CONTROLLER FOR INTERNAL COMBUSTION ENGINE

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2024-217701, filed on December 12, 2024, the entire contents of which are incorporated herein by reference.

BACKGROUND

1. Field

The present disclosure relates to a controller for an internal combustion engine.

2. Description of Related Art

JP2006-257996A discloses an exhaust passage of an internal combustion engine. The exhaust passage includes a filter that traps particulate matter (PM) in exhaust gas. An accumulated amount of PM that has been accumulated in the filter is calculated by a controller. The PM is discharged from combustion chambers of the internal combustion engine to the exhaust passage. The PM is burned in the filter.

SUMMARY

This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

In one general aspect, a controller for an internal combustion engine includes processing circuitry. The processing circuitry is configured to execute an accumulation amount calculation process and a burn-off rate calculation process. The accumulation amount calculation process calculates an accumulation amount of particulate matter that has accumulated in a filter. The filter is provided in an exhaust passage of the internal combustion engine. The filter traps the particulate matter in exhaust gas in the exhaust passage. The accumulation amount is calculated based on a discharge rate of the particulate matter discharged from the internal combustion engine to the exhaust passage and a burn-off rate of the particulate matter burned in the filter. The accumulation amount varies along an exhaust gas flow direction within the filter. The burn-off rate calculation process calculates the burn-off rate in accordance with a degree of variation in the accumulation amount along the exhaust gas flow direction.

This configuration improves the estimation accuracy of the burn-off rate of the particulate matter in the filter.

In order to accurately calculate the accumulation amount of the particulate matter, it is desirable to accurately calculate the burn-off rate of the particulate matter. The above-described configuration improves this accuracy.

Other features and aspects will be apparent from the following detailed description, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing the configuration of an internal combustion engine in which a controller according to an embodiment is employed.

FIG. 2 is a flowchart showing a procedure of a burn-off rate calculation process executed by the controller of the embodiment.

FIG. 3 is a graph showing the relationships among a degree of variation in accumulation amount, an accumulation density counter, a correction factor, and an amount of particulate matter burned per unit time.

FIG. 4 is a flowchart showing a procedure of an index value calculation process executed by the controller of the embodiment.

FIG. 5A to FIG. 5E are timing diagrams showing operation of the embodiment. FIG. 5A shows changes in the execution state of a fuel cutoff process. FIG. 5B shows changes in an accumulation density counter. FIG. 5C shows changes in a PM burn-off amount per unit time. FIG. 5D shows changes in a PM discharge amount per unit time. FIG. 5E shows changes in a PM accumulation amount.

Throughout the drawings and the detailed description, the same reference numerals refer to the same elements. The drawings may not be to scale, and the relative size, proportions, and depiction of elements in the drawings may be exaggerated for clarity, illustration, and convenience.

DETAILED DESCRIPTION

This description provides a comprehensive understanding of the methods, apparatuses, and/or systems described. Modifications and equivalents of the methods, apparatuses, and/or systems described are apparent to one of ordinary skill in the art. Sequences of operations are exemplary, and may be changed as apparent to one of ordinary skill in the art, with the exception of operations necessarily occurring in a certain order. Descriptions of functions and constructions that are well known to one of ordinary skill in the art may be omitted.

Exemplary embodiments may have different forms, and are not limited to the examples described. However, the examples described are thorough and complete, and convey the full scope of the disclosure to one of ordinary skill in the art.

In this specification, “at least one of A and B” should be understood to mean “only A, only B, or both A and B.”

FIGS. 1 to 5E illustrate an embodiment of a controller for an internal combustion engine. For example, in the present embodiment, “upstream” represents upstream in the flow direction of the exhaust gas. “Downstream” represents downstream in the flow direction of the exhaust gas.

Configuration of the Internal Combustion Engine

As shown in FIG. 1, an internal combustion engine 10 that uses gasoline as fuel includes a plurality of cylinders 10a. An intake passage 13 is connected to the intake port of each of the cylinders 10a. The intake passage 13 includes a throttle valve 14 that adjusts an intake air amount.

