JP2011174426A - Air-fuel ratio control device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To further reduce the amount of HC, CO and NOx exhaust by keeping the exhaust gas purifying efficiency of a catalyst high while improving the estimating accuracy of the amount of oxygen release from the catalyst. <P>SOLUTION: This air-fuel ratio control device 1 includes: a first air-fuel ratio sensor 11 provided upstream of the catalyst mounted in an exhaust passage of an internal combustion engine; a second air-fuel ratio sensor 12 provided downstream of the catalyst; an air-fuel ratio control part 13 for estimating the amount of oxygen release from the catalyst with reference to the output of at least the first air-fuel ratio sensor 11 and feedback-controlling the amount of oxygen release to be a target value; and a learning part 14 for learning a learning parameter to be used for reducing an error of the estimated amount of oxygen release, during the occurrence of fuel cut in the internal combustion engine. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to air-fuel ratio control performed for the purpose of increasing exhaust gas purification efficiency by a catalyst.

Generally, the exhaust passage such as an automobile, HC contained in the exhaust gas discharged, the three-way catalyst to harmless by oxidation / reduction of CO and NO _x are mounted from the internal combustion engine. In order to efficiently purify all of HC, CO, and NO _x , it is necessary to make the air-fuel ratio converge to a certain range near the theoretical air-fuel ratio called a window.

  For this purpose, it is customary to arrange an air-fuel ratio sensor upstream and downstream of the catalyst and perform feedback control to control the output of the air-fuel ratio sensor to a target value (see, for example, Patent Documents 1 to 4 below) ). In the conventional air-fuel ratio control method, it is determined whether the output of the air-fuel ratio sensor downstream of the catalyst is rich or lean, and the correction amount is calculated according to the determination result. This correction amount serves to maintain the air-fuel ratio of the gas in the catalyst within the window by displacing the control center in the air-fuel ratio feedback control with reference to the output of the air-fuel ratio sensor upstream of the catalyst to the lean side or the rich side. .

Recently, the oxygen storage capacity (OSC) of catalysts tends to increase in response to stricter exhaust gas regulations. If the oxygen storage capacity is large, even if the air-fuel ratio fluctuates upstream of the catalyst, the output signal of the air-fuel ratio sensor downstream of the catalyst does not change immediately. Therefore, when the output of the air-fuel ratio sensor downstream of the catalyst showed a transition from lean to rich, the oxygen in the catalyst was already insufficient, and the HC and CO emissions could increase. . On the contrary, when the output of the air-fuel ratio sensor downstream of the catalyst shows a transition from rich to lean, the inside of the catalyst is already excessive in oxygen, which in turn causes an increase in NO _x emission.

  Therefore, the inventor of the present invention constructed a model of the oxygen ratio, which is the ratio of the amount of oxygen stored in the catalyst and the oxygen storage capacity of the catalyst, and determined the amount of oxygen released from the catalyst according to the model formula. An air-fuel ratio control device was devised that feedback-controls the oxygen release amount to a target value (see Patent Document 5 below). According to this air-fuel ratio control apparatus, it is possible to effectively avoid the conventional problem that the fluctuation of the output signal of the air-fuel ratio sensor downstream of the catalyst is delayed with respect to the fluctuation of the air-fuel ratio in the catalyst.

  The above-mentioned air-fuel ratio control apparatus is excellent and useful. However, an error may be mixed in the estimated value of the oxygen release amount due to modeling errors caused by individual differences of the air-fuel ratio sensors, output variations due to secular changes, deterioration of the catalyst itself, and the like. This error in the estimated value leads to a reduction in exhaust gas purification efficiency by the catalyst and a deterioration in emissions.

Japanese Patent No. 2790896 Japanese Patent No. 2912478 JP 2007-187119 A JP 2008-248862 A Japanese Patent Application No. 2009-205204 Specification

The present invention aims to improve the estimation accuracy of the amount of oxygen released from the catalyst, thereby maintaining a high exhaust gas purification efficiency by the catalyst, and further reducing the emission of HC, CO and NO _x. And

