Abstract:
To prevent RPM decrease, misfire, and engine stall by refraining from correcting, the amount of fuel to shift an air-fuel ratio toward a lean side to the extent of exceeding a combustion limit when the internal combustion engine operates at a low load, a control apparatus is provided for controlling operation of an internal combustion engine. The apparatus includes an air-fuel ratio state determiner, a characteristic retainer and a fuel correction amount calculator, in which a coolant temperature coefficient of a coolant temperature coefficient characteristic is set to be smaller than a constant value in a region where a coolant temperature is lower than a constant temperature.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to fuel control of an internal combustion engine, and more particularly to a device for correcting a fuel injection amount of an internal combustion engine, which performs feedback control according to an output value of an oxygen sensor provided in an exhaust pipe, and to a control apparatus for an internal combustion engine employing the device. 
   2. Description of the Related Art 
   A conventional fuel injection control apparatus for an internal combustion engine performs control with a control gain that is set larger than usual until initial inversion occurs after the start of O 2  feedback (e.g., see JP 2003-232248 A). 
   In this conventional fuel injection control apparatus for an internal combustion engine, the control gain is set larger than usual until initial inversion occurs after the start of O 2  feedback. The speed of following a stoichiometric air-fuel ratio (i.e., a theoretical air-fuel ratio) after the start of O 2  feedback is thereby increased. 
   Combustion is unstable and the range allowing combustion on a lean side of an air-fuel ratio A/F is narrow when an internal combustion engine is at a low temperature. For instance, although combustion is possible at an air-fuel ratio of A/F=17 or less after an internal combustion engine has warmed up, combustion is impossible at an air-fuel ratio of A/F=15 or more when an internal combustion engine is cold. 
   Even if the air-fuel ratio A/F is within a range allowing combustion, the torque of an internal combustion engine drastically decreases when the air-fuel ratio A/F shifts to the lean side. Therefore, there is a problem in that the RPM of an internal combustion engine sharply decreases when a large feedback gain is set to shift the air-fuel ratio A/F to the lean side at an early stage. 
   Furthermore, there is another problem in that misfire, which leads to engine stall in some cases, is caused when the combustion state of an internal combustion engine exceeds a combustion limit (on the lean side). 
   Immediately after the start of an internal combustion engine as well, combustion is unstable and the feedback is set large as in a period in which the internal combustion engine is cold. Therefore, there is a problem in that a decrease in RPM, misfire, engine stall, and the like are caused when an attempt is made to shift the air-fuel ratio to the lean side at an early stage. 
   The range allowing combustion on the lean side of the air-fuel ratio A/F is narrower in a low-load operation range than in a high-load operation range, and, in particular, the feedback gain is set large especially in the low-load operation range immediately after the start of an internal combustion engine as well. Therefore, there is a problem in that a decrease in RPM, misfire, engine stall, and the like are caused when an attempt is made to shift the air-fuel ratio to the lean side at an early stage. 
   SUMMARY OF THE INVENTION 
   The present invention has been made to solve the above-mentioned problems. It is a first object of the present invention to provide a control apparatus for an internal combustion engine which can prevent a decrease in RPM, misfire, and engine stall by refraining from correcting the amount of fuel to shift an air-fuel ratio A/F toward a lean side to the extent of exceeding a combustion limit when the internal combustion engine is at a low temperature. 
   It is a second object of the present invention to provide a control apparatus for an internal combustion engine which can prevent a decrease in RPM, misfire, and engine stall by refraining from correcting the amount of fuel to shift an air-fuel ratio A/F toward a lean side to the extent of exceeding a combustion limit immediately after the internal combustion engine has been started. 
   It is a third object of the present invention to provide a control apparatus for an internal combustion engine which can prevent a decrease in RPM, misfire, and engine stall by refraining from correcting the amount of fuel to shift an air-fuel ratio A/F toward a lean side to the extent of exceeding a combustion limit when the internal combustion engine operates at a low load. 
   According to the present invention, there is provide a control apparatus for controlling operation of an internal combustion engine, including: air-fuel ratio detecting means provided in an exhaust system of the internal combustion engine, for detecting an air-fuel ratio to be used to control operation of the internal combustion engine; RPM detecting means for detecting RPM to be used to control operation of the internal combustion engine; an intake pipe pressure sensor for detecting an intake pipe pressure to be used to control operation of the internal combustion engine; coolant temperature detecting means for detecting a coolant temperature to be used to control operation of the internal combustion engine; air-fuel ratio state determining means for determining whether the air-fuel ratio detected by the air-fuel ratio detecting means is in a rich state or in a lean state; characteristic retaining means for retaining an integral gain characteristic in which a value of an integral gain is determined by RPM and an intake pipe pressure, a proportional gain characteristic in which a value of a proportional gain is determined by RPM and an intake pipe pressure, and a coolant temperature coefficient characteristic in which a coolant temperature coefficient for correcting the integral gain is determined according to a coolant temperature; and fuel correction amount calculating means for multiplying the integral gain by the coolant temperature coefficient in calculating a correction amount of a fuel injection amount using a sign obtained from a determination result of the air-fuel ratio state determining means, the integral gain, and the proportional gain, in which the coolant temperature coefficient of the coolant temperature coefficient characteristic is set to be smaller than a constant value in a region where the coolant temperature is lower than a constant temperature. 
   According to the present invention, an updated value of an air-fuel ratio correction amount calculated by air-fuel ratio correction amount calculating means is calculated according to a temperature of the internal combustion engine. This updated value is set to be smaller as the temperature of the internal combustion engine lowers. Thus, the amount of fuel is not corrected to shift the air-fuel ratio A/F toward the lean side to the extent of exceeding a combustion limit when the internal combustion engine is in a combustion state. As a result, a decrease in RPM, the occurrence of misfire, the occurrence of engine stall, and the like can be prevented. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
       FIG. 1  is a view showing a control apparatus for an internal combustion engine according to a first embodiment of the present invention; 
       FIG. 2  is a flowchart showing a process of making a determination on a mode for calculating a fuel injection amount calculated by an ECU; 
       FIG. 3  is a flowchart showing a process of deriving a correction amount of the fuel injection amount calculated by the ECU; 
       FIG. 4  is a flowchart showing the concrete contents of a process for calculating an O 2  feedback correction amount (CFB) in Step of  FIG. 3 ; 
       FIG. 5  is a table showing a proportional gain (Gp) used as a value corresponding to RPM (Ne) and an intake pipe pressure (Pb); 
       FIG. 6  is a table showing an integral gain (Gi) used as a value corresponding to RPM (Ne) and an intake pipe pressure (Pb); 
       FIG. 7  is a characteristic diagram showing a coolant temperature characteristic of a coolant temperature coefficient (Kwt(WT)) by which an integral gain (Kit) is multiplied; 
       FIG. 8  is a time chart showing how the RPM (Ne), an amount of remaining oxygen, an O 2  feedback correction coefficient (CFB), and a change of an air-fuel ratio A/F when an internal combustion engine is started at a coolant temperature of 20° C.; 
       FIG. 9  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to a second embodiment of the present invention; 
       FIG. 10  is a characteristic diagram showing a characteristic of a post-start elapsed time correction coefficient, by which an integral gain (Kit) is multiplied, with respect to an elapsed time; 
       FIG. 11  is a characteristic diagram showing a characteristic of a post-start elapsed time correction coefficient, by which the integral gain (Kit) is multiplied, with respect to an elapsed time; 
       FIG. 12  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to a third embodiment of the present invention; 
       FIG. 13  is a characteristic diagram showing characteristics of an integral upper limit (SkiMX) and an integral lower limit (SkiMN) with respect to a post-start elapsed time; 
       FIG. 14  is a characteristic diagram showing characteristics of the integral upper limit (SkiMX) and the integral lower limit (SkiMN) with respect to a post-start elapsed time; 
       FIG. 15  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to a fourth embodiment of the present invention; 
       FIG. 16  is a diagram showing characteristics of a post-start elapsed time correction coefficient, by which an integral gain (Kit) is multiplied, with respect to an elapsed time after the start of the internal combustion engine; 
       FIG. 17  is a diagram showing characteristics of the post-start elapsed time correction coefficient, by which the integral gain (Kit) is multiplied, with respect to an elapsed time after the start of the internal combustion engine; 
       FIG. 18  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to a fifth embodiment of the present invention; 
       FIG. 19  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to a sixth embodiment of the present invention; 
