Patent Publication Number: US-6904899-B2

Title: Air-fuel ratio controller for internal-combustion engine

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to air-fuel ratio controllers for internal-combustion engines, and more particularly to an air-fuel ratio controller for an internal-combustion engine that has respective exhaust gas sensors disposed on both the upstream and downstream sides of a catalyst and controls the supply rate of a fuel in accordance with the output signals sent from the exhaust gas sensors. 
   2. Background Art 
   The apparatuses have heretofore been known which have a wide-area air-fuel ratio sensor (A/F sensor) disposed on the upstream side of a catalyst in an exhaust gas passageway and a dioxide gas sensor (O 2  sensor) on the downstream side of the catalyst, and thus which control the air-fuel ratio in accordance with the output signals sent from the two exhaust gas sensors. The A/F sensor is an exhaust gas sensor exhibiting linear output characteristics with respect to an air-fuel ratio. The O 2  sensor is an exhaust gas sensor exhibiting the so-called Z-characteristics with respect to the air-fuel ratio, in which case the output of the sensor suddenly changes between rich and lean sides with a theoretical air-fuel ratio as its reference. In a conventional controller having these two exhaust gas sensors, the amount of fuel injection is feedback-controlled in accordance with the output signal (air-fuel ratio signal) from the A/F sensor to ensure that the air-fuel ratio of the exhaust gases flowing into the catalyst equals a target air-fuel ratio (hereinafter, the control is referred to as the main feedback control). Along with the main feedback control, control is conducted by feeding the output signal from the O 2  sensor back into the amount of fuel injection (hereinafter, the control is referred to as sub-feedback control). 
   Sub-feedback control is executed to complement the main feedback control and improve the emission characteristics of the internal-combustion engine. The target air-fuel ratio for use in the main feedback control is set to an air-fuel ratio at which the catalyst can purify the exhaust gases with the highest achievable efficiently, and for the main feedback control, a feedback correction value is calculated according to the particular deviation between the air-fuel ratio signal from the A/F sensor and the target air-fuel ratio. The effects of various parameter changes in the internal-combustion engine, however, may cause the actual air-fuel ratio of the exhaust gases with respect to the target air-fuel ratio to tend to be biased to the rich side or the lean side, despite the main feedback control being conducted. If such a tendency continues, the will be exhausted of occluded oxygen before too long, and hydrocarbon (HC) and carbon monoxide (CO) will become unable to be purified (if the actual air-fuel ratio tends to be biased to the rich side). Conversely, the oxygen-occluding state of the catalyst will saturate and nitrogen oxides (NOx) will become unable to be purified (if the actual air-fuel ratio tends to be biased to the lean side). 
   The output signal from the O 2  sensor represents the oxygen-occluding state of the catalyst, and if the catalyst is exhausted of the occluded oxygen, the output signal from the O 2  sensor will be a rich-state output, whereas, if the oxygen-occluding state of the catalyst saturates, the output signal from the O 2  sensor will be a lean-state output. When the output signal from the O 2  sensor reverses to indicate a rich state, therefore, it can be judged that the actual air-fuel ratio of the exhaust gases flowing into the catalyst is biased to the rich side. Conversely, when the output signal from the O 2  sensor reverses to indicate a lean state, it can be judged that the actual air-fuel ratio is biased to the lean side. 
   For sub-feedback control, a sub-feedback correction value is calculated in accordance with the output signal from the O 2  sensor and then the sub-feedback correction value is fed back for the main feedback control, whereby the deviation between the air-fuel ratio signal from the A/F sensor and the target air-fuel ratio is corrected. Thus, the deviation between the air-fuel ratio signal from the A/F sensor and the target air-fuel ratio can be brought close to the deviation between an actual air-fuel ratio signal and a target air-fuel ratio, and thus, control accuracy of the air-fuel ratio by the main feedback control can be enhanced. 
   The conventional controllers known to control the air-fuel ratio by conducting sub-feedback control together with the main feedback control include, for example, the controller disclosed in Japanese Patent Laid-open No. 8-291738. During the sub-feedback control in this device, an air-fuel ratio correction value is calculated by conducting proportional and integral control (PI control) based on the output signal sent from the O 2  sensor and performing computations for a proportional term (P-term) and an integral term (I-term). Also, a weighted-averaging process is performed on this air-fuel ratio correction value and the result is calculated as an air-fuel ratio learning rate. After this, a target air-fuel ratio is corrected by adding thereto both the air-fuel ratio correction value and the air-fuel ratio learning rate to complement the main feedback control. 