  In the present invention, a first air-fuel ratio sensor provided upstream of an exhaust gas purifying catalyst mounted in an exhaust passage of an internal combustion engine, a second air-fuel ratio sensor provided downstream of the catalyst, and at least the first Referring to the output of one air-fuel ratio sensor, oxygen was occluded in the catalyst up to the oxygen occlusion capacity according to a model formula of the oxygen ratio, which is the ratio of the oxygen amount occluded in the catalyst and the oxygen occlusion capacity of the catalyst An air-fuel ratio control unit that estimates the amount of released oxygen from the state and feedback-controls the released amount to a target value, and a learning parameter for reducing an error in the released amount estimated according to the model formula A learning unit for storing, the learning unit calculates the learning parameter when a fuel cut occurs in the internal combustion engine, and the output of the second air-fuel ratio sensor becomes lean from the start of the fuel cut. The time difference is reduced according to the time difference between the elapsed time until reaching a predetermined value indicating that the fuel has been cut and the elapsed time from the start of fuel cut until the release amount estimated in accordance with the model formula becomes zero. The learning parameter is increased or decreased in the direction in which the air-fuel ratio is controlled, and the air-fuel ratio control unit performs feedback control after taking into account the learning parameter stored in the learning unit.

  The model formula is expressed, for example, in the form of the following formula (Equation 1).

According to the present invention, it is possible to improve the estimation accuracy of the amount of oxygen released from the catalyst, to keep the exhaust gas purification efficiency by the catalyst high, and to further reduce the exhaust amount of HC, CO and NO _x .

The figure explaining the component of the air fuel ratio control apparatus of embodiment of this invention. The figure which shows the hardware resource structure of the same air fuel ratio control apparatus. The figure which shows the relationship between a front air fuel ratio signal output and a rear air fuel ratio signal output. The figure which shows the relationship between oxygen storage time and oxygen release time. The figure which shows the relationship between inflow air amount and reaction rate ratio. The figure which shows the relationship between inflow air amount and reaction rate ratio. The figure which shows the aspect of control of the oxygen release amount after completion | finish of a fuel cut. Shows an example of the elapsed time T _A, T _D, T _C and T _D from the fuel cut start. The flowchart which shows the example of the procedure of the process which the same air fuel ratio control apparatus performs.

An embodiment of the present invention will be described with reference to the drawings. The present air-fuel ratio control system 1 is for controlling the air-fuel ratio in the catalyst 3 to detoxifying harmful substances HC, CO, NO _x generated by burning fuel in an internal combustion engine 2, as shown in FIG. 1 In addition, a first air-fuel ratio sensor 11 that outputs an output signal corresponding to the air-fuel ratio or oxygen concentration on the upstream side of the catalyst 3 and a first output signal that corresponds to the air-fuel ratio or oxygen concentration on the downstream side of the catalyst 3 are output. Two air-fuel ratio sensors 12, an air-fuel ratio control section 13 that performs air-fuel ratio control with reference to the output signals of both sensors 11, 12, and a learning parameter β (to be described later) referred to by the air-fuel ratio control section 13 And a learning unit 14 for performing learning.

FIG. 2 shows an outline of the hardware configuration. The internal combustion engine 2 is, for example, a multi-cylinder fuel injection engine for automobiles. Combustion gas generated in the internal combustion engine 2 is discharged into the atmosphere from the exhaust port through the exhaust manifold 41, the exhaust pipe 42, and the catalyst 3. The air-fuel ratio sensors 11 and 12 output a voltage signal corresponding to the oxygen concentration in the exhaust gas by reacting in contact with the exhaust gas. The first air-fuel ratio sensor 11 upstream of the catalyst 3 is preferably a linear A / F sensor that outputs a signal proportional to the air-fuel ratio of the exhaust gas. The second air-fuel ratio sensor 12 downstream of the catalyst 3 may be a linear A / F sensor or an O ₂ sensor having non-linear output characteristics with respect to the air-fuel ratio of the exhaust gas.

  The first air-fuel ratio sensor 11 and the second air-fuel ratio sensor 12 together with various sensors (not shown) such as an intake negative pressure sensor, an engine speed sensor, a vehicle speed sensor, a coolant temperature sensor, a cam position sensor, and a throttle sensor. The electronic control unit (ECU) 5 is electrically connected. The electronic control unit 5 is a microcomputer system including a processor 51, a RAM 52, a ROM (or flash memory) 53, an I / O interface 54, and the like. The I / O interface 54 is responsible for receiving output signals of various sensors and transmitting control signals, and includes an A / D conversion circuit and / or a D / A conversion circuit. A program to be executed by the processor 51 is stored in the ROM 53, and is read from the ROM 53 into the RAM 52 and decoded by the processor 51 at the time of execution. Therefore, the electronic control unit 5 exhibits functions as the air-fuel ratio control unit 13 and the learning unit 14 according to the program.