       FIG. 20  is a view showing the concrete contents of another process for calculating an O 2  feedback correction amount (CFB) in Step S 302  of  FIG. 3 ; 
       FIG. 21  is a view showing the concrete contents of still another process for calculating an O 2  feedback correction amount (CFB) in Step S 302  of  FIG. 3 ; and 
       FIG. 22  is a view showing the concrete contents of still another process for calculating an O 2  feedback correction amount (CFB) in Step S 302  of  FIG. 3 . 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   First Embodiment 
     FIG. 1  is a view showing a control apparatus for an internal combustion engine according to the first embodiment of the present invention. 
   An internal combustion engine  101  is equipped with an air cleaner  102 , an intake pipe  103 , a throttle valve  104 , a pressure sensor  105 , an injector  106 , an exhaust pipe  107 , an O 2  sensor  108 , a three-way catalyst  109 , an ignition coil  110 , an ignition plug  111 , a cam angle sensor  112 , a cam angle sensor plate  113 , a crank angle sensor  114 , a crank angle sensor plate  115 , coolant  116 , a coolant temperature sensor  117 , and a control unit (hereinafter referred to as an “ECU”)  118 . The air cleaner  102  purifies air sucked by the internal combustion engine  101 . The throttle valve  104  adjusts an amount of air sucked by the internal combustion engine  101 . The pressure sensor  105  measures a pressure in the intake pipe  103  at a position downstream of the throttle valve  104 . The injector  106  supplies fuel to air sucked by the internal combustion engine  101 , thereby forming a mixture. The O 2  sensor  108  measures an amount of air remaining in exhaust gas discharged from the internal combustion engine  101 . The three-way catalyst  109  converts harmful components contained in exhaust gas, that is, HC, CO, and NOx, into harmless components, that is, CO 2  and H 2 O. The ignition coil  110  causes a high voltage to be generated in a secondary coil by supplying an electric current to a primary coil and cutting off the supply of an electric current to the primary coil. The ignition plug  111  generates a spark through the high voltage generated in the ignition coil  110 . The cam angle sensor  11  generates a cam angle signal. A protrusion or a recess for causing the cam angle sensor  112  to generate a signal is formed on or in the cam angle sensor plate  113 . The crank angle sensor  114  generates a crank angle signal. A protrusion or a recess for causing the crank angle sensor  114  to generate a signal is formed on or in the crank angle sensor plate  115 . The coolant  116  cools the internal combustion engine  101 . The coolant temperature sensor  117  detects temperature of the coolant  116 . Output signals from the cam angle sensor  112 , the crank angle sensor  114 , the pressure sensor  105 , the O 2  sensor  108 , the coolant temperature sensor  117 , and the like are inputted to the ECU  118 . The ECU  118  calculates a fuel injection amount, an ignition timing, and the like based on the output signals inputted thereto, and outputs signals to the injector  106  and the ignition coil  110 . 
     FIG. 2  is a flowchart showing a process for making a determination on a mode for calculating a fuel injection amount calculated by the ECU  118 . 
   A control processing based on the flowchart shown in  FIG. 2  is performed by the ECU  118  at, for example, each ignition timing. 
   Although flowcharts other than the one shown in  FIG. 2  are used as well in the following description, it should be noted that a control processing based on anyone of those flowcharts is performed at each ignition timing. 
   The ECU  118 , which is a control apparatus for controlling operation of the internal combustion engine  101 , functions especially as the following means, namely, (1) air-fuel ratio state determination means, (2) characteristic retaining means, and (3) fuel correction amount calculating means. The air-fuel ratio state determination means determines whether an air-fuel ratio detected by air-fuel ratio detecting means is in a lean state or in a rich state. The characteristic retaining means retains characteristics of an integral gain and a proportional gain that are determined according to the RPM of an engine and an intake pipe pressure, and a coolant temperature coefficient characteristic in which a coolant temperature coefficient for correcting the integral gain is determined according to a temperature of the coolant  116 . In calculating a correction amount of a fuel injection amount using a sign, an integral gain, and a proportional gain that are obtained from a determination result of the air-fuel ratio state determining means, the fuel correction amount calculating means multiplies the integral gain by the coolant temperature coefficient. 
   The characteristic retaining means may not necessarily be a memory in the ECU  118 . In other words, the characteristic retaining means may be an external memory. 
   In Step S 201 , it is determined whether or not an intake pipe pressure (Pb) is equal to or higher than an upper-limit intake pipe pressure (Pbmax) in an O 2  feedback mode (F/B). 
   When it is determined in Step S 201  that the intake pipe pressure (Pb) is equal to or higher than the upper-limit intake pipe pressure (Pbmax) in the O 2  feedback mode (F/B), the flow proceeds to Step S 204 . 
   In Step S 204 , it is determined that an enrichment mode (E/R) has been entered. 
   On the other hand, when it is determined in Step S 201  that the intake pipe pressure (Pb) is not equal to or higher than the upper-limit intake pipe pressure (Pbmax) in the O 2  feedback mode (F/B), the flow proceeds to Step S 202 . 
   In Step S 202 , it is determined whether or not the intake pipe pressure (Pb) is lower than a lower-limit in take pipe pressure (Pbmin) in the O 2  feedback mode (F/B). 
   When it is determined in Step S 202  that the intake pipe pressure (Pb) is lower than the lower-limit intake pipe pressure (Pbmin) in the O 2  feedback mode (F/B), the flow proceeds to Step S 205 . 
   In Step S 205 , it is determined that an open loop mode (O/L) has been entered. 
   When it is determined in Step S 202  that the intake pipe pressure (Pb) is not lower than the lower-limit intake pipe pressure (Pbmin) in the O 2  feedback mode (F/B), the flow proceeds to Step S 203 . 
   In Step S 203 , it is determined whether or not a coolant temperature (WT) is equal to or higher than a coolant temperature (Kwt) for performing O 2  feedback and the O 2  sensor  108  is in its activated state. 
   When it is determined in Step S 503  that the coolant temperature (WT) is equal to or higher than the coolant temperature (Kwt) for performing O 2  feedback and the O 2  sensor  108  is in its activated state, the flow proceeds to Step S 206 . 
   In Step S 206 , the O 2  feedback mode (F/B) is entered. 
   On the other hand, when it is determined in Step S 203  that the coolant temperature (WT) is not equal to or higher than the coolant temperature (Kwt) for performing O 2  feedback or that the O 2  sensor  108  is not in its activated state, the open loop mode (O/L) is entered. 
   It is determined whether or not the O 2  sensor  108  is in its activated state, depending on whether or not an output voltage of the O 2  sensor  108  is equal to or higher than a threshold (0.45 V). 
   The open loop mode (O/L) is a control mode in which an output from the O 2  sensor  108  is not feedback-controlled. In the open loop mode (O/L), a fuel injection amount is controlled according to a base map of a fuel injection amount which is determined by RPM and load of the internal combustion engine  101 . 
     FIG. 3  is a flowchart showing a process of deriving a correction amount of a fuel injection amount calculated by the ECU  118 . 
   In Step S 301 , it is determined whether or not the O 2  feedback mode (F/B) has been entered. 
   When it is determined in Step S 301  that the O 2  feedback mode (F/B) has been entered, the flow proceeds to Step S 302 . 
   In Step S 302 , a proportional correction amount (Kp) and an integral correction amount (SKi) are summed to obtain a fuel correction amount (CFB). 
   A method of calculating the fuel correction amount (CFB) will be described later. 
   When it is determined in Step S 301  that the O 2  feedback mode (F/B) has not been entered, the flow proceeds to Step S 303 . 
   In Step S 303 , the fuel correction amount (CFB) is set to 1.0. 
   In Step S 304 , it is determined whether or not the enrichment mode (E/R) has been entered. 
   When it is determined in Step S 304  that the enrichment mode (E/R) has been entered, the flow proceeds to Step S 305 . 
   In Step S 305 , referring to a map of a correction amount of a fuel injection amount which is available as a combination of RPM (Ne) and an intake pipe pressure (Pb), a value corresponding to the RPM (Ne) and an intake pipe pressure (Pb) at that moment is set as an enrichment correction amount (CER). 
   This map, which represents a correction amount for correcting an air-fuel ratio toward the rich side based on RPM and an intake pipe pressure, is known and therefore will not be described below. 
   On the other hand, when it is determined in Step S 304  that the enrichment mode (E/R) has not been entered, the flow proceeds to Step S 306 . 
   In Step S 306 , the enrichment correction amount (CER) is set to 1.0. 
     FIG. 4  is a flowchart showing the concrete contents of a process for calculating the O 2  feedback correction amount (CFB) in Step S 302  of  FIG. 3 . That is, the processing shown in  FIG. 4  is performed by the ECU  118 . 
   In Step S 401 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio is in the rich state (RICH). 
   The output from the O 2  sensor  108  is approximately equal to 1 V when the air-fuel ratio of exhaust gas is rich with respect to the stoichiometric air-fuel ratio, and is approximately equal to 0 V when the air-fuel ratio of exhaust gas is lean with respect to the stoichiometric air-fuel ratio. Thus, a threshold for determining whether the air-fuel ratio of exhaust gas is rich or lean with respect to the stoichiometric air-fuel ratio is set to 0.45 V, and a determination on the state of the air-fuel ratio is made using this threshold. 
   When it is determined in Step S 401 , based on the output signal from the O 2  sensor  108 , that the air-fuel ratio is rich (RICH), the flow proceeds to Step S 402 . 
   In Step S 402 , a proportional value (Kp) is calculated using the following equation.
 