   For the conventional controller disclosed in Japanese Patent Laid-open No. 8-291738, the air-fuel ratio learning rate is derived as a learning value from the air-fuel ratio correction value, and this air-fuel ratio correction value contains the P-term and I-term obtained by conducting PI control of the output signal sent from the 02 sensor. The I-term is a steady component indicating the steady-state deviation of the O 2  sensor output signal, whereas the P-term is a variable component that varies according to a particular change in the output signal of the O 2  sensor. For this reason, acquisition of the P-term to learning also causes a variable component to be included in the learning value. 
   Accordingly, the conventional controller has had the inconvenience in which the learning value during sub-feedback control significantly fluctuates or in which obtaining a stable learning value becomes a time-consuming operation. A significant fluctuation in the learning value or a decrease in the learning rate means that biasing of the air-fuel ratio of the exhaust gases toward the lean or rich side is allowed, thus making it impossible to maintain stable emission characteristics. 
   SUMMARY OF THE INVENTION 
   The present invention has been made in order to solve the above problems, and an object of the invention is to provide an air-fuel ratio controller for an internal-combustion engine that is constructed so that stable emission characteristics can be maintained by allowing stable acquisition of a learning value during sub-feedback control. 
   In accordance with one aspect of the present invention, the air-fuel ratio controller for an internal-combustion engine comprises an upstream-side exhaust gas sensor, a downstream-side exhaust gas sensor, main feedback means and sub-feedback means. 
   The upstream-side exhaust gas sensor is disposed upstream of a catalyst in an exhaust passageway of the internal-combustion engine. The downstream-side exhaust gas sensor is disposed downstream of the catalyst. The main feedback means feeds back an output signal received from the upstream-side exhaust gas sensor into a fuel injection rate so that an air-fuel ratio of the exhaust gases flowing out from the catalyst may match a target air-fuel ratio. The sub-feedback means feeds back the output signal received from the downstream-side exhaust gas sensor into the fuel injection rate so as to complement the feedback control conducted by the main feedback means. 
   The said sub-feedback means includes integral-data calculation means, smoothing means and learning means. 
   The integral-data calculation means calculates an integral value of a deviation between a value of the output signal of the downstream-side exhaust gas sensor and a reference value. the smoothing means smoothes the integral-data signal received from said integral-data calculation means. The learning means learns from the integral-data signal smoothed, a learning value which compensates for a permanent error included in the output signal of the upstream-side exhaust gas sensor. 
   Other objects and further features of the present invention will be apparent from the following detailed description when read in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram showing the configuration of an air-fuel ratio controller according to a first embodiment of the present invention. 
       FIG. 2  is a block diagram showing the configuration of a comparison object device. 
       FIG. 3  is a flowchart illustrating a sub-feedback control routine that is executed in the first embodiment of the present invention. 
       FIG. 4A  shows a graph of time-varying changes in the output signal of the O 2  sensor. 
       FIG. 4B  shows a graph of time-varying changes in the integral value obtained when I-control is conducted based on such output signal states as shown in FIG.  4 A. 
       FIG. 5  is a flowchart illustrating a learning routine that is executed in a second embodiment of the present invention. 
       FIG. 6  is a flowchart illustrating a learning routine that is executed in a third embodiment of the present invention. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENT 
   First Embodiment 
   A first embodiment of the present invention is described below referring to  FIGS. 1  to  4 . 
     FIG. 1  is a block diagram showing the configuration of an air-fuel ratio controller according to the first embodiment of the present invention.  FIG. 2  is a block diagram showing the configuration of an air-fuel ratio controller which was devised during drafting of the present invention (hereinafter, this air-fuel ratio controller is referred to as the comparison object device). Hereunder, these two air-fuel ratio controllers are contrasted to make features of the air-fuel ratio controller of the present embodiment clear and obvious. Although the air-fuel ratio controller of the present embodiment can conduct main feedback control and sub-feedback control, only sections related to the sub-feedback control are extracted and shown below. A method of conducting the main feedback control is not detailed below since the method does not form a major part of the present invention. The same reference numeral is assigned to those elements in both figures that are common thereto. 
   First, the configuration of the comparison object device is described. The conventional controller described in Japanese Patent Laid-open No. 8-291738 uses PI control to calculate an air-fuel ratio correction value and then correct a target air-fuel ratio. The comparison object device, however, uses PID control to calculate an air-fuel ratio correction value and then correct an A/F sensor air-fuel ratio signal according to the air-fuel ratio correction value. 