  The electronic control unit 5 as the air-fuel ratio control unit 13 receives signals output from the first air-fuel ratio sensor 11, the second air-fuel ratio sensor 12 and other sensors via the I / O interface 54. Then, the required fuel injection amount is calculated, and a control signal corresponding to the required fuel injection amount is input to the fuel injection valve 21 via the I / O interface 54 to control the fuel injection of the internal combustion engine 2. The required fuel injection amount is obtained by referring to the intake pipe negative pressure and the engine speed, etc., and the basic injection amount is corrected according to environmental conditions such as engine cooling water temperature and the following feedback control. And finally decide.

  In the present embodiment, in controlling the air-fuel ratio, the output signal of the second air-fuel ratio sensor 12 is not used as a control amount (control output). In this embodiment, the state in which oxygen is stored in the catalyst 3 up to the oxygen storage capacity is used as a reference, and the amount of released oxygen from that state is estimated by a model formula. Then, the estimated oxygen release amount is used as a control amount, and feedback control is performed to reach the required target value.

First, the amount of oxygen stored in the catalyst 3 can be considered to be obtained by multiplying the time integral of the flow rate of oxygen flowing into the catalyst 3 by the reaction rate coefficient. The reaction rate coefficient indicates the rate at which the catalyst 3 occludes oxygen. If the ratio between the reaction rate coefficient and the oxygen storage capacity (reaction rate coefficient / oxygen storage capacity) is the model parameter θ ₁ , the model formula for the oxygen concentration O can be defined as the following formula (Equation 2).

The value of the oxygen ratio O in the above formula (Equation 2) takes a range of 0 ≦ O ≦ 1. α is the ratio of oxygen contained in the air, and G _a is the flow rate of air flowing into the catalyst 3. The value of α is, for example, 0.21. α may be incorporated into the model parameter θ ₁ . In that case, θ ₁ = α × (reaction rate coefficient / oxygen storage capacity). Inflow air quantity G _a is the air-fuel ratio of the inflowing gas detected through the first air-fuel ratio sensor 11, it is calculated by multiplying the demand fuel injection amount calculated in the electronic control unit 5. Thus, on the unnecessary to use an expensive air flow sensor for measuring the G _a, also improves the accuracy of the values of G _a. However, it does not prevent the estimation of G _a from the intake pipe negative pressure and the engine speed.

  λ is an excess air ratio indicating a deviation of the air-fuel ratio of the exhaust gas from the target air-fuel ratio. In principle, the excess air ratio λ is a ratio of the air / fuel ratio of the gas detected via the first air / fuel ratio sensor 11 to the target air / fuel ratio to be finally realized (upstream measured air / fuel ratio / target air / air ratio). (Fuel ratio). The target air-fuel ratio is usually the stoichiometric air-fuel ratio, which is about 14.7 for a gasoline engine, but may increase or decrease from the stoichiometric air-fuel ratio during lean burn operation.

The oxygen storage capacity, oxygen storage rate, and oxygen release rate of the catalyst 3 are influenced by the deterioration of the catalyst 3 with time. Therefore, the model parameter θ ₁ is also affected by the deterioration of the catalyst 3 over time. However, the reaction rate ratio, which is the ratio of the oxygen storage rate to the oxygen release rate, can be regarded as constant regardless of the deterioration of the catalyst 3 over time.

  Hereinafter, the reaction rate ratio is additionally described. FIG. 3 shows an experiment in which the air-fuel ratio of the gas flowing into the catalyst 3 is intentionally increased or decreased, and the output signal of the first air-fuel ratio sensor 11 and the output signal of the second air-fuel ratio sensor 12 are observed. . It can be said that the output of the first air-fuel ratio sensor 11 displays the air-fuel ratio of the gas flowing into the catalyst 3 as it is. On the other hand, the output of the second air-fuel ratio sensor 12 is delayed with respect to the output of the first air-fuel ratio sensor 11 and consequently the fluctuation of the air-fuel ratio of the gas flowing into the catalyst 3.