 Kp =1.0 −Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 403 , an integral gain (Kit) is set using the following equation.
 
Kit=− Gi  
 
   When it is determined in Step S 401 , based on the output signal from the O 2  sensor  108 , that the air-fuel ratio is not in the rich state (RICH), the flow proceeds to Step S 404 . 
   In Step S 404 , a proportional value (Kp) is calculated using the following equation.
 
 Kp =1.0 +Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 405 , the integral gain (Kit) is set to Gi. 
   In a subsequent step S 406 , the integral gain (Kit) is multiplied by a coolant temperature coefficient (Kwt(WT)) to calculate the last integral gain (Ki). The coolant temperature coefficient (Kwt(WT)) will be described later with reference to  FIG. 7 . 
   Furthermore, in Step S 407 , the second last integral value (SKi(i−1)) and the final integral gain (Ki) are summed to obtain an integral value (SKi). 
   In a subsequent step S 408 , it is determined whether or not the integral value (SKi) is larger than an integral upper limit (SKiMX). 
   When it is determined in Step S 408  that the integral value (SKi) is larger than the integral upper limit (SKiMX), the flow proceeds to Step S 409 . 
   In Step S 409 , the integral value (SKi) obtained in Step S 407  is set as the integral upper limit (SKiMX). 
   In a subsequent step S 410 , it is determined whether or not the integral value (SKi) is smaller than an integral lower limit (SKiMN). 
   When it is determined in Step S 410  that the integral value (SKi) is smaller than the integral lower limit (SKiMN), the flow proceeds to Step S 411 . 
   In Step S 411 , the integral value (SKi) is set to the integral lower limit (SKiMN). 
   Furthermore, in a subsequent step S 412 , the O 2  feedback correction amount (CFB) is set to the sum of the proportional value (Kp) and the integral value (SKi). 
   When it is determined in Step S 408  that the integral value (SKi) is equal to or smaller than the integral upper limit (SKIMX), the flow proceeds to Step S 410 . 
   When it is determined in Step S 410  that the integral value (SKi) is equal to or larger than the integral lower limit (SKIMN), the flow proceeds to Step S 412 . 
     FIG. 5  is a table showing the proportional gain (Gp) used as a value corresponding to the RPM (Ne) and the intake pipe pressure (Pb). 
     FIG. 6  is a table showing the integral gain (Gi) used as a value corresponding to the RPM (Ne) and the intake pipe pressure (Pb). 
   Thus, the values of the proportional gain (Gp) and the integral gain (Gi) are set for each of the zones that are separated from one another according to the RPM (Ne) and the intake pipe pressure (Pb), and those values of the proportional gain (Gp) and the integral gain (Gi) which correspond to the conditions on the RPM (Ne) and the intake pipe pressure (Pb) are selected. When an output value of a throttle sensor indicates that the throttle valve  104  is substantially fully closed, it is determined that the internal combustion engine  101  is in its idling state, so an idling gain is used. 
   The idling gain is a value in the lower left block (which is adjacent to the origin) in each of the characteristics shown in the tables of  FIGS. 5 and 6 . 
     FIG. 7  is a characteristic diagram showing a characteristic of the coolant temperature coefficient (Kwt(WT)), by which the integral gain (Kit) is multiplied, with respect to a coolant temperature. 
   In a region of low coolant temperatures, the coolant temperature coefficient (Kwt(WT)) is set to be small (to a first level (0.5)), so the final integral gain (Ki) that has been multiplied by the coolant temperature coefficient (Kwt(WT)) assumes a small value. As the coolant temperature rises, the coolant temperature coefficient (Kwt(WT)) is linearly changed over to a second level (1.0), which is larger than the first level, in a predetermined coolant temperature range (between 20° C. and 80° C.). Alternatively, the coolant temperature coefficient (Kwt (WT)) may be changed over nonlinearly. Also, the coolant temperature coefficient (Kwt(WT)) may be changed over to the second level, which is larger than the first level, at a predetermined coolant temperature. 
   In order to adjust an injector open-valve time (Ti) to regulate an amount of fuel supplied to the intake pipe  103 , the injector open-valve time (Ti) corresponding to the amount of supplied fuel is calculated using the following equation.
 