   As shown in  FIG. 2 , the comparison object device has an A/F sensor  6  disposed between an internal-combustion engine  2  and a catalyst  4 , and an O 2  sensor  8  disposed downstream of the catalyst  4 . An air-fuel ratio signal  100  that linearly responds to an air-fuel ratio of the exhaust gases flowing into the catalyst  4  is output from the A/F sensor  6 . A signal  102  that indicates a lean or rich state of the air-fuel mixture included in the exhaust gases flowing out from the catalyst  4  is output from the O 2  sensor. The output signal  102  from the O 2  sensor  8  is compared with a sub-feedback (SFB) target value (reference value)  104  by a comparator  12 . The SFB target value  104  is an output value equivalent to a theoretical air-fuel ratio. When the air-fuel mixture included in the exhaust gases flowing out from the catalyst  4  is rich, the output signal  102  from the O 2  sensor  8  indicates a value greater than the SFB target value  104 . Conversely, when the above air-fuel mixture is lean, the output signal  102  indicates a value smaller than the SFB target value  104 . The comparator  12  outputs an output deviation  106  which is an error between the SFB target value  104  and the output signal  102  from the O 2  sensor  8 . 
   The output deviation  106  that has been output from the comparator  12  is input to a sub-PB controller  20 . The sub-FB controller  20  conducts PID control in accordance with the output deviation  106  that has been input, and calculates a sub-FB correction value (air-fuel ratio correction value)  110 . The operational expression shown with a frame in the sub-FB controller  20  of  FIG. 2  indicates a transfer function for PID control. In the figure, “Gp sfb ” denotes a proportional gain of a proportional term (P-term), “Gi sfb ” denotes an integral gain of an integral term (I-term), and “Gd sfb ” denotes a derivative gain of a derivative term (D-term). The sub-FB correction value  110  that has been calculated during PID control is added to the air-fuel ratio signal  100  of the A/F sensor  6 , in an adder  14 . When the output signal  102  from the O 2  sensor  8  reverses to indicate a rich state, i.e., when the air-fuel ratio of the exhaust gases flowing into the catalyst  4  is biased to the rich side, the calculated sub-FB correction value  110  is updated to a negative value so that a level of an after-correction air-fuel ratio signal  116  is reduced for a rich state. Conversely, when the output signal  102  from the O 2  sensor  8  reverses to indicate a lean state, i.e., when the air-fuel ratio of the exhaust gases flowing into the catalyst  4  is biased to the lean side, the calculated sub-FB correction value  110  is updated to a positive value so that the level of the after-correction air-fuel ratio signal  116  is increased for a lean state. 
   Sub-feedback learning is also conducted for the comparison object device. Sub-feedback learning is the control where a displacement of a stoichiometric point (theoretical air-fuel ratio equivalent output) of the air-fuel ratio signal  100  from the A/F sensor  6  is obtained as a learning value  114 . Here, a sub-FB learning unit  22  is equipped as sub-feedback learning means, and the sub-FB correction value  110  from the sub-FB controller  20  is input. In the sub-FB learning unit  22 , an average value of the sub-FB correction value  110  is transferred to the learning value  114  in suitable timing. 
   More specifically, the sub-FB learning unit  22  includes a low-pass filter  24  and an SRAM (Static Random Access Memory)  26 . The operational expression shown with a frame in the low-pass filter  24  of  FIG. 2  represents a transfer function that indicates a configuration of the low-pass filter. In the figure, a primary delay element is used as the low-pass filter. After being input to the sub-FB learning unit  22 , the sub-FB correction value  110  has its high-frequency components cut off by passing through the low-pass filter  24 . 
   The sub-FB correction value  110  that has passed through the low-pass filter  24  is acquired into the SRAM  26  in required timing (for example, at a required fuel injection count). The operational expression shown with a frame in the SRAM  26  of  FIG. 2  indicates the integral action intended to acquire a sub-FB correction value  112  into the SRAM  26 . The learning value  114  is stored in the SRAM  26 , and the air-fuel ratio correction value  112  newly acquired is integrated into the learning value  114  by the integral action. This means that each time a new sub-FB correction value  112  is acquired, the learning value  114  is updated to the value obtained by adding the particular sub-FB correction value  112 . Since the sub-FB correction value  112  is integrated in this manner, the correction value for the permanent error included in the air-fuel ratio signal  100  is transferred from the sub-FB correction value  112  to the learning value  114 . When the sub-FB correction value  112  is transferred from the low-pass filter  24  to the SRAM  26 , a state quantity of the low-pass filter  24  is cleared and the I-term of the sub-FB controller  20  is corrected according to the particular state quantity of the low-pass filter  24 . 