Fuel injection valves 11 are disposed in the combustion chambers of the respective cylinders 10a. In the combustion chamber of each of the cylinders 10a, a mixture of air taken in through the intake passage 13 and fuel injected from the fuel injection valve 11 is combusted. The air-fuel mixture is ignited by spark discharge to be combusted. Exhaust gas generated by combustion of the air-fuel mixture in the combustion chamber is discharged to the exhaust passage 15. The exhaust passage 15 has been connected to an exhaust port of the combustion chamber.

A three-way catalyst 17 is provided in the exhaust passage 15. The three-way catalyst 17 generates water and carbon dioxide by oxidizing hydrocarbon (HC) and carbon monoxide (CO) contained in the exhaust gas. The three-way catalyst 17 generates nitrogen by reducing nitrogen oxides (NOx) contained in the exhaust gas.

A gasoline particulate filter (hereinafter referred to as GPF) 18 is provided in the exhaust passage 15 downstream of the three-way catalyst 17. The GPF 18 is a PM trapping filter carrying a three-way catalyst. PM is particulate matter (appropriately referred to as PM) in the exhaust gas.

The controller 100 includes a CPU 110, a memory 120, and the like. The controller 100 performs various controls of the internal combustion engine 10 by the CPU 110 executing a program stored in the memory 120.

Detection signals of various types of sensors are input to the controller 100. As the various sensors, for example, a crank angle sensor 53 is provided in the vicinity of a crankshaft of the internal combustion engine 10. The controller 100 calculates an engine speed NE of the internal combustion engine 10 based on the detection signal of the crank angle sensor 53. The internal combustion engine 10 is also provided with an air flow meter 54 that detects an intake air amount GA and a water temperature sensor 55 that detects a coolant temperature THW. The coolant temperature THW is the temperature of the coolant of the internal combustion engine 10.

The controller 100 controls fuel injection of the fuel injection valve 11, an opening degree of the throttle valve 14, and the like. Further, the controller 100 executes the fuel cutoff process when the output required of the internal combustion engine 10 is 0. In the fuel cutoff process, fuel injection from the fuel injection valve 11 is stopped.

The controller 100 calculates the PM accumulation amount Ps by the accumulation amount calculation process. The PM accumulation amount Ps is the amount of PM accumulated in the GPF 18. The controller 100 performs various controls based on the PM accumulation amount Ps. For example, when the PM accumulation amount Ps becomes equal to or larger than a predetermined excessive accumulation determination value α, the controller 100 issues a warning for prompting maintenance of the GPF 18. The maintenance is performed in a repair shop, for example, to burn and remove the PM accumulated in the GPF 18.

Calculation of PM Accumulation Amount Ps

For example, the controller 100 acquires the engine speed NE, the charging efficiency η, and the coolant temperature THW. The charging efficiency η is calculated by the controller 100 based on the engine speed NE and the intake air amount GA.

The controller 100 calculates the PM discharge rate Pa based on the engine speed NE, the charging efficiency η, and the coolant temperature THW. The PM discharge rate Pa is the amount of PM discharged from the internal combustion engine 10 to the exhaust passage 15 per unit time.

Further, the controller 100 calculates a PM burn-off rate Pb by executing a burn-off rate calculation process described later. The PM burn-off rate Pb is the amount of PM burned in the GPF 18 per unit time.

The controller 100 substitutes a value obtained by subtracting the PM burn-off rate Pb from the PM discharge rate Pa for the update amount ΔPs. Therefore, when the PM discharge rate Pa is greater than the PM burn-off rate Pb, the update amount ΔPs is a positive value. When the PM burn-off rate Pb is greater than the PM discharge rate Pa, the update amount ΔPs is a negative value.