 Ti =( Pb×Kp 2 t×K 1× CFB )+( Tacc−Tdec )+ Td  
 
   Here, Ti represents an injector open-valve time [msec], that Pb represents an intake pipe pressure [kPa], that Kp2t represents an intake pipe pressure/open-valve time conversion coefficient [msec/kPa], that K1 represents various correction coefficients (for enrichment correction, warm-up correction, and the like), that CFB represents an O 2  feedback coefficient, that Tacc represents an acceleration increase amount [msec], that Tdec represents a decrease in RPM [msec], and that Td represents a dead time [msec]. 
   The fuel supplied to the intake pipe  103  is mixed with sucked air, burnt in the internal combustion engine  101 , and then discharged to the exhaust pipe  107 . Then, the O 2  sensor  108  measures an amount of oxygen remaining in the exhaust gas. 
   In the O 2  feedback mode (F/B), an amount of increase or decrease in the final integral gain (Ki) is adjusted based on an output value of the O 2  sensor  108 , by means of the O 2  feedback correction coefficient (CFB). 
     FIG. 8  is a time chart showing how the RPM (Ne), the amount of remaining oxygen, the O 2  feedback correction coefficient CFB, and the air-fuel ratio A/F change when the internal combustion engine  101  is started at a coolant temperature of 20° C. 
   The internal combustion engine  101  is started at a time point A, and cylinders thereof are identified based on outputs from the crank angle sensor  114  and the cam angle sensor  112 . After the cylinders have been identified, fuel is supplied to each of the cylinders and ignited. As a result, the operation of the internal combustion engine  101  is started. 
   The RPM of the internal combustion engine  101  is stabilized at a time point B. The O 2  sensor  108  does not generate a correct output unless its temperature has risen to a certain temperature, so the air-fuel ratio A/F is on the rich side due to warm-up correction. Thus, as the temperature of the O 2  sensor  108  rises, the output therefrom rises as well. 
   When the output from the O 2  sensor  108  exceeds a threshold at a time point C, the ECU  118  determines that the O 2  sensor  108  has reached a temperature allowing generation of a correct output value and has been activated. 
   O 2  feedback control is started as soon as the ECU  118  makes this determination. 
   While broken lines indicate characteristics in the case where the conventional control apparatus for the internal combustion engine performs control, solid lines indicate characteristics in the case where the control apparatus for the internal combustion engine according to the present invention performs control. 
   In the case of conventional control (the broken lines), after O 2  feedback control has been started, the integral gain of O 2  feedback is set large until initial inversion occurs. When the internal combustion engine is cold, the integral gain is too large, so the air-fuel ratio A/F is too lean. As a result, the RPM of the internal combustion engine decreases. 
   A lean limit of the air-fuel ratio A/F allowing combustion is lower when the internal combustion engine is cold than when the internal combustion engine is being warmed up. When a combustion limit is exceeded, a more drastic decrease in RPM or engine stall may be caused. 
   On the other hand, in the case of control according to the present invention (the solid lines), the integral gain of O 2  feedback is made smaller than the value at the time when the internal combustion engine  101  is being warmed up, thereby eliminating overcorrection toward the lean side. As a result, it is possible to make the air-fuel ratio A/F lean, and to restrain the RPM of the internal combustion engine  101  from decreasing drastically or the internal combustion engine  101  from stalling. 
   As described above, the integral gain of O 2  feedback is corrected according to a coolant temperature which corresponds to an engine temperature, and is set to be smaller when the coolant temperature is low than when the coolant temperature is high. Thus, the air-fuel ratio A/F and the behavior of engine rotation can be stabilized even at a low temperature, that is, even with a low combustion limit. 
   Second Embodiment 
     FIG. 9  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to the second embodiment of the present invention. A method of calculating the O 2  feedback correction amount (CFB) shown in  FIG. 9  is different from the method of calculating the O 2  feedback correction amount (CFB) according to the first embodiment of the present invention. 
   The ECU  118 , which is the control apparatus for controlling operation of the internal combustion engine according to the second embodiment of the present invention, functions especially as the following means:
     (1) air-fuel ratio state determining means;   (2) characteristic retaining means; and   (3) fuel correction amount calculating means.   

   The air-fuel ratio state determining means determines whether an air-fuel ratio detected by the air-fuel ratio detecting means is in a rich state or in a lean state. The characteristic retaining means retains an integral gain characteristic and a proportional gain characteristic in which the values of an integral gain and a proportional gain are determined by RPM and an intake pipe pressure, and an elapsed time coefficient characteristic in which an elapsed time coefficient for correcting the integral gain is determined by a post-start elapsed time. The fuel correction amount calculating means multiplies the integral gain by the elapsed time coefficient in calculating a correction amount of a fuel injection amount using a sign obtained according to a determination result of the air-fuel ratio state determining means, the integral gain, and the proportional gain. 
   The characteristic retaining means need not be a memory in the ECU  118  but may be an external memory. 
   As shown in  FIG. 9 , first in Step S 901 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio A/F is rich (RICH). 
   The output from the O 2  sensor  108  is approximately 1 V when the air-fuel ratio of exhaust gas is rich with respect to the stoichiometric air-fuel ratio, and is approximately 0 V when the air-fuel ratio of exhaust gas is lean with respect to the stoichiometric air-fuel ratio. Thus, a threshold for determining whether the air-fuel ratio of exhaust gas is rich or lean with respect to the stoichiometric air-fuel ratio is set to 0.45 V, and a determination on the state of the air-fuel ratio is made using this threshold. 
   When it is determined in Step S 901  that the air-fuel ratio A/F is rich (RICH) because the output from the O 2  sensor  108  is larger than the threshold (0.45 V), the flow proceeds to Step S 902 . 
   In Step S 902 , a proportional value (Kp) is calculated using the following equation.
 
 Kp =1.0 −Gp  
 
   Here, Gp represents a proportional gain. 
   In Step S 903 , an integral gain (Kit) is set using the following equation.
 
Kit=− Gi  
 
   On the other hand, when it is determined in Step S 901  that the air-fuel ratio A/F is lean because the output from the O 2  sensor  108  is equal to or smaller than the threshold (0.45 V), the flow proceeds to Step S 904 . 
   In Step S 904 , a proportional gain (Kp) is calculated using the following equation.
 