   The learning value  114 , after being stored into the SRAM  26 , is input to the adder  14 , together with the air-fuel ratio correction value  110  that was calculated by the sub-FB controller  20 , and then the learning value  114  is added to the air-fuel ratio signal  100  sent from the A/F sensor  6 . Thus, the air-fuel ratio signal  100  from the A/F sensor  6  is corrected in a direction of offsetting a bias of an actual air-fuel ratio to the lean side or the rich side. The after-correction air-fuel ratio signal  116  that has thus been obtained is converted from a voltage value into the air-fuel ratio, in a conversion map  10 , and the main feedback control is executed in accordance with an air-fuel ratio  118  which has been obtained by the conversion from the after-correction air-fuel ratio signal  116 . 
   According to the comparison object device of the configuration described above, calculation of the sub-FB correction value (air-fuel ratio correction value)  110  by means of PID control allows the sub-FB correction value  110  to be converged more rapidly than in the conventional controller adapted to calculate the air-fuel ratio correction value by means of PI control. Also, since the sub-FB correction value  110  is converged rapidly, the learning value  114  derived from the sub-FB correction value  110  is considered to become more stable. 
   However., the sub-FB correction value  110  includes the P-term and D-term, which are variable components. For this reason, the learning value  114  where the P-term and the D-term are acquired during learning also includes variable components. The learning value  114  is therefore affected by a change in the output signal of the O 2  sensor  8 . In addition, when the sub-FB correction value  112  is acquired into the SRAM  26 , although the I-term of the sub-FB controller  20  is corrected according to the acquired sub-FB correction value  112  in order to establish matching, the correction also causes the I-term to be affected by a change in the output signal of the O 2  sensor  8 , since the sub-FB correction value  112  includes a P-term and a D-term. 
   Therefore, the configuration described below has been adopted for the air-fuel ratio controller of the present embodiment in order to break through such inconvenient aspects of the comparison object device as mentioned above. 
   As shown in  FIG. 1 , the air-fuel ratio controller of the present embodiment is constructed as a double-sensor system which has an A/F sensor  6  serving as an upstream-side exhaust gas sensor disposed upstream of a catalyst  4 , and an O 2  sensor  8  serving as a downstream-side exhaust gas sensor disposed downstream of the catalyst  4 . During the main feedback control whose description is omitted, an air-fuel ratio signal  100  from the A/F sensor  6  is used to calculate a feedback correction value for correcting a fuel injection rate. During the sub-feedback control described below, an output signal  102  from the O 2  sensor  8  is used to calculate a sub-FB correction value (air-fuel ratio correction value) and a learning value. 
   The output signal  102  from the O 2  sensor  8  is first input to a comparator  12 . In the comparator  12 , the output signal  102  from the O 2  sensor  8  is compared with a sub-feedback (SFB) target value (reference value)  104  that is an output value equivalent to a theoretical air-fuel ratio, and an output deviation  106  between the SFB target value  104  and the output signal  102  from the O 2  sensor  8  is output. The output deviation  106  takes a negative value when an air-fuel ratio of the exhaust gases flowing out from the catalyst  4  indicates a rich state, and takes a positive value when the air-fuel ratio of the exhaust gases flowing out from the catalyst  4  indicates a lean state. 
   The air-fuel ratio controller of the present embodiment has a sub-FB controller  30  and a sub-FB learning unit  32 . The output deviation  106  that has been output from the comparator  12  is concurrently input to the sub-FB controller  30  and the sub-FB learning unit  32 . The sub-FB controller  30  is means for calculating a sub-FB correction value  120  responsive to a change in the output signal  102  of the O 2  sensor  8 . Although PID control is conducted in the sub-FB controller  20  of the comparison object device, PD control is conducted in the sub-FB controller  30  of the present embodiment. The operational expression shown with a frame in the sub-FB controller  30  of  FIG. 1  indicates a transfer function for PD control. In the figure, “Gp sfb ” denotes a proportional gain of a proportional term (P-term) and “Gd sfb ” denotes a derivative gain of a derivative term (D-term). The sub-FB correction value  120  that has been calculated by the sub-FB controller  30  during PD control is added to the air-fuel ratio signal  100  of the A/F sensor  6 , in an adder  14 . When the output signal  102  from the O 2  sensor  8  reverses to indicate a rich state, the sub-FB correction value  120  is updated to a negative value so that a level of an after-correction air-fuel ratio signal  128  may be reduced for a rich state. Conversely, when the output signal  102  from the O 2  sensor  8  reverses to indicate a lean state, the sub-FB correction value  120  is updated to a positive value so that the level of the after-correction air-fuel ratio signal  128  may be increased for a lean state. 