Next, the controller 100 updates the PM accumulation amount Ps by adding the update amount ΔPs to the currently calculated PM accumulation amount Psp. Accordingly, when the PM discharge rate Pa is greater than the PM burn-off rate Pb, the PM accumulation amount Ps increases. In contrast, when the PM burn-off rate Pb is greater than the PM discharge rate Pa, the PM accumulation amount Ps decreases. The PM accumulation amount Ps is calculated by executing such processes.

Burn-off Rate Calculation Process

FIG. 2 shows a procedure of a burn-off rate calculation process executed by the controller 100. The series of processes shown in FIG. 2 is realized by the CPU 110 executing a program stored in the memory 120 of the controller 100 at predetermined intervals. As appropriate, a number preceded by S represents a step number.

In the series of processes shown in FIG. 2, the controller 100 first acquires the PM accumulation amount Psp, the GPF temperature T, and the intake air amount GA that have been calculated at present. The controller 100 calculates a basic burn-off rate Pbb based on the currently calculated PM accumulation amount Psp, the GPF temperature T, and the intake air amount GA (S100). The basic burn-off rate Pbb is a base value of the PM burn-off rate Pb. The currently calculated PM accumulation amount Psp, GPF temperature T, and intake air amount GA are values correlated with the PM burn-off rate. The basic burn-off rate Pbb is the maximum burn-off amount of PM per unit time. The maximum burn-off amount is estimated based on the currently calculated PM accumulation amount Psp, the GPF temperature T, and the intake air amount GA. The GPF temperature T is the temperature of the GPF 18. The controller 100 calculates the GPF temperature T based on the engine rotation speed NE and the charging efficiency η. The GPF temperature T may be detected using a sensor or the like.

When the S100 process is executed, next, the controller 100 executes the S110 process.

In the process of S110, the controller 100 calculates a correction factor Kd based on the accumulation density counter Cd. The accumulation density counter Cd is an index value indicating the degree of variation in the amount of PM accumulated in the GPF 18 along the exhaust gas flow direction within the GPF 18. In some cases, the degree of variation in the accumulation amount represents the degree of variation in the accumulation amount of PM within the GPF 18 along the exhaust gas flow direction. The degree of variation in the accumulation amount in a case in which the accumulation density counter Cd is small is greater than the degree of variation in the accumulation amount in a case in which the accumulation density counter Cd is large. In other words, when the degree of variation of the accumulation amount decreases, the accumulation density counter Cd increases. When the degree of variation in the accumulation amount increases, the accumulation density counter Cd decreases.

The correction factor Kd is a correction value used to correct the basic burn-off rate Pbb. The correction factor Kd is variably set according to the accumulation density counter Cd. As shown in FIG. 3, for example, as the accumulation density counter Cd increases, the correction factor Kd increases. The correction factor Kd is larger than 0 and less than or equal to 1.

When the S110 process is executed, next, the controller 100 executes the S120 process. In the process of S120, the controller 100 calculates various correction factors Kn other than the correction factor Kd. Examples of the various correction factors Kn include a correction factor corresponding to the degree of deterioration of the GPF 18.

When the S120 process is executed, next, the controller 100 executes the S130 process. In the process of S130, the controller 100 multiplies the basic burn-off rate Pbb by a correction factor Kd and various correction factors Kn. The controller 100 executes a process of substituting the multiplied value for the PM burn-off rate Pb.

When the S130 process is executed, the controller 100 ends the execution of this process in the current cycle.

Accumulation Density Counter

FIGS. 3 and 4 illustrate the accumulation density counter Cd.

For example, when oxygen supply by the fuel cutoff process is started with respect to the GPF 18 at a high temperature, the PM is burned in the upstream portion of the GPF 18. On the other hand, since oxygen is consumed by PM burning in the upstream portion, burning of PM is less likely to proceed in the downstream portion of the GPF 18. Therefore, when PM is burned, the degree of variation in the amount of accumulation of PM in the exhaust gas flow direction of the GPF 18 tends to increase. On the other hand, when the PM is not burned, the PM discharged from the internal combustion engine 10 is trapped by the GPF 18, so the degree of variation in the amount of accumulation of the PM in the direction of flow of the exhaust gas in the GPF 18 tends to become smaller.