 Kp =1.0 +Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 905 , the integral gain (Kit) is set to Gi. 
   Furthermore, in a subsequent step S 906 , the integral gain (Kit) is multiplied by a post-start elapsed time correction coefficient (Kst(ST)) to obtain the last integral gain (Ki). 
   In Step S 907 , the second last integral value (SKi(i−1)) and the final integral gain (Ki) are summed to obtain an integral value (SKi). 
   Here, the second last integral value (SKi(i−1)) means an integral value obtained last time in an engine control processing that is performed at each ignition timing. 
   In a subsequent step S 908 , it is determined whether or not the integral value (SKi) is larger than an integral upper limit (SKiMX). 
   When it is determined in Step S 908  that the integral value (SKi) is larger than the integral upper limit (SKiMX), the flow proceeds to Step S 909 . 
   In Step S 909 , the integral value (SKi) is set to the integral upper limit (SKiMX). 
   Furthermore, in a subsequent step S 910 , it is determined whether or not the integral value (SKi) is smaller than an integral lower limit (SKiMN). 
   When it is determined in Step S 910  that the integral value (SKi) is smaller than the integral lower limit (SKiMN), the flow proceeds to Step S 911 . 
   In Step S 911 , the integral value (SKi) is set to the integral lower limit (SKiMN). 
   Furthermore, in a subsequent step S 912 , the proportional value (Kp) and the integral value (SKi) are summed to obtain the O 2  feedback correction amount (CFB). 
   When it is determined in Step S 908  that the integral value (SKi) is equal to or smaller than the integral upper limit (SKIMX), the flow proceeds to Step S 910 . 
   When it is determined in Step S 910  that the integral value (SKi) is equal to or larger than the integral lower limit (SKiMN), the flow proceeds to Step S 912 . 
     FIG. 10  is a characteristic diagram showing a characteristic of a post-start elapsed time correction coefficient, by which the integral gain (Kit) is multiplied, with respect to an elapsed time. 
   The correction coefficient is set to be small (to a first level (0.5)) in a region where the post-start elapsed time is not very long (within 60 seconds). The correction coefficient is set to a second level (1.0, that is, with no correction), which is larger than the first level, after a predetermined post-start elapsed time (60 seconds) has passed. 
     FIG. 11  is a characteristic diagram showing a characteristic of a post-start elapsed time correction coefficient, by which the integral gain (Kit) is multiplied, with respect to an elapsed time. 
   According to the characteristic shown in  FIG. 11 , unlike the characteristic shown in  FIG. 10 , the correction coefficient gradually increases as time elapses after the start of the engine. The characteristic indicating how the post-start elapsed time correction coefficient, by which the integral gain (Kit) is multiplied, changes with respect to an elapsed time is not limited to the characteristic shown in  FIG. 10 . It is also possible to adopt the characteristic as shown in  FIG. 11  in which the post-start elapsed time correction coefficient is linearly changed over to the second level, which is larger than the first level. Alternatively, the post-start elapsed time correction coefficient may be changed over nonlinearly. 
   As described above, the integral gain of O 2  feedback is corrected depending on the time that has elapsed after the start of the engine. That is, the integral gain of O 2  feedback is set to be smaller when only a short time has elapsed after the start of the engine than when a sufficiently long time has elapsed after the start of the engine. As a result, the air-fuel ratio A/F and the behavior of engine rotation can be stabilized even immediately after the start of the engine, that is, even with a low combustion limit. 
   Third Embodiment 
     FIG. 12  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to the third embodiment of the present invention. 
   As shown in  FIG. 12 , in Step S 1201 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio A/F is rich (RICH). 
   The output from the O 2  sensor  108  is approximately 1 V when the air-fuel ratio of exhaust gas is rich with respect to the stoichiometric air-fuel ratio, and is approximately 0 V when the air-fuel ratio of exhaust gas is lean with respect to the stoichiometric air-fuel ratio. Thus, a threshold for determining whether the air-fuel ratio of exhaust gas is rich or lean with respect to the stoichiometric air-fuel ratio is set to 0.45 V, and a determination on the state of the air-fuel ratio is made using this threshold. 
   When it is determined in Step S 1201 , based on the output signal from the O 2  sensor  108 , that the air-fuel ratio A/F is rich, the flow proceeds to Step S 1202 . 
   In Step S 1202 , a proportional value (Kp) is obtained using the following equation.
 
 Kp =1.0 −Gp  
 
   Here, Gp represents a proportional gain. 
   In Step S 1203 , an integral gain (Kit) is set using the following equation.
 
Kit=− Gi  
 
   On the other hand, when it is determined in Step S 1201  that the air-fuel ratio A/F is lean because the output from the O 2  sensor  108  is equal to or smaller than the threshold (0.45 V), the flow proceeds to Step S 1204 . 
   In Step S 1204 , a proportional value (Kp) is obtained using the following equation.
 
 Kp =1.0 +Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 1205 , the integral gain (Kit) is set to Gi. 
   Furthermore, in a subsequent step S 1206 , the second last integral value (SKi(i−1)) and the integral gain (Ki) are summed to obtain an integral value (SKi). 
   In Step S 1207 , an integral upper limit (SKIMX) is obtained referring to a map of post-start elapsed time (Kmx(ST)). 
   In a subsequent step S 1208 , an integral lower limit (SKIMN) is obtained referring to a map of post-start elapsed time (Kmn(ST)). 
     FIGS. 13 and 14  each are a characteristic diagram showing the characteristics of the integral upper limit (SKIMX) and the integral lower limit (SKIMN) with respect to a post-start elapsed time. 
   Furthermore, in a subsequent step S 1209 , it is determined whether or not the integral value (SKi) is larger than the integral upper limit (SKiMX). 
   When it is determined in Step S 1209  that the integral value (SKi) is larger than the integral upper limit (SKiMX), the flow proceeds to Step S 1210 . 
   In Step S 1210 , the integral value (SKi) is set to the integral upper limit (SKiMX). 
   In a subsequent step S 1211 , it is determined whether or not the integral value (SKi) is smaller than the integral lower limit (SKiMN). 
   When it is determined in Step S 1211  that the integral value (SKi) is smaller than the integral lower limit (SKiMN), the flow proceeds to Step S 1212 . 
   In Step S 1212 , the integral value (SKi) is set to the integral lower limit (SKiMN). 
   In Step S 1213 , the O 2  feedback correction amount (CFB) is set to the sum of the proportional value (Kp) and the integral value (SKi). 
     FIG. 13  is a characteristic diagram showing characteristics of set values of the integral upper limit (SKIMX) and the integral lower limit (SKIMN) with respect to a time after the start of the engine. 
   As shown in  FIG. 13 , the range between the integral upper limit (SKIMX) and the integral lower limit (SKIMN) is set narrow in a region where a sufficient length of time has not elapsed after the start of the engine (within 60 seconds after the start of the engine), and is set wide after a predetermined post-start elapsed time has passed (60 seconds or more after the start of the engine). 
   That is, the ECU  118  functioning as the fuel correction amount calculating means functions as fuel correction amount calculating means that calculates a gain for obtaining a correction amount of a fuel injection amount using characteristics of an integral upper limit and an integral lower limit in integral calculation. According to those characteristics, as the coolant temperature rises or as time elapses after the start of the engine, the integral upper limit in integral calculation is increased to a second upper-limit level, which is higher than a first upper-limit level, and the integral lower limit in integral calculation is reduced to a second lower-limit level, which is lower than a first lower-limit level. 
   The characteristic retaining means for retaining the characteristics may be a memory in the ECU  118  or a memory outside the ECU  118 . 
     FIG. 14  is a characteristic diagram showing characteristics of set values of the integral upper limit (SKiMX) and the integral lower limit (SKiMN) with respect to an elapsed time after the start of the engine. The characteristics of  FIG. 14  are different from those of  FIG. 13  in that the characteristics show a transient region where the range between the integral upper limit (SKiMX) and the integral lower limit (SKiMN) is gradually increased from a narrow range to a wide range. 
   By using the characteristics, which show the transient region, of set values of the integral upper limit (SKiMX) and the integral lower limit (SKiMN) with respect to an elapsed time after the start of the engine, a finer control processing can be performed. 
   As described above, with the control apparatus for the internal combustion engine according to the third embodiment of the present invention, the range between the upper limit and the lower limit of the integral gain of the O 2  feedback correction coefficient is changed according to the elapsed time after the start of the engine. Thus, the air-fuel ratio A/F and the behavior of engine rotation can be stabilized by setting the range between the upper limit and the lower limit of the integral gain to be narrow when a sufficient length of time has not elapsed after the start of the engine. 
   Fourth Embodiment 
     FIG. 15  is a flowchart showing the contents of a process for obtaining an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to the fourth embodiment of the present invention. 
   As shown in  FIG. 15 , in Step S 1501 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio A/F is rich (RICH). 
   The output from the O 2  sensor  108  is approximately 1 V when the air-fuel ratio of exhaust gas is rich with respect to the stoichiometric air-fuel ratio, and is approximately 0 V when the air-fuel ratio of exhaust gas is lean with respect to the stoichiometric air-fuel ratio. Thus, a threshold for determining whether the air-fuel ratio of exhaust gas is rich or lean with respect to the stoichiometric air-fuel ratio is set to 0.45 V, and a determination on the state of the air-fuel ratio is made using this threshold. 
   When it is determined in Step S 1501 , based on the output signal of the O 2  sensor  108 , that the air-fuel ratio A/F is rich, the flow proceeds to Step S 1502 . 
   In Step S 1502 , a proportional value (Kp) is obtained using the following equation.
 