   The sub-FB learning unit  32  is means for learning, as a learning value  126 , the permanent error included in the air-fuel ratio signal  100  of the A/F sensor  6 , i.e., a displacement of a stoichiometric point of the air-fuel ratio signal  100 . In the comparison object device, the learning value  114  is derived from the sub-FB correction value  110  that contains a P-term, an I-term, and a D-term, whereas, in the air-fuel ratio controller of the present embodiment, the learning value  126  is obtained only from the integral term (I-term) obtained by integral control (I-control) of the output deviation  106 . The sub-FB learning unit  32  according to the present embodiment includes an integrator  34 , a low-pass filter  36 , and an SRAM  38 . The I-control based on the output deviation  106  is conducted by the integrator  34  serving as an integral-data calculator in the present invention, and the deviation signal  106  from the comparator  12  is integrated by the integrator  34 . The operational expression shown with a frame in the integrator  34  of  FIG. 1  indicates a transfer function for I-control. In the figure, “Gi fab ” denotes an integral gain of an I-term. The integral-term signal (integral-data signal)  122  obtained by the integrator  34  during I-control indicates a steady-state deviation of the output signal  102  of the O 2  sensor  8  with respect to the SFB target value  104 . 
   The integral-term signal  122  that has been obtained during I-control is concurrently input from the integrator  34  to the adder  14  and the low-pass filter  36 . After being input to the low-pass filter  36 , the integral-term signal  122  has its high-frequency components cut off and smoothed by the low-pass filter  36  functioning as smoothing means in the present invention. The operational expression shown with a frame in the low-pass filter  36  of  FIG. 1  represents a transfer function that indicates a configuration of the low-pass filter. In the figure, a primary delay element is used as the low-pass filter, and “τ sfbg ” denotes a response time constant of the low-pass filter. The transfer function shown in the figure is only an example of a low-pass filter, and a low-pass filter represented by other transfer functions may be used. Alternatively, a smoothing method other than low-pass filtering, such as weighted averaging, may be used, only if the method actually used allows signal smoothing by cutting off high-frequency components. 
   An integral-term signal (integral-data signal)  124  that is obtained as a result of smoothing through the low-pass filter  36  is acquired into the SRAM  38  in required timing (for example, at a required fuel injection count). The operational expression shown with a frame in the SRAM  38  of  FIG. 1  represents the integral action for acquiring the integral-term signal  124  into the SRAM  38 . The learning value  126  is stored in the SRAM  38 , and each time a new integral-term signal  124  is acquired, the learning value  126  is derived and updated to the value obtained by integrating the integral-term signal  124 . Thus, the correction value for the permanent error included in the air-fuel ratio signal  100  is transferred from the integral-term signal  124  to the learning value  126 . When the integral-term signal  124  is transferred from the low-pass filter  36  to the SRAM  38 , a state quantity of the low-pass filter  36  is cleared and a state quantity (I-term) of the integrator  34  is corrected according to the cleared state quantity of the low-pass filter  36 . 
   The learning value  126 , after being stored into the SRAM  38 , is input to the adder  14 , together with the above-mentioned sub-FB correction value  120  and the integral-term signal  124 , and then added to the air-fuel ratio signal  100  sent from the A/F sensor  6 . Thus, the air-fuel ratio signal  100  from the A/F sensor  6  is corrected in a direction of offsetting a bias of an actual air-fuel ratio to the lean side or the rich side. The after-correction air-fuel ratio signal  128  that has thus been obtained is converted from a voltage value into the air-fuel ratio, in a conversion map  10 , and the main feedback control is executed in accordance with an air-fuel ratio  130  obtained by the conversion. 
   In the above-described configuration of the air-fuel ratio controller, the comparator  12 , the adder  14 , the sub-FB controller  30 , the sub-learning unit  32 , and the conversion map  10  are realized as functional components of the electronic control unit (ECU) that totally controls the internal-combustion engine. The ECU functions as the main feedback control means and sub-feedback control means according to the present invention, and the ECU, when functioning as the sub-feedback control means, receives the output signals supplied from the A/F sensor  6  and the O 2  sensor  8  and implements sub-feedback control in accordance with the routine shown in FIG.  3 . 
     FIG. 3  is a flowchart for explaining the flow of the sub-feedback control implemented by the ECU in the present embodiment. The routine shown in  FIG. 3  is executed in required timing with each fuel injection operation, and a judgment is made as to whether conditions for executing the sub-feedback control are established in a first step (step  100 ). The execution conditions here mean that the O 2  sensor  8  must be active and that a cooling water temperature must have risen to a required temperature. If the judgment indicates that the conditions for executing the sub-feedback control are established, the output signal from the O 2  sensor  8  is acquired in step  102 . 
   In step  104 , the sub-FB correction value is calculated from the output signal of the O 2  sensor  8 , according to expressions (1) and (2) shown below. Expression (1) is associated with the process conducted by the comparator  12  in the controller of  FIG. 1 , and expression (2) is associated with the process conducted by the sub-FB controller  30 .
 
