Engine control apparatus

Abstract

An ECU 30 calculates a target temperature of a bed temperature of a DOC 22a under PM regeneration control at each control period by the elements M1 to M9. Among these elements, the estimating section M7 estimates a passing SO.sub.3 amount at each control period by using an inflow SOx amount and a representative temperature. The estimating section M8 estimates a SO.sub.2 reduction rate, which is a ratio of reduction from SO.sub.3 to SO.sub.2 in the DOC 22a. Then, the calculating unit M9 calculates an amount of SO.sub.3 that is allowed to desorb from the DOC 22a as an allowable desorption SO.sub.3 amount at each control period, by using a constrained SO.sub.3 amount which corresponds to a constraint concerning sulfate white smoke, the passing SO.sub.3 amount, and the SO.sub.2 reduction rate.

Claims

1. An engine control apparatus comprising: a purifying device provided in an exhaust pipe of a diesel engine; a fuel adding valve for supplying unburnt fuel into the purifying device; and an electronic control unit that executes temperature increase control of increasing a temperature of the purifying device to a target temperature in a temperature range in which a particulate matter burns by supplying unburnt fuel from the fuel adding valve, the electronic control unit is configured to: acquire a representative temperature that is a representative value of the purifying device at each predetermined control period; estimate an amount of SOx flowing into the purifying device as an inflow SOx amount at each control period; estimate a final adsorbed SOx distribution by using the inflow SOx amount and the representative temperature at each control period, the final adsorbed SOx distribution expressed as a graph in which an amount of SOx that finally adsorbs to the purifying device in each temperature during temperature increase of the purifying device is related with the representative temperature; estimate an amount of SOx that flows into the purifying device in a state of SOx and passes without adsorbing to the purifying device to be converted in a state of SO.sub.3 as a passing SO.sub.3 amount at each control period, by using the inflow SOx amount and the representative temperature; estimate a SO.sub.2 reduction rate which is a ratio of reduction of SO.sub.3 to SO.sub.2 in the purifying device; calculate an amount of SO.sub.3 that is allowed to desorb from the purifying device as an allowable desorption SO.sub.3 amount at each control period, by using a constrained SO.sub.3 amount at a downstream side of the purifying device, which corresponds to a constraint concerning sulfate white smoke, the passing SO.sub.3 amount, and the SO.sub.2 reduction rate; and calculate the target temperature at each control period, by using the final adsorbed SOx distribution and the allowable desorption SO.sub.3 amount.

2. The engine control apparatus according to claim 1, wherein the electronic control unit is configured to estimate the SO.sub.2 reduction rate based on a relation between the SO.sub.2 reduction rate, a supplied amount of unburnt fuel from the fuel adding valve, and a gas amount flowing into the purifying device.

3. The engine control apparatus according to claim 1, wherein the electronic control unit is configured to: estimate a SOx saturation factor in the purifying device at each control period, by using an adsorbed SOx distribution expressed as a graph in which an amount of SOx that adsorbs to the purifying device in each temperature during temperature increase of the purifying device is related with the representative temperature of the purifying device and a saturation SOx distribution expressed as a graph in which an SOx maximum amount adsorbing to the purifying device in each temperature during temperature increase of the purifying device is related with the temperature of the purifying device; estimate an amount of SOx that flows into the purifying device and newly adsorbs to the purifying device as a newly adsorbing SOx amount at each control period by using the inflow SOx amount and the SOx saturation factor; estimate an amount of SOx that flows into the purifying device and passes without adsorbing to the purifying device as a passing SOx amount, by using the newly adsorbing SOx amount; and estimate the passing SO.sub.3 amount at each control period, by using a conversion rate map expressing a relation between a conversion rate of SO.sub.2 that is converted into SO.sub.3 in the purifying device and the representative temperature.

4. The engine control apparatus according to claim 1, wherein the electronic control unit is configured to: estimate an amount of SOx that newly desorbs from the purifying device as a newly desorbing SOx amount at each control period, by using the inflow SOx amount and the representative temperature; and estimate the final adsorbed SOx distribution at each control period, by using the newly desorbing SOx amount.

5. The engine control apparatus according to claim 1, wherein the electronic control unit is configured to acquire a gas temperature at a downstream side of the purifying device as the representative temperature.

6. The engine control apparatus according to claim 1, wherein the purifying device includes a filter that traps particulate matter flowing in the exhaust pipe, wherein the electronic control unit is configured to start the temperature increase control when an estimated value of an amount of particulate matter trapped by the filter reaches a removal request amount.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a diagram showing a system configuration of an embodiment of the present disclosure;

(2) FIG. 2 is a diagram for describing adsorption and desorption of SOx in a DOC 22a;

(3) FIG. 3 is a functional block diagram showing a logic for calculating a target bed temperature Ttrg;

(4) FIG. 4 is a diagram for describing an adsorbed SOx distribution and a saturation SOx distribution;

(5) FIG. 5 is a diagram for describing a relation between a reference saturation SOx distribution and a saturation SOx distribution after correction;

(6) FIG. 6 is a diagram for describing a total adsorption allowance SO.sub.2 amount;

(7) FIG. 7 is a view for describing a relation between a newly adsorbing SOx amount and a passing SOx amount;

(8) FIG. 8 is a diagram for describing an adsorption rate map;

(9) FIG. 9 is a diagram for describing an SOx distribution after adsorption;

