter Ln is set at 0. 
     During repetition, when a rear O 2  voltage is below DIZL in step S 120 , since a lean state is not necessary, the flow proceeds to step S 121  and the counter Ln is set at 0, namely, periodic forcible air-fuel ratio oscillation is prohibited by the forcible air-fuel ratio oscillation prohibiting means  37 , Ln is mapped in step S 123  after in step S 122 , and the flow proceeds to step S 125 . 
     Besides, as for the operations from step S 125  to step S 134 , the same operations are performed in a state in which a rich state and a lean state of an air-fuel ratio in steps S 114  to S 123  are reversed. In the above series of operations, an air-fuel ratio target value can be forcibly oscillated to a rich side and a lean side by DAF at predetermined periods. In this case, the condition is established in step S 130 , and a rear O 2  lean state determining voltage DIZH, which is compared with a rear O 2  voltage in step S 131 , is a second predetermined value. 
     FIG. 4 is a flowchart for setting a forcible air-fuel ratio oscillation width INJ driving time correction value. Referring to FIG. 4, the following will discuss setting of a forcible air-fuel ratio oscillation width INJ driving time correction value. 
     First, in step S 210 , determination is made if a mode is an O 2 FB mode or not. When a mode is not an O 2 FB mode, the flow proceeds to step S 225 , INJ driving time is computed while a forcible air-fuel ratio oscillation INJ driving time correction coefficient KINJ is set at 1.0, and the flow proceeds to EXIT. When a mode is an O 2 FB mode, the flow proceeds to step S 211 . 
     In step S 211 , determination is made if a DualO 2  control condition is established or not. When DualO 2  control is not established in step S 211 , a forcible air-fuel ratio oscillation INJ driving time correction coefficient KINJ is set at 1.0 in step S 224 , INJ driving time is computed, and the flow proceeds to EXIT. When the condition is established, the flow proceeds to step S 212 , and mapping is performed on a rich side forcible air-fuel ratio oscillation period Rn, a lean side forcible air-fuel ratio oscillation period Ln, and a rear O 2  target voltage TRVO 2  based on the number of revolutions of the engine and filling efficiency. 
     Next, the flow proceeds to step S 213 , and a rear O 2  voltage and a rear O 2  voltage target value are compared with each other. When a rear O 2  voltage is larger than a target voltage (rich state), the flow proceeds to step S 214 . And then, a forcible air-fuel ratio oscillation INJ driving time correction value DINJ is mapped in step S 214 , and KINJ is computed based on DINJ in step S 215  (injector driving time correction value computing means). In the next step S 216 , INJ driving time is computed which is biased to a lean state by DINJ from ordinary control based on DINJ computed in step S 215 . 
     In the next step S 217 , a lean side forcible air-fuel ratio oscillation period counter is subtracted by 1. In the next steps S 218  and S 219 , confirmation is made again if a mode is an O 2 FB mode or if DualO 2  control is established. When the condition is not established, the same operations are performed as steps S 210  and S 211 . Meanwhile, when the condition is established, a rear O 2  voltage and a rear O 2  lean state determining voltage DIZL are compared with each other in step S 220 . When a rear O 2  voltage is at DIZL or more, the flow proceeds to step S 222  and comparison is made if a counter Ln is 0 or not. When the counter Ln is not 0, the flow returns to step S 214  and the above same operations are performed and are repeated until the counter Ln is set at 0. 
     During repetition, when a rear O 2  voltage is below DIZL in step S 220 , since a lean state is not necessary, the flow proceeds to step S 221 , the counter Ln is set at 0, Ln is mapped in step S 223  after step S 222 , and the flow proceeds to step S 226 . As for the operations from step S 226  to step S 235 , the same operations are performed in a state in which a rich state and a lean state of an air-fuel ratio of steps S 214  to S 223  are reversed. In the above series of operations, INJ driving time can be forcibly oscillated to a rich side and a lean side by DINJ at predetermined periods. 
     FIG. 5 is a flowchart for computing Li and LR in the flowchart of FIG.  3 . Referring to FIG. 5, Li and LR will be discussed by calculation. 
     First, in step S 310 , determination is made if a DualO 2  control condition is established or not. When the condition is not established, in step S 316 , Li is set at the previous computation value, LR is set at 0, and the flow is ended. Meanwhile, when the DualO 2  condition is established, the flow proceeds to step S 311  and TRVO 2  is mapped. In the next step S 312 , a deviation from a rear O 2  voltage is obtained to compute ΔVr. 
     In the next step S 313 , an integral gain Ki is mapped according to ΔVr based on an integral gain table of FIG.  6 ( a ) that will be discussed later. In the next step S 314 , the product of ΔVr and Ki is integrated to compute an integral correction coefficient Li. Moreover, in the next step S 315 , a value is mapped according to the ΔVr based on a proportional correction value table of FIG.  6 ( b ). Li and LR are computed by the above operations under DualO 2  control. 