 doxs ( k )= oxsref ( k )− gaoxs ( k )  (1) 
 
 sfb ( k )= Gp   sfb   *doxs ( k )+Gd sfb   *{doxs ( k )− doxs ( k− 1)}  (2) 
 
   In above expression (1), “gaoxs” denotes a value of the output signal from the O 2  sensor  8  and “oxsref” denotes an SFB target value. Therefore, “doxs” denotes an output deviation of the output signal from the O 2  sensor  8 . In above expression (2), “sfb” denotes a sub-FB correction value, “Gp sfb ” denotes a proportional gain of the PD control conducted by the sub-FB controller  30 , and “Gd sfb ” denotes a derivative gain of the PD control. The symbol “k” in each term means that the term is the current value (the value calculated in the current cycle), and “k−1” means the previous value (the value calculated in the previous cycle). 
   In step  106 , the integral value for learning is calculated, according to expressions (3) and (4) shown below. Expressions (3) and (4) are associated with the respective processes conducted by the integrator  34  of the sub-FB learning unit  32  in the controller of FIG.  1 .
 
 sumdoxs=doxs ( k )+ sfbi ( k− 1)  (3) 
 
 sfbi ( k ) =Gi   sfb   *sumdoxs ( k− 1)  (4) 
 
   In above expressions (3) and (4), “sumdoxs” denotes an integral value of the output deviation “doxs”, and “sfbi” denotes the integral value obtained by multiplying “sumdoxs” by the gain “Gi sfb ”. In this case, “sfbi” is output from the integrator  34  as an integral-term signal, and “Gisfb” is an integral gain of the I-control conducted by the integrator  34  of the sub-FB learning unit  32 . 
   In step  108 , a low-pass filtering process for the integral-term signal is performed according to expression (5) shown below. Expression (5) is associated with the process conducted by the low-pass filter  36  of the sub-FB learning unit  32  in the controller of FIG.  1 .
 
 sfbism ( k )={ sfbi ( k− 1)−(1−τ sfbg )* sfbism ( k− 1)}/τ sfbg   (5) 
 
   In above expression (5), “sfbism” denotes the integral-term signal obtained after the low-pass filtering process, and “τ sfbg ” denotes the sampling rate (response time constant) used in the low-pass filtering process. 
   In step  110 , it is judged whether the condition for acquiring into the learning value the integral-term signal that underwent the low-pass filtering process in step  108 , i.e., an execution condition relating to learning, is established. This condition means that the total injection count from the previous learning operation must have reached a required count value. If the judgment indicates that the execution condition relating to learning is established, the integral-term signal that has underwent the low-pass filtering process in step  108  is written into the SRAM  38  and the learning value is derived and updated (step  112 ). 
   On execution of integral-term signal writing into the SRAM  38 , state quantities of both the integrator  34  and the low-pass filter  36  are corrected (cleared). First, the state quantity of the low-pass filter  36  is corrected in accordance with the following expressions (6) and (7):
 
 sfbi ( k− 1)=0  (6) 
 
 sfbism ( k− 1)=0  (7) 
 
   That is to say, values of all elements concerned with the low-pass filtering process in expression (5) are each reset to zero. 
   The state quantity of the integrator  34  is corrected in accordance with the following expression (8):
 
 sumdoxs=sumdoxs−sfbism ( k )/ Gi   sfb   (8) 
 