(10) FIG. 10 is a diagram for describing a total desorbable SOx amount;

(11) FIG. 11 is a diagram for describing a relation between a final desorbed SOx distribution and the SOx distribution after adsorption;

(12) FIG. 12 is a diagram for describing an SO.sub.3 conversion rate map;

(13) FIG. 13 is a diagram for describing an SO.sub.3 conversion rate correction map;

(14) FIG. 14 is a diagram for describing an SO.sub.2 reduction rate map:

(15) FIG. 15 is a view for describing an allowable desorption SO.sub.3 amount;

(16) FIG. 16 is a diagram for describing a target bed temperature Ttrg;

(17) FIG. 17 is a diagram illustrating an example of a hardware configuration of the ECU included in the system of the embodiment; and

(18) FIG. 18 is a diagram illustrating another example of a hardware configuration of the ECU included in the system of the embodiment.

DESCRIPTION OF EMBODIMENTS

(19) Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings. Note that when the numerals of the numbers, the quantities, the amounts, the ranges and the like of the respective elements are mentioned in the embodiment shown as follows, the present disclosure is not limited to the mentioned numerals unless specially explicitly described otherwise, or unless the disclosure is explicitly specified by the numerals theoretically. Further, structures, steps and the like that are described in the embodiment shown as follows are not always indispensable to the present disclosure unless specially explicitly shown otherwise, or unless the disclosure is explicitly specified by them theoretically.

First Embodiment

(20) A first embodiment will now be described referring to the accompanying drawings.

1. Explanation of System Configuration

(21) FIG. 1 is a diagram showing a system configuration of an embodiment. The system shown in FIG. 1 is configured as an engine control apparatus including a diesel engine 10 (also simply referred to as an engine 10 hereinafter) which is mounted on a vehicle. Respective cylinders of the engine 10 are provided with injectors 12 that inject light oil as fuel. The engine 10 drawn in FIG. 1 is an in-line four-cylinder engine, but the number of cylinders and arrangement of the cylinders of the engine 10 are not specially limited. Further, only one of the four injectors 12 is drawn in FIG. 1.

(22) An inlet of an exhaust turbine 16a of a turbocharger 16 is connected to an exhaust manifold 14 of the engine 10. The exhaust turbine 16a is connected to a compressor 16b which is provided in an intake pipe 18. The compressor 16b turbocharges intake air by driving by rotation of the exhaust turbine 16a. An exhaust pipe 20 is connected to an outlet of the exhaust turbine 16a. The exhaust pipe 20 is provided with an exhaust emission purifying device 22. The exhaust emission purifying device 22 includes a DOC (Diesel Oxidation Catalyst) 22a, and a DPF (Diesel Particulate Filter) 22b. The DOC 22a is a catalyst having a function of oxidizing hydrogen carbon (HC) and a carbon monoxide (CO) in exhaust emission and converting HC and CO into water (H.sub.2O) and a carbon dioxide (CO.sub.2). The DPF 22b is a filter that traps particulate matter (PM) contained in exhaust emission. A fuel adding valve 24 that adds unburnt fuel common to the injector 12 to the exhaust pipe 20 is provided upstream of the exhaust emission purifying device 22. The fuel adding valve 24 is an example of a fuel supplying means.

(23) The system shown in FIG. 1 includes an ECU (Electronic Control Unit) 30 as a control means. The ECU 30 is a microcomputer including a RAM (Random Access Memory), a ROM (Read Only Memory), a CPU (Central Processing Unit) and an input-output interface. The ECU 30 takes in signals from various sensors which are mounted on the vehicle through the input-output interface and processes the signals. The various sensors include an air flow meter 32 that is provided in a vicinity of an inlet of the intake pipe 18, a temperature sensor 34 that detects an outlet temperature of the DOC 22a, and a differential pressure sensor 36 that detects a pressure difference between an upstream and downstream sides of the DPF 22b. The ECU 30 processes the signals from the various sensors which the ECU 30 takes in and operates various actuators in accordance with a predetermined control program. The actuators operated by the ECU 30 include the injector 12 and the fuel adding valve 24 described above.

2. Regeneration Control of DPF 22b

(24) In the present embodiment, temperature increase control (also referred to as PM regeneration control hereinafter) of the DPF 22b is performed as engine control by the ECU 30. PM regeneration control is control that adds fuel from the fuel adding valve 24 when an estimated value of PM which is trapped by the DPF 22b reaches a removal request amount. For example, when the pressure difference detected by the differential pressure sensor 36 reaches a predetermined value, it can be determined that the estimated value of PM reaches the removal request amount. Fuel is added from the fuel adding valve 24, whereby the added fuel is oxidized in the DOC 22a, and a bed temperature of the DPF 22b is increased to 600 C. or more by oxidation reaction heat. Thereby, PM which is trapped by the DPF 22b can be burned and removed, and therefore, the trapping function of the DPF 22b can be restored. An addition fuel amount (hereinafter, a DPF fuel amount) from the fuel adding valve 24 for increasing the bed temperature of the DPF 22b to 600 C. or more is determined on the basis of a map that relates the addition fuel amount with the bed temperature of the DPF. The map like this is stored in the ROM of the ECU 30, for example, and can be properly read in accordance with an actual bed temperature of the DPF 22b.