 Kp =1.0 −Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 1503 , an integral gain (Kit) is set using the following equation.
 
Kit=− Gi  
 
   On the other hand, when it is determined in Step S 1501  that the air-fuel ratio A/F is lean because the output from the O 2  sensor  108  is equal to or smaller than the threshold (0.45 V), the flow proceeds to Step S 1504 . 
   In Step S 1504 , a proportional value (Kp) is obtained using the following equation.
 
 Kp =1.0 +Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 1505 , the integral gain (Kit) is set to Gi. 
   Furthermore, in a subsequent step S 1506 , the integral gain (Kit) is multiplied by a post-start correction coefficient (Kst(ST, WT)) to obtain the last integral gain (Ki). 
   In Step S 1507 , the second last integral value (SKi (i−1)) and the final integral gain (Ki) are summed to obtain an integral value (SKi). 
   In a subsequent step S 1508 , it is determined whether or not the integral value (SKi) is larger than an integral upper limit (SKiMX). 
   When it is determined in Step S 1508  that the integral value (SKi) is larger than the integral upper limit (SKiMX), the flow proceeds to Step S 1509 . 
   In Step S 1509 , the integral value (SKi) is set to the integral upper limit (SKiMX). 
   In a subsequent step S 1510 , it is determined whether or not the integral value (SKi) is smaller than an integral lower limit (SKiMN). 
   When it is determined in Step S 1510  that the integral value (SKi) is smaller than the integral lower limit (SKiMN), the flow proceeds to Step S 1511 . 
   In Step S 1511 , the integral value (SKi) is set to the integral lower limit (SKiMN). 
   In a subsequent step S 1512 , an O 2  feedback correction amount (CFB) is set to the sum of the proportional value (Kp) and the integral value (SKi). 
     FIG. 16  is a characteristic diagram showing characteristics of a post-start elapsed time correction coefficient, by which the integral gain (Kit) is multiplied, with respect to an elapsed time after the start of the engine. 
   The ECU  118 , which is the control apparatus for controlling operation of the internal combustion engine according to the fourth embodiment of the present invention, performs operation control of the internal combustion engine  101  using coolant temperature detected by the coolant temperature detecting means as well as an air-fuel ratio and a post-start elapsed time. The characteristic retaining means further has a coolant temperature coefficient characteristic in which a coolant temperature coefficient for correcting an integral gain is determined by a coolant temperature. The ECU  118  functioning as the fuel correction amount calculating means further multiplies an integral gain by a coolant temperature coefficient in obtaining a correction amount of a fuel injection amount. 
   More specifically, the integral gain correction coefficient is set to be small (0.5) in a region where a sufficient length of time has not elapsed after the start of the engine, and is set to be large (1.0, that is, with no correction) after a predetermined time has elapsed since the start of the engine. 
   As indicated by broken lines (at a coolant temperature of 40° C.) and alternate dot and dash lines (at a coolant temperature of 20° C.) in  FIG. 16 , the post-start elapsed time for changing over the integral gain correction coefficient from the small value to the large value is changed according to the coolant temperature. When the timing for this changeover is retarded as the coolant temperature lowers, an integral gain corresponding to the coolant temperature is set. As a result, a much finer control processing can be realized. 
     FIG. 17  is a characteristic diagram showing characteristics of a post-start elapsed time correction coefficient, by which the integral gain (Kit) is multiplied, with respect to an elapsed time after the start of the engine. 
   The characteristics of  FIG. 17  are different from those of  FIG. 16  in that the characteristics show a transient region where the post-start elapsed time correction coefficient is gradually increased from a small value to a large value. 
   By using the characteristics, which show the transient region, of the post-start elapsed time correction coefficient with respect to the elapsed time, a finer control processing can be performed. 
   As described above, the integral gain of the O 2  feedback correction coefficient is corrected according to the elapsed time after the start of the engine. That is, the integral gain is corrected to a small value when a sufficient length of time has not elapsed after the start of the engine. Further, the time period during which the integral gain is corrected to the small value is prolonged as the coolant temperature lowers. Therefore, the air-fuel ratio A/F can be made lean, and as a result, the behavior of engine rotation can be stabilized. 
   Fifth Embodiment 
     FIG. 18  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to the fifth embodiment of the present invention. 
   The ECU  118 , which is the control apparatus for controlling operation of the internal combustion engine according to the fifth embodiment of the present invention, functions as fuel correction amount calculating means for setting again for obtaining a correction amount of a fuel injection amount based on coolant temperature or a post-start elapsed time only when air-fuel state determining means determines that the air-fuel ratio is rich. 
   As shown in  FIG. 18 , in Step S 1801 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio A/F is rich (RICH). 
   The output from the O 2  sensor  108  is approximately 1 V when the air-fuel ratio of exhaust gas is rich with respect to the stoichiometric air-fuel ratio, and is approximately 0 V when the air-fuel ratio of exhaust gas is lean with respect to the stoichiometric air-fuel ratio. Thus, a threshold for determining whether the air-fuel ratio of exhaust gas is rich or lean with respect to the stoichiometric air-fuel ratio is set to 0.45 V, and a determination on the state of the air-fuel ratio is made using this threshold. 
   When it is determined in Step S 1801 , based on the output signal of the O 2  sensor  108 , that the air-fuel ratio A/F is rich, the flow proceeds to Step S 1802 . 
   In Step S 1802 , a proportional value (Kp) is obtained using the following equation.
 
 Kp =1.0 −Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 1803 , an integral gain (Kit) is set using the following equation.
 
Kit=− Gi  
 
   In subsequent Step S 1804 , the integral gain (Kit) is multiplied by a coolant temperature coefficient (Kwt(WT)) to obtain the last integral gain (Ki). 
   On the other hand, when it is determined in Step S 1801  that the air-fuel ratio A/F is lean because the output from the O 2  sensor  108  is equal to or smaller than the threshold (0.45 V), the flow proceeds to Step S 1805 . 
   In Step S 1805 , a proportional value (Kp) is obtained using the following equation.
 