   That is to say, the integral value in expression (3) is corrected to match the magnitude of the integral-term signal which was acquired into the SRAM  38 . The “sumdoxs” term on the right side of expression (8) denotes the integral value before it is corrected, and “sumdoxs” on the left side denotes the integral value after it has been corrected. 
   When the above control is executed, the air-fuel ratio signal  100  from the A/F sensor  6  is corrected according to the particular sub-FB correction value and learning value, in a direction of offsetting a bias of an actual air-fuel ratio to the lean side or the rich side. Thus, operation in the neighborhood of a target air-fuel ratio becomes possible. In the controller of the present embodiment, in particular, as described above, I-control is conducted on the basis of the output deviation between the output signal from the O 2  sensor  8  and the SFB target value, and the learning value is derived only from the integral term obtained by the I-control. For these reasons, unlike the conventional controller, the controller of the present embodiment does not suffer the instability of learning due to the effects of variable components. 
     FIG. 4A  shows a graph of time-varying changes in the output signal of the O 2  sensor  8 , and  FIG. 4B  shows a graph of time-varying changes in the integral value obtained when I-control is conducted based on such output signal states as shown in FIG.  4 A. As shown in  FIG. 4A , during the operation of the internal-combustion engine  2 , the output signal from the O 2  sensor  8  is constantly changing between a lean-state output and a rich-state output. Accordingly, as shown in  FIG. 4B , the integral term obtained by I-control causes secondary vibration coupled with the changes in the output signal of the O 2  sensor  8 . Although an amplitude of the secondary vibration caused by the integral term is small in comparison with that of the vibration caused by derivative or proportional terms, the appropriate error in the learning value according to the particular amplitude of the secondary vibration occurs, depending on the timing of learning (the timing of writing into the SRAM  38 ). 
   A general method of reducing the vibration components included in the integral term is by reducing the control gain of I-control. However, reduction in the control gain correspondingly delays response, hence reducing the learning rate. Regarding this, the air-fuel ratio controller of the present embodiment uses the low-pass filter  36  to cut off the high-frequency components included in the integral term. Use of the low-pass filter  36  allows a learning value to be derived from a smooth integral-term signal free from high-frequency components, without reducing the learning rate. In short, according to the air-fuel ratio controller of the present embodiment, a learning value is derived from the integral term (integral value) indicating the steady-state deviation of the output signal of the O 2  sensor  8  and this integral term is smoothed; therefore, these characteristics not only keep the learning value free from any effects of such variable components as a proportional term and a derivative term, but also suppress secondary vibration due to the effects of the changes in the output signal of the O 2  sensor  8 . A stable learning value can be obtained as a result. 
   While, in the present embodiment, the sub-FB controller  30  conducts PD control, this controller may be adapted to conduct P-control. Additionally, while, in the present embodiment, the air-fuel ratio signal  100  from the A/F sensor  6  is corrected using a sub-FB correction value and a learning value, the target air-fuel ratio obtained by the main feedback control may be corrected using a sub-FB correction value and a learning value. Furthermore, although, in the present embodiment, the integral-term signal  124  is input to not only the low-pass filter  36  but also the adder  14  concurrently, this signal may be input only to the low-pass filter  36 . Besides, although an A/F sensor is used as the upstream-side exhaust gas sensor in the present embodiment, an O 2  sensor may be used similarly to the downstream-side exhaust gas sensor. 
   Second Embodiment 
   A second embodiment of the present invention is described below referring to FIG.  5 . 
   Multiple parameters are used to calculate a learning value in sub-feedback control of an air-fuel ratio controller. In the air-fuel ratio controller of the present invention, as described for the first embodiment, multiple parameters, “sfbi”, “sumdoxs”, and “sfbism”, are also used to calculate a learning value. In conventional devices, values of these parameters concerned with the calculation of a learning value are constantly updated as long as sub-feedback control is being executed under established sub-feedback control execution conditions. If the sub-feedback control execution conditions are not established, however, the above values are cleared and are newly calculated from the beginning when the sub-feedback control execution conditions are established next time. However, the fact that the parameters are cleared each time the sub-feedback control execution conditions fail to be established means that when sub-feedback control is restarted, it takes a great deal of time to converge the learning value and thus the learning rate decreases. 
   The air-fuel ratio controller according to the present embodiment, therefore, prevents a decrease in the learning rate during the restart of sub-feedback control, by making the ECU in the first embodiment further execute the routine shown in FIG.  5 . This routine is executed in required timing with each fuel injection operation, and whether the execution conditions relating to sub-feedback control are established is judged in a first step (step  200 ). 