3. Problem in PM Regeneration Control

(25) Incidentally, a sulfur is generally contained in fuel and a lubricating oil of a diesel engine, and with combustion of the fuel, SOx is generated from the sulfur like this. This similarly applies to the present embodiment, and SOx is generated with combustion of fuel in the engine 10. The generated SOx is discharged from the engine 10 to flow into the exhaust emission purifying device 22, and mainly adsorbs to the DOC 22a. However, when the bed temperature of the DOC 22a becomes high, the SOx adsorbing to the DOC 22a starts to desorb. Although there is variations depending on a composition of the DOC 22a and the like, SOx desorbs from the DOC 22a and is released to a downstream side, in a temperature range in which PM regeneration control is performed.

(26) Adsorption and desorption of SOx in the DOC 22a will be described with reference to FIG. 2. FIG. 2 is a diagram for describing adsorption and desorption of SOx in a DOC 22a. As shown in FIG. 2, the DOC 22a includes a coat material 22c that covers a surface of a base material (not illustrated), and a precious metal 22d (Pt, Pd or the like). The precious metal 22d is dispersively supported by the coat material 22c, and is an active spot at a time of oxidizing HC and CO. Note that SO.sub.2 in exhaust emission adsorbs to the precious metal 22d, or SO.sub.3 in the exhaust emission adsorbs to the coat material 22c. A part of SO.sub.2 adsorbing to the precious metal 22d desorbs from the precious metal 22d to return into the exhaust emission, or is oxidized on the precious metal 22d to be SO.sub.3, and adsorbs to the coat material 22c in a state of SO.sub.3. That is, SO.sub.2 adsorbs to the precious metal 22d, and SO.sub.3 derived from exhaust emission and SO.sub.3 derived from SO.sub.2 adsorb to the coat material 22c. In any event, as a result that SOx is adsorbed, the function of oxidizing HC and the like in the DOC 22a is inhibited.

(27) The SO.sub.3 adsorbing to the coat material 22c by the aforementioned two routes is desorbed when the bed temperature of the coat material 22c becomes high. Further, as a result that the bed temperature of the coat material 22c becomes high, conversion from SO.sub.2 to SO.sub.3 is promoted on the precious metal 22d, and therefore, SO.sub.3 like this is also desorbed from the coat material 22c. Accordingly, not only the trapping function of the DPF 22b described above but also the function of oxidizing HC and the like in the DOC 22a can be restored, by performing PM regeneration control. However, as shown in FIG. 2, the SO.sub.3 which is desorbed from the coat material 22c reacts with H.sub.2O that exists in the exhaust pipe 20, whereby H.sub.2SO.sub.4 is generated. When a concentration of the H.sub.2SO.sub.4 exceeds a fixed concentration, H.sub.2SO.sub.4 becomes white smoke (sulfate white smoke) which is visually recognizable, and therefore is likely to impair a commodity value of the vehicle on which the engine 10 is mounted.

4. Temperature Control of DOC 22a

(28) If fuel is added from the fuel adding valve 24 so that a concentration of H.sub.2SO.sub.4 in the exhaust emission which is downstream of the DOC 22a does not become excessively high, generation of sulfate white smoke in PM regeneration control can be restrained. Thus, the ECU 30 of the present embodiment calculates a concentration of SO.sub.3 by using a control model. The ECU 30 calculates a target temperature (hereinafter, also referred to as a target bed temperature Ttrg) of the bed temperature of the DOC 22a under PM regeneration control so that a concentration of SO.sub.3 at a downstream side of the DOC 22a satisfies a constraint concerning sulfate white smoke. A constraint SO.sub.3 concentration (an upper limit value of the SO.sub.3 concentration at the downstream side of the DOC 22a) like this can be stored in the ROM of the ECU 30, for example.

(29) The ECU 30 calculates a fuel amount to be added from the fuel addition valve 24 based on the target bed temperature Ttrg. In the following explanation, the fuel amount for realizing the target bed temperature Ttrg will be referred to as a constraint satisfying fuel amount. When the DPF fuel amount is larger than the constraint satisfying fuel amount, the constraint satisfying fuel amount is adopted instead of the DPF fuel amount. This makes it possible to restore the function of oxidizing HC and the like in the DOC 22a while satisfying the constraint on the sulfate white smoke.

5. Feature of Present Embodiment

(30) The inventor of the present application keenly studied on the SOx reaction at the DOC 22a under PM regeneration control. Then, the inventor noticed that not only the oxidation reaction from SO.sub.2 to SO.sub.3 but also the reduction reaction from SO.sub.3 to SO.sub.2 actively occurred in the DOC 22a under PM regeneration control. As in the conventional technique, in the control model not considering the reduction reaction, the amount of SO.sub.3 discharged from the DOC 22a is calculated more than it actually is. As a result, the target bed temperature Ttrg is set to a temperature lower than an actually allowed bed temperature. In this case, the execution period of PM regeneration control is prolonged, resulting in deterioration of fuel efficiency.

(31) In the system of the present embodiment, the reduction reaction of SO.sub.3 at the DOC 22a under PM regeneration control is included in the control model. As a result, the estimation accuracy of the amount of SO.sub.3 discharged from the DOC 22a can be increased, so that the target bed temperature Ttrg can be brought close to the actually allowed bed temperature. As a result, it is possible to suppress the execution period of the PM regeneration control from prolonging, so that deterioration of fuel economy is suppressed. Hereinafter, the calculation logic of the target bed temperature Ttrg executed in the system of the present embodiment will be described in detail.