During the period when the air-fuel ratio of the gas flowing into the catalyst 3 is lean, oxygen is occluded in the catalyst 3. In a period in which the air-fuel ratio of the gas flowing into the catalyst 3 is rich, oxygen stored in the catalyst 3 is released. In FIG. 3, a period T _{1 from} when the inflow gas rich in the air-fuel ratio becomes lean to the air-fuel ratio until it becomes rich again again is a period during which oxygen is stored in the catalyst 3. Then, after the inflowing gas that has been lean in the air-fuel ratio becomes rich in the air-fuel ratio, oxygen is released from the catalyst 3 during a period T ₂ until the output signal of the second air-fuel ratio sensor 12 reverses from lean to rich. It is a period. The inversion of the output of the second air-fuel ratio sensor 12 from lean to rich implies that the release of oxygen from the catalyst 3 has declined.

FIG. 4 is a graph in which the above experiment is performed with the inflow air amount G _a constant, and the oxygen storage period T ₁ and the oxygen release period T ₂ are respectively measured and plotted. FIG. 4 shows the results of experiments in which the combinations of the lean value and rich value of the air-fuel ratio of the gas flowing into the catalyst 3 are changed in three ways. Regardless of the value of the air-fuel ratio of the inflowing gas, there is a certain proportional relationship between the oxygen storage period T ₁ and the oxygen release period T ₂ . Here, the proportional coefficient, that is, the slope of the straight line drawn in FIG. 4, is referred to as the reaction rate ratio. The reaction rate ratio indicates the ratio of the oxygen storage rate to the oxygen release rate (T ₁ / T ₂ ).

Figure 5 performs the experiment by changing the inlet air amount G _a, in which the reaction rate ratio were measured. FIG. 6 shows the result of the same experiment performed using the new catalyst 3 and the old deteriorated catalyst 3, respectively. As apparent from FIG. 6, the reaction rate ratio can be regarded as being constant regardless of the deterioration of the catalyst 3 over time.

When the fuel cut for temporarily interrupting the fuel supply to the cylinders of the internal combustion engine 2 is executed, the air containing no fuel component flows into the catalyst 3 and the catalyst 3 is filled with oxygen. Therefore, at the time t ₁ immediately before the fuel cut is finished and the fuel supply is resumed, oxygen is stored in the catalyst 3 to the maximum oxygen storage capacity. Since the oxygen storage capacity decreases as the catalyst 3 deteriorates with time, the absolute amount of oxygen stored in the catalyst 3 at time t ₁ is unknown. However, as shown in FIG. 7, considering the amount of oxygen O released from the catalyst 3 after resumption of fuel supply, the oxygen release amount O at the fuel supply resumption time t ₁ can always be zero.

By substituting the model parameter θ ₁ with the model parameter θ ₂ indicating the oxygen storage rate or the oxygen release rate with the aid of the model formula (Equation 2), the following equation (Equation 3) can be obtained as a model formula for the oxygen release amount O.

  The oxygen release amount O is reset to 0 each time a fuel cut is performed, with the state in which the catalyst 3 is filled with oxygen as a reference (O = 0).

The model parameter θ ₂ is different between a period in which the catalyst 3 releases oxygen (λ ≦ 1) and a period in which the catalyst 3 occludes oxygen (λ> 1). However, it has been found that the reaction rate ratio k is constant regardless of the deterioration of the catalyst 3 over time. If the reaction rate ratio k (G _a ) shown in FIG. 5 is used, the model parameter θ ₂ can be set as in the following equation (Equation 4).

The model parameter θ _{2 in the} above equation (Equation 4) may be stored in the RAM 52 or ROM 53 as map data.

  The electronic control unit 5 appropriately sets a target value for the oxygen release amount O, and performs feedback control for converging the oxygen release amount O estimated according to the model formula to the target value. That is, the feedback correction amount of the fuel injection amount is calculated based on the deviation between the estimated current oxygen release amount O and the target value, and is added to the required fuel injection amount. Thereby, the vibration of the air-fuel ratio is suppressed and maintained in the window.

  In addition, in this embodiment, in order to improve the estimation accuracy of the oxygen release amount O from the catalyst 3, the estimation error is corrected and reduced to the estimation formulas (Equation 3) and (Equation 4) of the oxygen release amount O. Learning parameter β is introduced.