   If it is judged in step  200  that the sub-feedback control execution conditions are not established, the values of the parameters concerned with the calculation of the learning value are held. In other words, in step  202 , the values of the parameters are not cleared and they are maintained at the respective values existing before the sub-feedback control execution conditions were judged not to be established, i.e., the values existing in the previous cycle. 
   When the sub-feedback control execution conditions are established, sub-feedback control is restarted and acquisition of the learning value is also restarted. When learning is restarted, the parameter values that were held in step  202  are used as initial values in step  204 . This method, compared with calculating each parameter value from the beginning, makes it possible to shorten the time required for convergence of the learning value, and to maintain the learning rate even after sub-feedback control has been restarted. 
   In the above-described embodiment, the “execution conditions judging means” of the present invention is realized by execution of the process in step  200  by the ECU. Also, the “parameter data hold means” of the present invention is realized by execution of the process in step  202  by the ECU. 
   Third Embodiment 
   A third embodiment of the present invention is described below referring to FIG.  6 . 
   In internal-combustion engines, the fuel cutoff for temporarily stopping fuel injection is conducted if the vehicle speed exceeds a maximum speed limit, if the engine speed reaches a speed limit, or under other required operating conditions. When the fuel cutoff is executed, since unburnt fresh air directly flows into a catalyst  4 , an oxygen-occluding state of the catalyst  4  saturates in due course of time and an O 2  sensor continues to generate a lean-state output signal for a while after the fuel cutoff. If learning of the learning value in sub-feedback control is conducted under these conditions, the learning value is mis-learnt so that an air-fuel ratio signal  100  from an A/F sensor  6  is corrected to indicate a lean state. 
   The air-fuel ratio controller according to the present embodiment, therefore, prevents mis-learning of the learning value during fuel cutoff, by making the ECU in the first embodiment further execute the routine shown in FIG.  6 . This routine is executed in required timing with each fuel injection operation, and whether the fuel cutoff has been executed is judged in a first step (step  300 ). 
   After the fuel cutoff has been executed, it is next judged in step  302  whether an appropriate oxygen-occluding state of the catalyst  4  has been obtained. As one method of judging the oxygen-occluding state of the catalyst  4 , it is possible to judge that when the output signal from the O 2  sensor  8  reverses to indicate a rich state, an appropriate oxygen-occluding state of the catalyst  4  has been obtained. Alternatively, it may be possible to judge that when the rate of an estimated amount of oxygen desorption after fuel cutoff, with respect to a maximum amount of oxygen occlusion by the catalyst  4 , reaches a required value, an appropriate oxygen-occluding state of the catalyst  4  has been obtained. 
   In the air-fuel ratio controller of the present embodiment, after fuel cutoff, parameter values concerned with the calculation of the learning value are held until the appropriate oxygen-occluding state of the catalyst  4  has been obtained, i.e., until the condition required for the judgment in step  302  has been satisfied. In other words, the parameter values existing before fuel cutoff was executed are maintained intact without being updated, in step  304 . 
   The update process for the learning value is restarted when the condition required for the judgment in step  302  is satisfied. In step  306 , the parameter values that were held in step  304  are used as initial parameter values during the restart of the update process for the learning value. Use of this method makes it possible to learn using parameters not affected by fuel cutoff, and hence to prevent the learning value from being mis-learnt by a bias of the air-fuel ratio to the lean side. 
   In the above-described embodiment, the “fuel cutoff judging means” of the present invention is realized by execution of the process in step  300  by the ECU. Also, the “oxygen-occluding state judging means” of the present invention is realized by execution of the process in step  302  by the ECU. Furthermore, the “parameter data hold means” of the present invention is realized by execution of the process in step  304  by the ECU. 
   The major benefits of the present invention described above are summarized follows: 
   According to a first aspect of the present invention, since a learning value is derived from the integral value indicating a steady-state deviation of the output signal sent from the downstream exhaust gas sensor, the learning value is not affected by variable components such as a proportional value or derivative value. Additionally, since the integral value is smoothed, secondary vibration due to any effect of a change in the output signal of the downstream exhaust gas sensor is also suppressed and a stable learning value can be obtained. 
   According to a second aspect of the present invention, even if a feedback condition is not established, since parameter values related to calculation of the learning value will not be cleared and the parameter values existing before the feedback condition is not established will be maintained, the learning rate can be maintained, even after the restart of feedback. 
   According to a third aspect of the present invention, although a fuel cut saturates the oxygen-occluding state of the catalyst and, if learning is conducted in that saturated state, the learning value will be mis-learned for a bias toward the rich side, mis-learning of the learning value can be prevented since, until the oxygen-occluding state has stayed within an appropriate range, parameter values related to calculation of the learning value will be maintained at the values existing before the feedback conditions are not established.