6. Calculation Logic of Target Bed Temperature Ttrg

(32) FIG. 3 is a functional block diagram showing a logic for calculating the target bed temperature Ttrg, and this is realized by the ECU 30. As shown in FIG. 3, the ECU 30 includes an inflow SOx amount estimating section M1, a SOx saturation factor estimating section M2, a newly adsorbing SOx amount and passing SOx amount estimating section M3, a SOx distribution after adsorption estimating section M4, a newly desorbing SOx amount estimating section M5, a final adsorbed SOx distribution estimating section M6, a passing SO.sub.3 amount estimating section M7, an SO.sub.2 reduction rate estimating section M8, an allowable desorption SO.sub.3 amount calculating section M9, and a white smoke restraint target bed temperature calculating section M10, and calculates the target bed temperature Ttrg at each control period (more specifically, at each combustion cycle of the engine 10) by these elements M1 to M9. In the following explanation, the elements M1 to M9 will be simplified, and for example, the inflow SOx amount estimating section M1 will be also referred to as the estimating section M1.

(33) The estimating section M1 estimates an amount of SOx (hereinafter, also referred to as an inflow SOx amount) that flows into the DOC 22a. Note that SOx that flows into the DOC 22a mentioned in the present description includes not only SOx which is generated in the engine 10, and is discharged from the engine 10 to flow into the DOC 22a, but also SOx which is generated with an oxidation reaction in the DOC 22a, of the fuel added from the fuel adding valve 24 and flows on the DOC 22a.

(34) The estimating section M1 specifically estimates the inflow SOx amount in a t.sup.th cycle by formula (1) as follows having an injection fuel amount (an in-cylinder injection amount) from the injectors 12 and an added fuel amount (exhaust emission addition amount) from the fuel adding valve 24 as variables. A fuel S concentration in formula (1) is a sulfur concentration in fuel, and a detection value of a sulfur concentration sensor which is additionally provided in a fuel supply system may be used, or a set value may be used.
Inflow SOx amount(exhaust emission addition amount(t),incylinder injection amount(t)) [g/s]=inflow fuel amount(exhaust emission addition amount(t),incylinder injection amount(t)) [g/s]fuel S concentration [ppm](1)

(35) The inflow fuel amount (the exhaust emission addition amount (t), the in-cylinder injection amount (t)) in formula (1) is an amount in the t.sup.th cycle of the fuel from which SOx flowing into the DOC 22a is derived, and is calculated from formula (2) as follows by using a specific gravity (light oil specific gravity) of the fuel.
Inflow SOx amount(exhaust emission addition amount(t),incylinder injection amount(t)) [g/s]=(exhaust emission addition amount(t) [g/s]/1000light oil specific gravity [g/cm.sup.3]+incylinder injection amount(t) [g/s])(2)

(36) In the following explanation, the inflow SOx amount (exhaust emission addition amount (t), in-cylinder injection amount (t)) will be also referred to as an inflow SOx amount (t). Further, the inflow fuel amount (exhaust emission addition amount (t), in-cylinder injection amount (t)) will be also referred to as an inflow fuel amount (t).

(37) The estimating section M2 estimates a saturation factor of SOx (hereinafter, also referred to as a SOx saturation factor) in the DOC 22a. In estimation of the SOx saturation factor, a distribution (hereinafter, also referred to as an adsorbed SOx distribution) which is expressed as a graph in which an amount of SOx (hereinafter, also referred to as an adsorbed SOx amount) adsorbing to the DOC 22a in each of bed temperatures in increase of the bed temperature of the DOC 22a is related with the bed temperature of the DOC 22a, and a distribution (hereinafter, also referred to as a saturation SOx distribution) which is expressed as a graph in which a maximum amount of SOx (hereinafter, also referred to as a saturation SOx amount) adsorbing the DOC 22a in each of the bed temperatures in increase of the bed temperature of the DOC 22a is related with the bed temperature of the DOC 22a are used. First, the adsorbed SOx distribution and the saturation SOx distribution will be described with reference to FIG. 4 with SO.sub.3 as an example.

(38) FIG. 4 is a diagram for describing an adsorbed SOx distribution and a saturation SOx distribution. Data shown as adsorbed SO.sub.3 amount in FIG. 4 is collected by the following method. More specifically, the DOC 22a is caused to adsorb a sufficient amount of SOx in a bed temperature shown as a present temperature in FIG. 4, first. Subsequently, amounts of SO.sub.3 desorbed from the DOC 22a in the respective bed temperatures in increase of the bed temperature of the DOC 22a are measured under a condition with an increasing speed set as constant. Subsequently, a graph is created by relating the desorbed SO.sub.3 amounts with the bed temperatures of the DOC 22a. Thereby, the distribution expressing the desorbed SO.sub.3 amount (hereinafter, also referred to as a desorbed SO.sub.3 distribution) can be obtained. By a similar method to this, a graph (hereinafter, also referred to as a desorbed SO.sub.2 distribution) in which the amounts of SO.sub.2 desorbed from the DOC 22a in the respective bed temperatures in increase of the bed temperature of the DOC 22a is related with the bed temperature of the DOC 22a can be also obtained. The SO.sub.3 which is desorbed from the DOC 22a may be directly measured by a sensor, or may be calculated from a difference of SOx and SO.sub.2 by measuring both SOx and SO.sub.2 by using sensors for detecting SOx and SO.sub.2 (SO.sub.3=SOxSO.sub.2).