  The electronic control unit 5 as the learning unit 14 calculates a learning parameter β when a predetermined fuel cut condition is satisfied and a fuel cut that temporarily stops fuel supply (fuel injection) to the cylinder of the internal combustion engine 2 occurs. Perform learning. The fuel cut condition is in accordance with the existing automobile internal combustion engine 2. For example, the condition is that the engine speed is equal to or greater than a certain value and the idle switch is turned on (or the accelerator pedal depression amount is equal to or less than a threshold value). The fuel cut ends (resumption of fuel supply) when the engine speed falls below a predetermined return speed or the idle switch is turned off.

  The equation for calculating the oxygen release amount O with the learning parameter β introduced is as follows:

A / F is the air-fuel ratio of the gas detected via the first air-fuel ratio sensor 11, and A / F _targ is the target air-fuel ratio. Thus, in the present embodiment, the learning parameter β is added to the denominator of the excess air ratio λ.

When learning the parameter β, the electronic control unit 5 determines a predetermined value indicating that the output of the second air-fuel ratio sensor 12 has become lean since the start of fuel cut (when the second air-fuel ratio sensor 12 is an O ₂ sensor). For example, the elapsed time until the output voltage reaches 0.5 V) and the elapsed time until the discharge amount O estimated from the fuel cut start according to the model formula (Equation 5) becomes 0 are counted, In accordance with the time difference between the two, the parameter β is increased or decreased in a direction to decrease the time difference. However, in counting the elapsed time of the latter, as the excess air ratio λ applied to the model formula (formula 5), the following formula (formula 6), formula (formula 7), and formula (formula 8) are each Use.

β ₀ is a constant, here 0. Although e is also a constant, it is a value corresponding to the tolerance of the air-fuel ratio measured by the first air-fuel ratio sensor 11. If the tolerance of the first air-fuel ratio sensor 11 is ± 0.05, the absolute value of the tolerance is taken as e = 0.05.

  FIG. 9 shows the procedure of the parameter β learning process. When a fuel cut occurs in the internal combustion engine 2 (step S1), the electronic control unit 5 indicates that the output of the second air-fuel ratio sensor 12 is non-lean (for example, output voltage> 0.5V), and The oxygen release amount O (Equation 5) calculated by applying the excess air ratio λ shown in the equation (Equation 6), the equation (Equation 7), and the equation (Equation 8) is the same as that of the current fuel cut. The parameter β is learned on the condition that it has never become 0 during the period until the fuel cut starts (steps S2 and S3).

In the learning of the parameter β, the time T _A from the start of the fuel cut until the oxygen release amount O (Expression 5) to which the excess air ratio λ of Expression (Expression 6) is applied becomes 0, and the air of Expression (Expression 7). The time T _B until the oxygen release amount O to which the excess rate λ is applied becomes 0, and the time T _C until the oxygen release amount O to which the air excess rate λ of the formula (Equation 8) is applied become 0, respectively. Calculate (steps S4 to S6). Furthermore, from the start of fuel cut, the output of the second air-fuel ratio sensor 12 measures the time T _D to switch to a lean (e.g., output voltage ≦ 0.5V) (step S7). FIG. 8 shows examples of elapsed times T _A , T _B , T _C and T _D counted from the fuel cut start time t ₂ .

Then, the learning parameter β is determined so as to reduce the time difference between the elapsed time T _D and the elapsed time T _A. In the present embodiment, based on the time difference between T _D and T _A, it calculates a new parameter β by interpolation (interpolation). That is, if a T _D> T _A and (step S8) beta the formula (9) (step S9), T _D <T _A at which if it the beta following formula and (number 10) (step S10).

  The determined learning parameter β is stored and held in the RAM 52 or ROM 53 (step S11). This β is applied to the estimation formula (Equation 5) of the oxygen release amount O repeatedly calculated by the air-fuel ratio control unit 13 until the next fuel cut occurs in the air-fuel ratio control after the end of the current fuel cut. Is done.