The present inventors have found that the PM burn-off rate in the GPF 18 tends to change in accordance with the degree of variation in the accumulation amount. To be specific, the PM burn-off rate in the GPF 18 tends to be greater as the degree of variation in the accumulation amount is smaller. Therefore, as shown in FIG. 3, the PM burn-off rate Pb tends to increase as the degree of variation in the accumulation amount decreases. The PM burn-off rate Pb is a PM burn-off amount per unit time in the GPF 18.

On the other hand, the controller 100 of the present embodiment calculates the accumulation density counter Cd such that the accumulation density counter Cd increases as the degree of variation of the accumulation amount decreases. The accumulation density counter Cd is an index value indicating the degree of variation in the accumulation amount. The controller 100 calculates the correction factor Kd such that the correction factor Kd increases as the accumulation density counter Cd increases. Therefore, the controller 100 calculates the PM burn-off rate Pb such that the PM burn-off rate Pb increases as the degree of variation of the accumulation amount decreases.

FIG. 4 shows a procedure of an index value calculation process for calculating the accumulation density counter Cd. The series of processes shown in FIG. 4 is realized by the CPU 110 executing a program stored in the memory 120 of the controller 100 at predetermined intervals. The initial value of the accumulation density counter Cd is 0.

In the series of processes shown in FIG. 4, the controller 100 first determines whether the PM is currently combusted (S200). In the S200 process, for example, when the calculated PM accumulation amount Ps tends to decrease, the controller 100 determines that PM is currently combusted. On the other hand, when the calculated PM accumulation amount Ps does not tend to decrease, the controller 100 determines that the PM is not combusted at present.

In the process of S200, when it is determined that PM is currently combusted (S100: YES), the controller 100 executes a process of subtracting a predetermined decease value A from the current accumulation density counter Cd (S210). A lower limit density value is set in the accumulation density counter Cd. For example, the lower limit density value is 0. When the accumulation density counter value Cd after the subtraction in the S210 process is smaller than the lower limit value, the controller 100 substitutes the lower limit value for the accumulation density counter value Cd. Therefore, the lower limit guard of the accumulation density counter Cd is performed.

On the other hand, in the process of S200, when it is determined that the PM is not combusted at present (S100: NO), the controller 100 executes a process of adding a predetermined accumulation amount increase value B to the current accumulation amount counter Cd (S220). The amount of PM trapped by the GPF 18 when the PM discharge rate Pa is high is greater than the amount of PM trapped by the GPF 18 when the PM discharge rate Pa is low. Therefore, when the PM discharge rate Pa is high, the increase speed of the degree of variation of the accumulation amount is high. Therefore, the increase speed of the accumulation density counter Cd when the PM discharge rate Pa is high is preferably greater than the increase speed of the accumulation density counter Cd when the PM discharge rate Pa is low. In contrast, the controller 100 of the present embodiment variably sets the density increment value B such that the density increase value B increases as the calculated PM discharge rate Pa increases. However, the density increase value B may be a fixed value.

Further, an upper limit density value is set in the accumulation density counter Cd. For example, the upper limit density value is a value of the accumulation density counter Cd in the following case. That is, the accumulation amount of PM in the exhaust gas flow direction of the GPF 18 is uniform. And / or the degree of variation in the accumulation amount is the smallest. The upper limit density value is set to an appropriate value through a test or the like in advance. When the accumulation density counter Cd added in the S220 process is larger than the upper limit value, the controller 100 substitutes the upper limit value for the accumulation density counter Cd. Therefore, the upper limit guard of the accumulation density counter Cd is performed.

When either the S210 process or the S220 process is terminated, the controller 100 terminates the execution of this process in the current cycle.

Operations of the Present Embodiment

FIGS. 5A to 5E show the operation of the present embodiment. FIG. 5A shows changes in the execution state of a fuel cutoff process. FIG. 5B shows changes in an accumulation density counter. FIG. 5C shows changes in a PM burn-off amount per unit time. FIG. 5D shows changes in a PM discharge amount per unit time. FIG. 5E shows changes in a PM accumulation amount.