(39) Here, SO.sub.3 which is desorbed from the DOC 22a during increase of the bed temperature of the DOC 22a is actually SO.sub.3 which is adsorbed to the DOC 22a at the bed temperature shown as the present temperature in FIG. 4. However, SO.sub.3 which is desorbed from the DOC 22a at a certain bed temperature is SO.sub.3 that can continue to adsorb to the DOC 22a until the bed temperature reaches the certain bed temperature, and to describe more, can be also considered as SO.sub.3 that can adsorb to the DOC 22a at the certain bed temperature. If a vertical axis of the aforementioned desorbed SO.sub.3 distribution is replaced with amounts of SO.sub.3 which adsorbs to the DOC 22a at the respective bed temperatures in increase of the bed temperature of the DOC 22a, on the basis of an assumption as above, the graph of the data of the adsorbed SO.sub.3 amount shown in FIG. 4, that is, the adsorbed SO.sub.3 distribution can be obtained. By a method similar to this, an adsorbed SO.sub.2 distribution can be also obtained.

(40) Further, data shown as a saturation SO.sub.3 amount in FIG. 4 is collected by a method similar to the data of the adsorbed SO.sub.3 amount. The data of the saturation SO.sub.3 amount specifically corresponds to an amount of SO.sub.3 which is desorbed from the DOC 22a in each of the bed temperatures (intervals of 5 C., for example) under increase of the bed temperature of the DOC 22a under a condition that an increase speed is set as an extremely low speed. Since the increase speed of the bed temperature of the DOC 22a is an extremely low speed, the data of the saturation SO.sub.3 amount can be considered as a maximum value of the amount of SO.sub.3 which is desorbed from the DOC 22a. Further, the aforementioned assumption can be applied to the maximum value. That is, a maximum amount of SO.sub.3 that is desorbed from the DOC 22a at a certain bed temperature can be considered as equal to a maximum amount of SO.sub.3 that can adsorb to the DOC 22a at the certain bed temperature. If a vertical axis of the aforementioned desorbed SO.sub.3 distribution is replaced with the maximum amount of the SO.sub.3 described above on the basis of an assumption like this, the graph of the data of the saturation SO.sub.3 amount shown in FIG. 4, that is, the saturation SO.sub.3 distribution can be obtained. By a method similar to this, a saturation SO.sub.2 distribution can be also obtained.

(41) The estimating section M2 estimates the SOx saturation factor (T.sub.2(t), t) in the t.sup.th cycle by formula (3) as follows having a present bed temperature T.sub.2 of the DOC 22a in the t.sup.th cycle as a variable. As the present bed temperature T.sub.2 which is a representative value of the present bed temperature of the DOC 22a, a detection value of the temperature sensor 34 can be used, for example.
SOx saturation factor(T.sub.2(t),t)=1(total adsorption allowance amount(T.sub.2(t),t)/total saturation amount(T.sub.2(t),t))(3)

(42) A calculation process of the SOx saturation factor (T.sub.2(t), t) in formula (3) is as follows. First, by formulae (4) and (5) as follows having a bed temperature T.sub.1 under increase of the bed temperature of the DOC 22a and the present bed temperature T.sub.2 as variables, a saturation SO.sub.2 distribution (T.sub.1, T.sub.2(t), t) and a saturation SO.sub.3 distribution (T.sub.1, T.sub.2(t), t) in the t.sup.th cycle are respectively calculated.
Saturation SO.sub.2 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]=reference saturation SO.sub.2 distributionbed temperature correction SO.sub.2 map(T.sub.2(t)) [g/ C.](4)
Saturation SO.sub.3 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]=reference saturation SO.sub.3 distributionbed temperature correction SO.sub.3 map(T.sub.2(t)) [g/ C.](5)

(43) The reference saturation SO.sub.2 distribution in formula (4) is a saturation SO.sub.2 distribution which is created by setting the bed temperature (the present temperatures in FIG. 4) at the time of causing a sufficient amount of SOx to adsorb to the DOC 22a as a reference bed temperature (a bed temperature in a vicinity of 300 C. at which the aforementioned adsorption limit amount becomes maximum, for example). The same also applies to the reference saturation SO.sub.3 distribution in formula (5). The bed temperature correction SO.sub.2 map (T.sub.2(t)) in formula (4) is a map which sets a correction value for converting the reference saturation SO.sub.3 distribution into the saturation SO.sub.2 distribution at a present bed temperature T.sub.2. The bed temperature correction SO.sub.3 map (T.sub.2(t)) in formula (5) is similar to this. The reference saturation SOx distribution and the correction map like them can be stored in the ROM of the ECU 30, for example, and can be properly read in accordance with the present bed temperature T.sub.2.