 Kp =1.0 +Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 1806 , the integral gain (Kit) is set to Gi. 
   Furthermore, in a subsequent step S 1807 , the second last integral value (SKi (i−1)) and the final integral gain (Ki) are summed to obtain an integral value (SKi). 
   In Step S 1808 , it is determined whether or not the integral value (SKi) is larger than an integral upper limit (SKiMX). 
   When it is determined in Step S 1808  that the integral value (SKi) is larger than the integral upper limit (SKiMX), the flow proceeds to Step S 1809 . 
   In Step S 1809 , the integral value (SKi) is set to the integral upper limit (SKiMX). 
   In a subsequent step S 1810 , it is determined whether or not the integral value (SKi) is smaller than an integral lower limit (SKiMN). 
   When it is determined in Step S 1810  that the integral value (SKi) is smaller than the integral lower limit (SKiMN), the flow proceeds to Step S 1811 . 
   In Step S 1811 , the integral value (SKi) is set to the integral lower limit (SKiMN). 
   In a subsequent step S 1812 , the O 2  feedback correction amount (CFB) is set to the sum of the proportional value (Kp) and the integral value (SKi). 
   A coefficient obtained from the characteristic shown in  FIG. 7  is used as the coolant temperature coefficient (Kwt(WT)). 
   As described above, with the control apparatus for the internal combustion engine according to the fifth embodiment of the present invention, the integral correction amount of the O 2  feedback correction coefficient is corrected according to the coolant temperature only on a decremental side, and the integral gain at the time when the coolant temperature is low is reduced only on the decremental side, thereby keeping the air-fuel ratio A/F from being corrected toward the lean side. As a result, the air-fuel ratio A/F can be made lean, and the behavior of engine rotation can thereby be stabilized. 
   The response speed of an incremental operation is increased because the correction gain toward the incremental side is not reduced. Furthermore, an effect of keeping the air-fuel ratio A/F from becoming lean is achieved. 
   Sixth Embodiment 
     FIG. 19  is a flowchart showing the contents of a process for calculating an O 2  feedback correction amount (CFB) in a control apparatus for an internal combustion engine according to the sixth embodiment of the present invention. 
   The ECU  118 , which is the control apparatus for controlling operation of the internal combustion engine according to the sixth embodiment of the present invention, functions as fuel correction amount calculating means for setting again for obtaining a correction amount of a fuel injection amount based on a coolant temperature or a post-start elapsed time only when air-fuel state determining means determines that the air-fuel ratio is rich. 
   As shown in  FIG. 19 , in Step S 1901 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio A/F is rich (RICH). 
   The output from the O 2  sensor  108  is approximately 1 V when the air-fuel ratio of exhaust gas is rich with respect to the stoichiometric air-fuel ratio, and is approximately 0 V when the air-fuel ratio of exhaust gas is lean with respect to the stoichiometric air-fuel ratio. Thus, a threshold for determining whether the air-fuel ratio of exhaust gas is rich or lean with respect to the stoichiometric air-fuel ratio is set to 0.45 V, and a determination on the state of the air-fuel ratio is made using this threshold. 
   When it is determined in Step S 1901 , based on the output signal of the O 2  sensor  108 , that the air-fuel ratio A/F is rich, the flow proceeds to Step S 1902 . 
   In Step S 1902 , a proportional value (Kp) is obtained using the following equation.
 
 Kp =1.0 −Gp  
 
   Here, Gp represents a proportional gain. 
   In a subsequent step S 1903 , an integral gain (Kit) is set using the following equation.
 