According to the present embodiment, the first air-fuel ratio sensor 11 provided upstream of the exhaust gas purifying catalyst 3 mounted in the exhaust passage of the internal combustion engine 2 and the second air-fuel ratio provided downstream of the catalyst 3. Referring to the fuel ratio sensor 12 and at least the output 11 of the first air-fuel ratio sensor, in accordance with a model formula of the oxygen ratio, which is the ratio of the amount of oxygen stored in the catalyst 3 and the oxygen storage capacity of the catalyst 3, The air-fuel ratio control unit 13 that estimates the amount O of released oxygen from the state in which oxygen is stored in the catalyst 3 to the oxygen storage capacity and feedback-controls the released amount O to the target value, and is estimated according to the model equation. The learning unit 14 includes a learning unit 14 that calculates and stores a learning parameter β for reducing an error in the released amount O. When the fuel cut occurs in the internal combustion engine 2, the learning unit 14 Run the calculation of beta, and the elapsed time T _D from the fuel cut start until the output of the second air-fuel ratio sensor 12 reaches a predetermined value (0.5V) indicating that becomes lean, the fuel cut start The learning parameter β is increased / decreased in the direction of decreasing the time difference according to the time difference from the elapsed time T _A until the release amount O estimated according to the model formula becomes 0, and the air-fuel ratio control Since the unit 13 performs the feedback control in consideration of the learning parameter β stored in the learning unit 14, the estimation accuracy of the oxygen release amount O is improved, and the second air-fuel ratio sensor downstream of the catalyst 3 is improved. Thus, it is possible to effectively avoid the problem that the variation of the 12 output signals is delayed with respect to the variation of the air-fuel ratio in the catalyst 3. Therefore, the exhaust gas purification efficiency of the catalyst 3 can be kept high, and the emission amount of HC, CO, and NO _x can be further reduced, and the amount of noble metal used for the catalyst 3 can be reduced.

  The oxygen release amount O is a value based on the state in which the catalyst 3 is filled with oxygen (O = 0). By using this as a control amount, the oxygen release amount O corresponds to the degree of deterioration of the oxygen storage capacity of the catalyst 3. It is not necessary to change the target value setting. Further, each time a fuel cut is performed, the value of the oxygen release amount O is reset to 0 and the estimation error is also reset, so that highly accurate feedback control is realized. In addition, since the fuel cut opportunity often occurs during the driving of the automobile, the number of updates of the parameter β can be increased naturally.

The present invention is not limited to the embodiment described in detail above. In particular, the equation for calculating the learning parameter β is not limited to the equation (Equation 9) and the equation (Equation 10). For example, T _D> T a _A if β predetermined amount gamma (e.g., gamma = 0.001) only increases, decreases the β if T _D <T _A predetermined amount gamma, and so, and T _D Β may be increased or decreased according to the magnitude relationship with T _A.

  Other specific configurations of each part can be variously modified without departing from the spirit of the present invention.

  The present invention can be used for control of an internal combustion engine mounted on an automobile or the like.

DESCRIPTION OF SYMBOLS 1 ... Air fuel ratio control apparatus 11 ... 1st air fuel ratio sensor 12 ... 2nd air fuel ratio sensor 13, 5 ... Air fuel ratio control part (electronic controller)
14, 5 ... Learning unit (electronic control unit)
2 ... Internal combustion engine 3 ... Catalyst

Claims (2)

A first air-fuel ratio sensor provided upstream of an exhaust gas purifying catalyst mounted in an exhaust passage of the internal combustion engine;
A second air-fuel ratio sensor provided downstream of the catalyst;
At least referring to the output of the first air-fuel ratio sensor, oxygen is stored in the catalyst up to the oxygen storage capacity in accordance with a model formula of the oxygen ratio, which is the ratio of the amount of oxygen stored in the catalyst and the oxygen storage capacity of the catalyst. An air-fuel ratio control unit that estimates the amount of released oxygen from the state of occlusion and feedback-controls the released amount to a target value;
A learning unit that calculates and stores a learning parameter for reducing an error in the amount of emission estimated according to the model formula;
The learning unit performs the calculation of the learning parameter when a fuel cut occurs in the internal combustion engine, and a lapse of time from the start of the fuel cut until reaching a predetermined value indicating that the output of the second air-fuel ratio sensor has become lean. According to the time difference between the time and the elapsed time from the start of fuel cut until the release amount estimated according to the model formula becomes zero, the learning parameter is increased or decreased in a direction to decrease the time difference,
The air-fuel ratio control unit is configured to perform feedback control in consideration of the learning parameter stored in the learning unit. The air-fuel ratio control apparatus according to claim 1, wherein the model formula is expressed in the form of an expression (Equation 11).

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