(44) A relation between the reference saturation SOx distribution and the saturation SOx distribution after correction will be described with reference to FIG. 5 with SO.sub.2 as an example. FIG. 5 is a diagram for describing a relation between a reference saturation SOx distribution and a saturation SOx distribution after correction. Note that TL and TH in a horizontal axis in FIG. 6 respectively correspond to a temperature (a lower limit temperature) at which SO.sub.2 starts to desorb from the DOC 22a during increase of the bed temperature of the DOC 22a, and a temperature (an upper limit temperature) at which SO.sub.2 finishes desorbing from the DOC 22a. Difference among three kinds of distributions shown in FIG. 6 lies in the present bed temperature T.sub.2. That is, in a case where the present bed temperature T.sub.2 is equal to the reference temperature, a shape of the saturation SO.sub.2 distribution after correction corresponds to a shape of the reference saturation SO.sub.2 distribution (center). In a case where the present bed temperature T.sub.2 is lower than the reference temperature (a left side), and in a case where the present bed temperature T.sub.2 is higher than the reference temperature (a right side), the shapes of the saturation SO.sub.2 distributions after correction do not correspond to the shape of the reference saturation SO.sub.2 distribution. In the case where the present bed temperature T.sub.2 is higher than the reference temperature (the right side), the shape of the saturation SO.sub.2 distribution after correction is in such a shape that data at lower temperatures than the present bed temperature T.sub.2 are omitted. The reason is that it is conceivable that at the lower temperatures than the present bed temperature T.sub.2, SOx that could have originally continued to adsorb to the DOC 22a in the bed temperature range already desorbs from the DOC 22a.

(45) Subsequently, the saturation SO.sub.2 distribution (T.sub.1, T.sub.2(t), t) which is calculated by formula (4) is substituted into formula (6) as follows, and a total saturation SO.sub.2 amount (T.sub.2(t), t) in the t.sup.th cycle is calculated. Further, the saturation SO.sub.3 distribution (T.sub.1, T.sub.2(t), t) which is calculated by formula (5) is substituted into formula (7) as follows, and the total saturation SO.sub.3 amount in the t.sup.th cycle is calculated.
Total saturation SO.sub.2 amount(T.sub.2(t),t) [g]=.sub.TL.sup.THSaturation SO.sub.2 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]dT.sub.1(6)
Total saturation SO.sub.3 amount(T.sub.2(t),t) [g]=.sub.TL.sup.THSaturation SO.sub.3 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]dT.sub.1(7)

(46) After the total saturation SO.sub.2 amount (T.sub.2(t), t) and the total saturation SO.sub.3 amount (T.sub.2(t), t) are calculated, these amounts are substituted into formula (8) as follows, and a total saturation amount (T.sub.2(t), t) in the t.sup.th cycle is calculated.
Total saturation amount(T.sub.2(t),t)=Total saturation SO.sub.2 amount(T.sub.2(t),t)+Total saturation SO.sub.3 amount(T.sub.2(t),t)(8)

(47) In the following explanation, the total saturation SO.sub.2 amount (T.sub.2(t), t) will be also simply referred to as a total saturation SO.sub.2 amount (t). Further, the total saturation SO.sub.3 amount (T.sub.2 (t), t) will be also simply referred to as a total saturation SO.sub.3 amount (t). Further, the total saturation amount (T.sub.2(t), t) will be also simply referred to as a total saturation amount (t).

(48) After the total saturation amount (t) is calculated by formula (8), the saturation SO.sub.2 distribution (T.sub.1, T.sub.2(t), t), and a final adsorbed SO.sub.2 distribution (T.sub.1, t) in the t.sup.th cycle which is estimated in the estimating section M6 are substituted into formula (9) as follows, and an adsorption allowance SO.sub.2 distribution (T.sub.1, T.sub.2(t), t) in the t.sup.th cycle is calculated. Further, the saturation SO.sub.3 distribution (T.sub.1, T.sub.2(t), t) and a final adsorbed SO.sub.3 distribution (T.sub.1, t) in the t.sup.th cycle which is estimated in the estimating section M6 are substituted into formula (10) as follows, and adsorption allowance SO.sub.3 distribution (T.sub.1, T.sub.2(t), t) in the t.sup.th cycle is calculated.
Adsorption allowance SO.sub.2 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]=max{saturation SO.sub.2 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]final adsorbed SO.sub.2 distribution(T.sub.1,t) [g/ C.],0}(9)
Adsorption allowance SO.sub.3 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]=max{saturation SO.sub.3 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]final adsorbed SO.sub.3 distribution(T.sub.1,t) [g/ C.],0}(10)

(49) Subsequently, the adsorption allowance SO.sub.2 distribution (T.sub.1, T.sub.2(t), t) which is calculated by formula (9) is substituted into formula (11) as follows, and a total adsorption allowance SO.sub.2 amount (T.sub.2(t), t) in the t.sup.th cycle is calculated. Further, the adsorption allowance SO.sub.3 distribution (T.sub.1, T.sub.2(t), t) which is calculated by formula (10) is substituted into formula (12) as follows, and a total adsorption allowance SO.sub.3 amount (T.sub.2(t), t) in the t.sup.th cycle is calculated.
Total adsorption allowance SO.sub.2 amount(T.sub.2(t),t) [g]=.sub.TL.sup.THadsorption allowance SO.sub.2 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]dT.sub.1(11)
Total adsorption allowance SO.sub.3 amount(T.sub.2(t),t) [g]=.sub.TL.sup.THadsorption allowance SO.sub.3 distribution(T.sub.1,T.sub.2(t),t) [g/ C.]dT.sub.1(12)

(50) In the following explanation, the adsorption allowance SO.sub.2 distribution (T.sub.1, T.sub.2(t), t) will be also simply referred to as the adsorption allowance SO.sub.2 distribution (t). Further, the adsorption allowance SO.sub.3 distribution (T.sub.1, T.sub.2(t), t) will be also simply referred to as the adsorption allowance SO.sub.3 distribution (t). Further, the total adsorption allowance SO.sub.2 amount (T.sub.2(t), t) will be also simply referred to as the total adsorption allowance SO.sub.2 amount (t). Further, the total adsorption allowance SO.sub.3 amount (T.sub.2(t), t) will be also simply referred to as the total adsorption allowance SO.sub.3 amount (t).