Kit=− Gi  
 
   In Step S 1904 , the integral gain (Kit) is multiplied by a post-start correction coefficient (Kst(ST)) to obtain the last integral gain (Ki). 
   On the other hand, when it is determined in Step S 1901  that the air-fuel ratio is not rich, the proportional value (Kp) is obtained by adding the proportional gain (Gp) to 1.0 in Step S 1905 . In Step S 1906 , the final integral gain (Ki) is set to Gi. 
   In a subsequent step S 1907 , the second last integral value (SKi(i−1)) and the final integral gain (Ki) are summed to obtain an integral value (SKi). 
   In Step S 1908 , it is determined whether or not the integral value (SKi) is larger than an integral upper limit (SKIMX). When it is determined in Step S 1908  that the integral value (SKi) is larger than the integral upper limit (SKiMX), the integral value (SKi) is set to the integral upper limit (SKIMX) in Step S 1909 . 
   In Step S 1910 , it is determined whether or not the integral value (SKi) is smaller than an integral lower limit (SKIMN). When it is determined in Step S 1910  that the integral value (SKi) is smaller than the integral lower limit (SKIMN), the integral value (SKi) is set to the integral lower limit (SKIMN) in Step S 1911 . 
   In Step S 1912 , the O 2  feedback correction amount (CFB) is set to the sum of the proportional value (Kp) and the integral value (SKi). 
   The post-start correction coefficient (Kst(ST)) is a coefficient shown in  FIG. 10  or  FIG. 11 . 
   As described above, the integral correction amount of the O 2  feedback correction coefficient is corrected according to the post-start elapsed time only on a decremental side, and the integral gain at the time when a sufficient length of time has not elapsed after the start of the engine is reduced only on the decremental side, thereby keeping the air-fuel ratio A/F from being corrected toward the lean side. As a result, it is possible to restrain the air-fuel ratio A/F from becoming lean and the RPM from decreasing. The correction gain toward the incremental side of the air-fuel ratio A/F is not reduced, so the incremental operation is performed swiftly. Thus, it is possible to swiftly restrain the air-fuel ratio A/F from becoming lean. 
   Seventh Embodiment 
     FIG. 20  is a flowchart showing the concrete contents of another process for obtaining the O 2  feedback correction amount (CFB) in Step  302  of  FIG. 3 . 
   The ECU  118 , which is a control apparatus for controlling operation of an internal combustion engine according to the seventh embodiment of the present invention, functions as fuel correction amount calculating means for setting only a minimum value and not a maximum value in integral calculation in calculating a gain for obtaining a correction amount of a fuel injection amount. 
   As shown in  FIG. 20 , in Step S 2001 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio A/F is rich (RICH). The O 2  sensor  108  has a characteristic of generating an output of approximately 1 V when the air-fuel ratio A/F is rich with respect to the stoichiometric air-fuel ratio and generating an output of approximately 0 V when the air-fuel ratio A/F is lean with respect to the stoichiometric air-fuel ratio. Therefore, the determination is made depending on whether the output signal from the O 2  sensor  108  is higher or lower than a threshold (0.45 V). 
   When it is determined in Step S 2001  that the air-fuel ratio A/F is rich, a proportional value (Kp) is obtained by subtracting a proportional gain (Gp) from 1.0 in Step S 2002 , and an integral gain (Ki) is set to −Gi in Step S 2003 . 
   When it is determined in Step S 2001  that the air-fuel ratio A/F is not rich, a proportional value (Kp) is calculated by adding a proportional gain (Gp) to 1.0 in Step S 2004 , and an integral gain (Ki) is set to Gi in Step S 2005 . 
   In Step S 2006 , the second last integral value (SKi(i−1)) and the integral gain (Ki) are summed to obtain an integral value (SKi). 
   In Step S 2007 , an integral lower limit (SKiMN) is obtained from a post-start elapsed time. 
   In Step S 2008 , it is determined whether or not the integral value (SKi) is larger than an integral upper limit (SKIMX). When it is determined in Step S 2008  that the integral value (SKi) is larger than the integral upper limit (SKiMX), the integral value (SKi) is set to the integral upper limit (SKIMX) in Step S 2009 . 
   In Step S 2010 , it is determined whether or not the integral value (SKi) is smaller than an integral lower limit (SKIMN). When it is determined in Step S 2010  that the integral value (SKi) is smaller than the integral lower limit (SKIMN), the integral value (SKi) is set to the integral lower limit (SKIMN) in Step S 2011 . 
   In Step S 2012 , the O 2  feedback correction amount (CFB) is set to the sum of the proportional value (Kp) and the integral value (SKi). 
   The integral lower limit (SKIMN) obtained from the post-start elapsed time is a value indicated as SKIMN shown in  FIG. 13  or  FIG. 14 . 
   As described above, the lower limit of the O 2  feedback correction coefficient is set according to the post-start elapsed time, and the decrease in correction amount is suppressed as the post-start elapsed time is short. As a result, it is possible to restrain the air-fuel ratio A/F from becoming lean and the RPM from decreasing. 
   Eighth Embodiment 
     FIG. 21  is a flowchart showing the concrete contents of still another process for calculating an O 2  feedback correction amount (CFB) in Step S 302  of  FIG. 3 . 
   The ECU  118 , which is a control apparatus for controlling operation of an internal combustion engine according to the eighth embodiment of the present invention, is further equipped with RPM decrease detecting means for detecting a decrease in RPM of the internal combustion engine  101 . The ECU  118  functions as fuel correction amount calculating means for initializing a correction amount of a fuel injection amount when the RPM decrease detecting means has detected a decrease in RPM of the internal combustion engine  101  within a predetermined period from the start of the engine. 
   The RPM decrease detecting means can be realized by monitoring a detection signal of the crank angle sensor  114  by means of the ECU  118 . 
   As shown in  FIG. 21 , in Step S 2101 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio A/F is rich (RICH). The O 2  sensor  108  has a characteristic of generating an output of approximately 1 V when the air-fuel ratio A/F is rich with respect to the stoichiometric air-fuel ratio and generating an output of approximately 0 V when the air-fuel ratio A/F is lean with respect to the stoichiometric air-fuel ratio. Therefore, the determination is made depending on whether the output signal from the O 2  sensor  108  is higher or lower than the threshold (0.45 V). 
   When it is determined in Step S 2101  that the air-fuel ratio A/F is rich, a proportional value (Kp) is obtained by subtracting a proportional gain (Gp) from 1.0 in Step S 2102 , and an integral gain (Ki) is set to −Gi in Step S 2103 . 
   When it is determined in Step S 2101  that the air-fuel ratio A/F is not rich, a proportional gain (Kp) is obtained by adding a proportional gain (Gp) to 1.0 in Step S 2104 , and an integral gain (Ki) is set to Gi in Step S 2105 . 
   In Step S 2106 , the second last integral value (SKi(i−1)) and the integral gain (Ki) are summed to obtain an integral value (SKi). 
   In Step S 2107 , it is determined whether or not a post-start elapsed time (Tst) is equal to or shorter than a predetermined time (Kst) while the preceding deceleration decrease amount (Tdec(i−1)) is zero and a current deceleration decrease amount (Tdec) is not zero. 
   The deceleration decrease amount is set when the amount of a decreasing change in intake pipe pressure is equal to or larger than a predetermined value. A determination as to whether or not the deceleration decreasing amount has changed from zero to a value larger than zero means a determination as to whether or not deceleration has started. 
   Although the predetermined time (Kst) is a constant, it may be changed according to the coolant temperature at the time when the internal combustion engine  101  is started. 
   When the condition in Step S 2107  is fulfilled (Yes), the integral value (SKi) is set to zero in Step S 2108 . 
   In Step S 2109 , it is determined whether or not the integral value (SKi) is larger than an integral upper limit (SKIMX). When it is determined in Step S 2109  that the integral value (SKi) is larger than the integral upper limit (SKiMX), the integral value (SKi) is set to the integral upper limit (SKIMX) in Step S 2110 . 
   In Step S 2111 , it is determined whether or not the integral value (SKi) is smaller than an integral lower limit (SKIMN). When it is determined in Step S 2111  that the integral value (SKi) is smaller than the integral lower limit (SKIMN), the integral value (SKi) is set to the integral lower limit (SKIMN) in Step S 2112 . 
   In Step S 2113 , the O 2  feedback correction amount (CFB) is set to the sum of the proportional value (Kp) and the integral value (SKi). 
   As described above, the integral value of the O 2  feedback correction amount is reset to zero when the RPM starts decreasing, namely, when a transition to a low-load region corresponding to unstable combustion is made. The integral value of the O 2  feedback integral value is thereby corrected toward the decremental side, so the air-fuel ratio A/F can be immediately returned to the rich side even when it is lean. Consequently, it is possible not only to suppress the occurrence of misfire resulting from exceeding a combustion limit and a decrease in RPM but also to avoid engine stall. 
   Ninth Embodiment 
     FIG. 22  is a flowchart showing the concrete contents of still another process for obtaining the O 2  feedback correction amount (CFB) in Step S 302  of  FIG. 3 . 
   The ECU  118 , which is a control apparatus for controlling operation of an internal combustion engine according to the ninth embodiment of the present invention, functions as fuel correction amount calculating means for initializing a correction amount of a fuel injection amount only when the air-fuel ratio state determining means determines that the air-fuel ratio is rich. 
   In Step S 2201 , it is determined based on an output signal from the O 2  sensor  108  whether or not the air-fuel ratio A/F is rich (RICH). The O 2  sensor  108  has a characteristic of generating an output of approximately 1 V when the air-fuel ratio A/F is rich with respect to the stoichiometric air-fuel ratio and generating an output of approximately 0 V when the air-fuel ratio A/F is lean with respect to the stoichiometric air-fuel ratio. Therefore, the determination is made depending on whether the output signal from the O 2  sensor  108  is higher or lower than the threshold (0.45 V). 
   When it is determined in Step S 2201  that the air-fuel ratio A/F is rich, a proportional value (Kp) is obtained by subtracting a proportional gain (Gp) from 1.0 in Step S 2202 , and an integral gain (Ki) is set to −Gi in Step S 2203 . 
   When it is determined in Step S 2201  that the air-fuel ratio A/F is not rich, a proportional value (Kp) is obtained by adding a proportional gain (Gp) to 1.0 in Step S 2204 , and an integral gain (Ki) is set to Gi in Step S 2205 . 
   In Step S 2206 , the second last integral value (SKi (i−1)) and the integral gain (Ki) are summed to obtain an integral value (SKi). 
   In Step S 2207 , it is determined whether or not a post-start elapsed time (Tst) is equal to or shorter than a predetermined time (Kst) while a last decrease amount of RPM (Tdec(i−1)) is zero and a current decrease amount of RPM (Tdec) is not zero. 
   The ECU  118  is so set as to make a determination on the decrease amount of RPM when the change amount on the negative side of intake pipe pressure is equal to or larger than a predetermined value. A determination as to whether or not the decrease amount of RPM has increased from zero to a value larger than zero means a determination as to whether or not the RPM has started decreasing. 
   Although the predetermined time (Kst) is a constant, it may be changed according to the coolant temperature at the time when the internal combustion engine  101  is started. 
   When the condition in Step S 2207  is fulfilled (Yes), it is determined in Step S 2208  whether or not the integral value (SKi) is smaller than zero. 
   When it is determined in Step S 2208  that the integral value (SKi) is smaller than zero, the integral value (SKi) is set to zero in Step S 2209 . 
   In Step S 2210 , it is determined whether or not the integral value (SKi) is larger than an integral upper limit (SKiMX). 
   When it is determined in Step S 2210  that the integral value (SKi) is larger than the integral upper limit (SKIMX), the integral value (SKi) is set to the integral upper limit (SKIMX) in Step S 2211 . 
   In Step S 2212 , it is determined whether or not the integral value (SKi) is smaller than an integral lower limit (SKiMN). 
   When it is determined in Step S 2212  that the integral value (SKi) is smaller than the integral lower limit (SKIMN), the integral value (SKi) is set to the integral lower limit (SKIMN) in Step S 2213 . 
   In Step S 2214 , the O 2  feedback correction amount (CFB) is set to the sum of the proportional value (Kp) and the integral value (SKi). 
   As described above, the integral correction amount is reset to zero if the integral value of the O 2  feedback correction amount is smaller than zero (i.e., in a decremental correction state) especially when the RPM starts decreasing, namely, when a transition to a low-load region corresponding to unstable combustion is made. The integral value of O 2  feedback is thereby corrected toward the decremental side. Thus, the air-fuel ratio A/F can be immediately returned to the rich side even when it is lean. Consequently, it is possible not only to suppress the occurrence of misfire resulting from exceeding a combustion limit and a decrease in RPM but also to avoid engine stall.