     FIG. 6 is a graph showing an integral gain and a proportional correction value that are used in the flowchart of FIG.  5 . An integral gain and a proportional correction value are both shown in tables of ΔVr. The tables are configured as follows: when ΔVr is negative, namely, when the state of a catalyst is rich, a value is obtained in a direction for setting an air-fuel ratio target value at a lean state. When ΔVr is positive, namely, when the state of the catalyst is lean, a value is obtained in a direction for setting an air-fuel ratio target value at a rich state. 
     FIG. 7 shows zones of table axes regarding (a) a reference air-fuel ratio target value, (b) a forcible air-fuel ratio oscillation width target value, and (c) a forcible air-fuel ratio oscillation width INJ driving time correction value of FIG. 8 that will be discussed later. The zones are determined by the number of revolutions of the engine and filling efficiency. 
     FIG. 8 shows tables for setting (a) a reference air-fuel ratio target value, that is, a reference value of a target air-fuel ratio provided upstream of the catalyst, (b) a forcible air-fuel ratio variation width target value, that is, a target value oscillation width during forcible oscillation control, (c) a forcible air-fuel ratio oscillation width INJ driving time correction value, that is, an INJ driving time correction width, and (d) a forcible air-fuel ratio oscillation period. A reference value of a target air-fuel ratio, a target value oscillation width during forcible oscillation control, and an INJ driving time correction width are shown in tables corresponding to the zones of FIG. 7. A table for setting a forcible air-fuel ratio oscillation period is a table indicating the number of revolutions of the engine. 
     In this manner, according to the present embodiment, when an air-fuel ratio is biased to a rich side or a lean side after the catalyst converter, forcible air-fuel ratio oscillation is prohibited and a state of an air-fuel ratio is continued in a direction for offsetting the bias, thereby immediately bringing the catalyst converter into an optimum state. 
     Embodiment 2 
     FIG. 9 is a flowchart for setting a forcible air-fuel ratio oscillation width target value in Embodiment 2 of the present invention. Besides, since the present embodiment is substantially identical to Embodiment 1 in circuit configuration, the description thereof is omitted. 
     The basic operations are substantially the same as setting of a forcible air-fuel ratio oscillation width target shown in FIG. 3 of Embodiment 1. The difference is that when NO (Lean) is selected in step S 414 , a rich side forcible air-fuel ratio oscillation period counter Rn is extended in the next step S 426  by a post-F/C rich period extending counter Rnn, which performs mapping according to F/C time. The catalyt normally adsorbs oxygen to a full capacity during F/C. After returning to F/C, NOx is likely to be generated in a lean state. Therefore, since a quantity of adsorbed oxygen is immediately brought into a suitable state by extending a rich state after an F/C state, it is possible to suppress the generation of NOx in a lean state. 
     FIG. 10 is a flowchart for setting a forcible air-fuel ratio oscillation width INJ driving time correction value. The basic operations thereof are the same as the correction of forcible air-fuel ratio oscillation width INJ driving time that is shown in FIG. 4 of Embodiment 1. The difference is the same as that of FIG. 9, and the effect is also the same as that of FIG.  9 . 
     FIG. 11 is a flowchart for computing a forcible air-fuel ratio oscillation rich period post-fuel cutting extension counter. Referring to FIG. 11, the following will discuss a computation of a forcible air-fuel ratio oscillation rich period post-F/C extension counter. 
     In step S 610 , determination is made if a mode is an F/C mode or not. When a mode is not an F/C mode, the counter does not need to be extended. Thus, Rnn is reset (=0) in step S 615 . Meanwhile, in the case of an F/C mode, an F/C time counter FCCNT is reset in step S 611 . Next, in step S 612 , determination is made if F/C return is made or not. When a mode is an F/C mode, the flow proceeds to step S 613  and FCCNT is added by 1. 
     Thereafter, in steps S 612  and S 613 , FCCNT is added by 1 (+1) and F/C duration is counted until F/C return is made. And then, when F/C return is found in step S 612 , the flow proceeds to step S 614 . A count value of the post-F/C rich period extension counter Rnn is mapped according to an F/C duration FCCNT based on a post-F/C rich period extension counter table of FIG.  12 . 
     FIG. 12 is a graph showing the relationship between fuel cutting time and a post-fuel cutting rich period extension counter value. The relationship is characterized in that as F/C duration is longer, a counted value of the post-F/C rich period extension counter Rnn is increased, and when F/C duration is at a predetermined value or more, the extension counter Rnn remains constant. 
     In this manner, according to the present embodiment, after returning to fuel cutting, a control period on a rich side is extended, thereby immediately optimizing the state of the catalytic converter.