(51) With reference to FIG. 6, the total adsorption allowance SO.sub.2 amount (t) will be described. The same applies to the total adsorption allowance SO.sub.3 amount (t). As shown in FIG. 7, the total adsorption allowance SO.sub.2 amount (t) can be expressed as an area obtained by excluding an overlapping portion of the saturation SO.sub.2 distribution and the adsorbed SO.sub.2 distribution from the saturation SO.sub.2 distribution. As shown as a region A in a distribution at a right side of FIG. 7, in a case where an amount of SO.sub.2 adsorbing to the DOC 22a in each of the bed temperatures under increase of the bed temperature of the DOC 22a, that is, the adsorbed SO.sub.2 amount exceeds a maximum amount thereof, that is, the saturation SO.sub.2 amount, the adsorbed SO.sub.2 amount is excluded from calculation of the total adsorption allowance SO.sub.2 amount (t), because the DOC 22a is considered to be saturated. Further, the reason why in the distribution at the right side, data at lower temperatures than the present bed temperature T.sub.2 are omitted is as described in FIG. 5.

(52) After the total adsorption allowance SO.sub.2 amount (t) and the total adsorption allowance SO.sub.3 amount (t) are calculated, these amounts are substituted into formula (13) as follows, and a total adsorption allowance amount (T.sub.2(t), t) in the t.sup.th cycle is calculated.
Total adsorption allowance amount(T.sub.2(t),t)=Total adsorption allowance SO.sub.2 amount(T.sub.2(t),t)+Total adsorption allowance SO.sub.3 amount(T.sub.2(t),t)(13)

(53) Further, if the total saturation amount (t) which is calculated by formula (8), and the total adsorption allowance amount (t) which is calculated by formula (13) are substituted into formula (3), the saturation factor (T.sub.2(t), t) can be calculated. In the following explanation, the saturation factor (T.sub.2(t), t) will be also simply referred to as the saturation factor (t).

(54) Returning to FIG. 3, explanation of the calculation logic of the target bed temperature Ttrg will be continued. The estimating section M3 estimates an amount of SOx (hereinafter, also referred to as a newly adsorbing SOx amount) that is SOx flowing into the DOC 22a and newly adsorbs to the DOC 22a, and an amount of SOx (hereinafter, also referred to as a passing SOx amount) that is SOx flowing into the DOC 22a and passes through the DOC 22a without adsorbing to the DOC 22a. First of all, a relation between the newly adsorbing SOx amount and the passing SOx amount will be described with reference to FIG. 7. FIG. 7 is a view for describing a relation between a newly adsorbing SOx amount and a passing SOx amount. As shown by arrows in FIG. 7, a sum of the newly adsorbing SOx amount and the passing SOx amount is equal to the inflow SOx amount. The reason is that a part of SOx flowing into the DOC 22a adsorbs to the DOC 22a, and the remainder passes through the DOC 22a without adsorbing to the DOC 22a.

(55) The estimating section M3 estimates the newly adsorbing SOx amount by formula (14) as follows having the inflow SOx amount (t) which is estimated in the estimating section M1 and the saturation rate (t) which is estimated in the estimating section M2 as variables, and estimates the passing SOx amount by formula (15) as follows.
Newly adsorbing SOx amount (inflow SOx amount(t),saturation factor(t)) [g/s]=inflow SOx amount(t)adsorption rate map(saturation factor(t))(14)
Passing SOx amount(inflow SOx amount(t),saturation factor(t)) [g/s]=inflow SOx amount(t){1adsorption rate map(saturation factor(t))}(15)

(56) In the following explanation, the newly adsorbing SOx amount (inflow SOx amount (t), saturation factor (t)) will be also simply referred to as the newly adsorbing SOx amount (t). Further, the passing SOx amount (inflow SOx amount (t), saturation factor (t)) will be also simply referred to as the passing SOx amount (t).

(57) The adsorption rate map in formulae (14) and (15) is a map which is created on the basis of a characteristic that a ratio (that is, an adsorption rate) of SOx adsorbing to the DOC 22a of SOx flowing into the DOC 22a in the t.sup.th cycle varies in accordance with the saturation factor (t). FIG. 8 is a diagram for describing an adsorption rate map. The characteristic of the adsorption rate map is such that the adsorption rate is high in a region where the saturation factor (t) is low, and as the saturation factor (t) becomes higher, the adsorption rate gradually reduces, as shown in FIG. 8. The map like this can be stored in the ROM of the ECU 30, for example, and can be properly read in accordance with the present bed temperature T.sub.2.

(58) Returning to FIG. 3, the estimating section M4 estimates a SOx distribution after adsorption by reflecting the newly adsorbing SOx amount estimated in the estimating section M3 in the adsorption SOx distribution. The SOx distribution after adsorption will be described with reference to FIG. 9 with SO.sub.2 as an example. FIG. 9 is a diagram for describing an SOx distribution after adsorption. As shown in FIG. 9, the SO.sub.2 distribution after adsorption is estimated by adding a distribution (hereinafter, also referred to as a newly adsorbing SO.sub.2 distribution) expressing an amount of SO.sub.2 that newly adsorbs to the DOC 22a in a cycle of this time (for example, the t.sup.th cycle) to a final adsorbed SO.sub.2 distribution in a cycle of a previous time (for example, a t1.sup.th cycle).