When the combustion of the air-fuel mixture in the internal combustion engine 10 is started at the time t1, the PM discharge rate Pa increases as shown in FIG. 5D. Therefore, the PM accumulation amount Ps increases as shown in the graph 5E. Since the PM accumulation amount Ps shown in FIG. 5E does not tend to decrease, the controller 100 determines that PM is not combusted at present. Therefore, as shown in FIG. 5B, the accumulation density counter Cd increases.

When the PM discharge rate Pa decreases as shown in FIG. 5D at the time t2, the PM accumulation amount Ps increases as shown in FIG. 5E, but the increase rate of the accumulation density counter Cd decreases as shown in FIG. 5B. In other words, when the PM discharge rate Pa decreases as shown in FIG. 5D, the density increase value B decreases. Therefore, the accumulation density counter Cd increases as shown in FIG. 5B, but the increasing speed of the accumulation density counter Cd decreases as shown in FIG. 5B.

If the fuel cutoff process is executed at the time t3 when the temperature of the GPF 18 is equal to or higher than the PM combustion necessary temperature, PM is combusted in the GPF 18. In the case in which PM is burned, when the PM burn-off rate Pb is calculated, the PM accumulation amount Ps tends to decrease as shown in FIG. 5E. The controller 100 determines that the PM is currently combusted. Therefore, after the time t3, the accumulation density counter Cd decreases as shown in FIG. 5B. When the accumulation density counter Cd decreases, the correction factor Kd also decreases. Therefore, the PM burn-off rate Pb, which is corrected by being multiplied by the correction factor Kd, decreases as shown in FIG. 5C as the accumulation density counter Cd shown in FIG. 5B decreases.

Since the fuel injection is stopped during the execution of the fuel cutoff process, the air-fuel mixture is not combusted. Therefore, after the time t3, the PM discharge rate Pa becomes 0 as shown in FIG. 5D. Therefore, the PM accumulation amount Ps decreases by the amount corresponding to the PM burn-off rate Pb, as shown in FIG. 5E.

When the fuel cutoff process is stopped at the time t4, the combustion of the air-fuel mixture in the internal combustion engine 10 is restarted. Therefore, as the PM discharge rate Pa increases, the PM accumulation amount Ps increases. That is, since the PM accumulation amount Ps does not tend to decrease, the controller 100 determines that the PM is not combusted at present. The accumulation density counter Cd is again incremented.

Advantages of the Present Embodiment

(1) The PM burn-off rate in the GPF 18 tends to change in accordance with the degree of variation in the amount of PM accumulated in the GPF 18 in the exhaust gas flow direction. In contrast, the controller 100 of the present embodiment executes the burn-off rate calculation process. In the burn-off rate calculation process, the PM burn-off rate Pb is calculated according to the degree of variation in the accumulation amount of PM in the exhaust gas flow direction of the GPF 18. Therefore, in the present embodiment, the estimation accuracy of the PM burn-off rate Pb in the GPF 18 can be increased, for example, as compared with the case in which the PM burn-off rate Pb has been calculated without considering the degree of variation in the accumulation amount. The estimation accuracy of the PM accumulation amount Ps is also improved. This is because the PM accumulation amount Ps is calculated by the balance between the PM burn-off rate Pb and the PM discharge rate Pa.

(2) In the burn-off rate calculation process, the PM burn-off rate Pb in the case in which the degree of variation of the accumulation amount is small is calculated to be larger than the PM burn-off rate Pb in the case in which the degree of variation is large.

The PM burn-of rate in the GPF 18 when the degree of variation in the accumulation amount is small tends to be greater than the PM burn-of rate in the GPF 18 when the degree of variation in the accumulation amount is large. In contrast, in the present embodiment, the PM burn-off rate Pb in the case in which the degree of variation in the accumulation amount is small is calculated to be greater than the PM burn-off rate Pb in the case in which the degree of variation in the accumulation amount is large. Therefore, the PM burn-off rate Pb can be appropriately calculated in accordance with the degree of variation in the accumulation amount.

(3) The controller 100 executes an index value calculation process for calculating the accumulation density counter Cd. The accumulation density counter Cd is an index value indicating the degree of variation in the accumulation amount. In the index value calculation process, the accumulation density counter Cd in a case in which PM is being burned is updated so as to indicate that the degree of variation in the accumulation amount is large. In contrast, the accumulation density counter Cd in a case in which PM is not being burned is updated so as to indicate that the degree of variation in the accumulation amount is small.

When oxygen supply is started by the fuel cutoff process with respect to the high-temperature GPF 18, PM is combusted in the upstream portion of the GPF 18. Since oxygen is consumed by burning of PM in the upstream portion, the PM burning is less likely to proceed in the downstream portion of the GPF 18. Therefore, when PM is burned, the degree of variation in the accumulation amount of PM in the exhaust gas flow direction of the GPF 18 tends to be large. On the other hand, when the PM is not burned, the GPF 18 traps the PM discharged from the combustion chamber. Therefore, when the PM is not burned, the degree of variation in the accumulation amount of the PM in the exhaust gas flow direction of the GPF 18 tends to be small.

In contrast, the accumulation density counter Cd is calculated in the present embodiment. The accumulation density counter Cd is an index value related to the degree of variation in the accumulation amount. The degree of variation in the accumulation amount in a case in which the accumulation density counter Cd is small is greater than the degree of variation in the accumulation amount in a case in which the accumulation density counter Cd is large. In other words, when the degree of variation of the accumulation amount decreases, the accumulation density counter Cd increases.

When the PM burns, the degree of variation in the accumulation amount increases. In this case, the accumulation density counter Cd is updated so as to indicate that the degree of variation of the accumulation amount increases. That is, when the PM is burned, the accumulation density counter Cd is updated to be smaller. On the other hand, when the PM is not burned, the degree of variation in the accumulation amount is small. In this case, the accumulation density counter Cd is updated so as to indicate that the degree of variation decreases. That is, when PM is not burned, the accumulation density counter Cd is updated so as to increase. Therefore, it is possible to appropriately calculate the index value indicating the degree of variation in the accumulation amount.

(4) The burn-off rate calculation process includes a process of calculating the basic burn-off rate Pbb based on a value correlated with the PM burn-off rate. The basic burn-off rate Pbb is a base value of the burn-off rate. The burn-off rate calculation process further includes a process of calculating the correction factor Kd based on the index value. The correction factor Kd is a correction value used to correct the basic burn-off rate Pbb.

The accumulation density counter Cd is an index value indicating the degree of variation in the accumulation amount. The PM burn-off rate tends to increase as the degree of variation in the accumulation amount decreases. Therefore, the correction value used for correcting the PM burn-off rate can be calculated based on the accumulation density counter Cd. In contrast, in the present embodiment, the basic burn-off rate Pbb is calculated based on a value correlated with the PM burn-off rate Pb. The basic burn-off rate Pbb is a base value of the PM burn-off rate Pb. The correction factor Kd is a correction value used to correct the basic burn-off rate Pbb. The correction factor Kd is calculated based on the accumulation density counter Cd. The degree of variation in the accumulation amount affects the PM burn-off rate. Therefore, the basic burn-off rate Pbb can be corrected in accordance with a value that affects the PM burn-off rate.

(5) The PM accumulation amount Ps is calculated by the balance between the PM burn-off rate Pb and the PM discharge rate Pa. If the estimation accuracy of the PM burn-off rate Pb is low, in order to compensate for the variation in the estimation accuracy of the PM burn-off rate Pb, for example, a comparative example in which the compensation term for the emission rate Pa is increased can be considered. However, in this comparative example, the calculated PM discharge rate Pa may deviate from the actual PM discharge rate. As a result, in some cases, the estimation accuracy of the PM accumulation amount Ps may decrease. In contrast, according to the present embodiment, the estimation accuracy of the PM burn-off rate Pb is improved. Therefore, the compensation term can be reduced. Therefore, the calculated PM discharge rate Pa approaches the actual PM discharge rate. Therefore, the estimation accuracy of the PM accumulation amount Ps is improved.

(6) According to the present embodiment, the estimation accuracy of the PM accumulation amount Ps is improved. Therefore, the accuracy of various controls based on the PM accumulation amount Ps is also improved.

For example, in the present embodiment, when the PM accumulation amount Ps becomes equal to or larger than the excessive accumulation determination value α, a warning for prompting maintenance in a repair shop is issued in order to burn and remove PM accumulated in the GPF 18. Here, when the estimation accuracy of the PM accumulation amount Ps is low, there is the following concern. That is, when the calculated PM accumulation amount is larger than the actual PM accumulation amount, a warning may be erroneously issued at an early stage. In this regard, in the present embodiment, the estimation accuracy of the PM accumulation amount Ps is improved. Therefore, a possibility that the warning is erroneously notified at an early stage is reduced.

Modifications

The above-described embodiment may be modified as follows. The above-described embodiment and the following modifications can be combined as long as the combined modifications remain technically consistent with each other.

In the process of S200 shown in FIG. 4, it is determined whether or not PM is combusted based on the tendency of change in the PM accumulation amount Ps, but it may be determined whether or not PM is combusted by another method. For example, when the calculated PM burn-off rate Pb is larger than 0, it may be determined that the PM is combusted. Further, for example, based on the engine speed NE and the engine load factor, it may be determined whether or not PM is burned.

In the above embodiment, the degree of variation in the accumulation amount when the accumulation density counter Cd is small is larger than the degree of variation in the accumulation amount when the accumulation density counter Cd is large. Conversely, the degree of variation in the accumulation amount when the accumulation density counter Cd is small may be smaller than the degree of variation in the accumulation amount when the accumulation density counter Cd is large. In the case of this modification, by variably setting the correction factor Kd so that the smaller the accumulation density counter Cd, the larger the value of the correction factor Kd, the same effect as in the above embodiment can be obtained.

The basic burn-off rate Pbb may be calculated in a manner different from the above-described embodiment.

The PM discharge rate Pa may be calculated in a manner different from the above-described embodiment.

The position of the GPF 18 in the exhaust passage 15 can be changed as appropriate.

The GPF 18 may be a filter that does not carry a three-way catalyst.

The controller 100 is not limited to a device that includes a CPU and a memory module and executes software processing. For example, the controller 100 may include hardware circuits, for example, an application-specific integrated circuit (ASIC)), dedicated to executing at least part of the processes executed by the software in the above-described embodiment. That is, the controller 100 may be modified as long as it includes processing circuitry that has any one of the following configurations (a) to (c). (a) Processing circuitry including one or more processors that execute all of the above-described processes according to programs and one or more program storage devices such as ROMs that store the programs. (b) Processing circuitry including one or more processors and one or more program storage devices that execute part of the above-described processes according to the programs and one or more dedicated hardware circuits that execute the remaining processes. (c) Processing circuitry including one or more dedicated hardware circuits that execute all of the above-described processes. The program storage devices, which are computer-readable media, include any type of medium that is accessible by a general-purpose computer or a dedicated computer.

Various changes in form and details may be made to the examples above without departing from the spirit and scope of the claims and their equivalents. The examples are for the sake of description only, and not for purposes of limitation. Descriptions of features in each example are to be considered as being applicable to similar features or aspects in other examples. Suitable results may be achieved if sequences are performed in a different order, and/or if components in a described system, architecture, device, or circuitry are combined differently, and/or replaced or supplemented by other components or their equivalents. The scope of the disclosure is not defined by the detailed description, but by the claims and their equivalents. All variations within the scope of the claims and their equivalents are included in the disclosure.