(59) The estimating section M4 specifically calculates the newly adsorbing SO.sub.2 distribution in the t.sup.th cycle by formula (16) as follows having the newly adsorbing SOx amount (t), the total adsorption allowance amount (t) and the adsorption allowance SO.sub.2 distribution (t) as variables. Similarly to the newly adsorbing SO.sub.2 distribution, the estimating section M4 calculates a distribution (hereinafter, also referred tows a newly adsorbing SO.sub.3 distribution) expressing an amount of SO.sub.3 which newly adsorbs to the DOC 22a from formula (17) as follows. For the adsorption allowance SO.sub.2 distribution (t) and the total adsorption allowance amount (t), the values calculated in the estimating section M2 are used.
Newly adsorbing SO.sub.2 distribution(newly adsorbing SOx amount(t),adsorption allowance SO.sub.2 distribution(t),total adsorption allowance amount(t)) [g/ C.]=adsorption allowance SO.sub.2 distribution(t) [g/ C.]{newly adsorbed SOx amount(t)/total adsorption allowance amount(t)}(16)
Newly adsorbing SO.sub.3 distribution(newly adsorbing SOx amount(t),adsorption allowance SO.sub.3 distribution(t),total adsorption allowance amount(t)) [g/ C.]=adsorption allowance SO.sub.3 distribution(t) [g/ C.]{newly adsorbed SOx amount(t)/total adsorption allowance amount(t)}(17)

(60) In the following explanation, the newly adsorbing SO.sub.2 distribution (newly adsorbing SOx amount (t), adsorption allowance SO.sub.2 distribution (t), total adsorption allowance amount (t)) will be also simply referred to as the newly adsorbing SO.sub.2 distribution (t). Further, the newly adsorbing SO.sub.3 distribution (newly adsorbing SOx amount (t), adsorption allowance SO.sub.3 distribution (t), total adsorption allowance amount (t)) will be also simply referred to as the newly adsorbing SO.sub.3 distribution (t).

(61) Subsequently, the estimating section M4 substitutes the calculated newly adsorbing SO.sub.2 distribution, and the final adsorbed SO.sub.2 distribution (t1) in the t1.sup.th cycle into formula (18) as follows, and calculates the SO.sub.2 distribution after adsorption. Further, the estimating section M4 substitutes the calculated newly adsorbing SO.sub.3 distribution, and the adsorbed SO.sub.3 distribution (t1) estimated in the estimating section M6 in the t1.sup.th cycle into formula (19) as follows, and calculates the SO.sub.3 distribution after adsorption.
SO.sub.2 distribution after adsorption(t) [g/ C.]=final adsorbed SO.sub.2 distribution(t1) [g/ C.]+newly adsorbing SO.sub.2 distribution(t) [g/ C.](18)
SO.sub.3 distribution after adsorption(t) [g/ C.]=final adsorbed SO.sub.3 distribution(t1) [g/ C.]+newly adsorbing SO.sub.3 distribution(t) [g/ C.](19)

(62) Returning to FIG. 3, the estimating section M5 estimates an amount of SOx (hereinafter, also referred to as a newly desorbing SOx amount) which newly desorbs from the DOC 22a, on the basis of the SOx distribution after adsorption which is estimated in the estimating section M4.

(63) First of all, the estimating section M5 specifically estimates a total amount of SOx (hereinafter, also referred to as a total desorbable SOx amount) that can desorb from the DOC 22a. The total desorbable SOx amount will be described with reference to FIG. 10 with SO.sub.2 as an example. FIG. 10 is a diagram for describing a total desorbable SOx amount. Note that TL and TH in a horizontal axis in FIG. 10 respectively correspond to the lower limit temperature and the upper limit temperature described above. As shown in FIG. 10, the total desorbable SOx amount corresponds to an area of the SOx distribution after adsorption at a side of lower temperatures than the present bed temperature T.sub.2 and at a side of higher temperatures than the lower limit temperature TL.

(64) A total amount of SO.sub.2 that can desorb from the DOC 22a, that is, the total desorbable SO.sub.2 amount is calculated from formula (20) as follows having the present bed temperature T.sub.2 as a variable. A total amount of SO.sub.3 that can desorb from the DOC 22a, that is, a total desorbable SO.sub.3 amount is calculated by formula (21) as follows having the present bed temperature T.sub.2 as a variable.

(65) $\begin{array}{cc}\mathrm{Total}\mathrm{desorbable}{\mathrm{SO}}_2\mathrm{amount}\left(T_2\left(t\right),t\right)\left[g\right]=\{\begin{array}{cc}0& \left(T_2\left(t\right)<\mathrm{TL}\right)\\ {}_{T1}^{T2\left(t\right)}{\mathrm{SO}}_2\mathrm{distribution}\mathrm{after}\mathrm{adsorption}\left(t\right){\mathrm{dT}}_1& \left(T_2\left(t\right)\mathrm{TL}\right)\end{array}& \left(20\right)\\ \mathrm{Total}\mathrm{desorbable}{\mathrm{SO}}_3\mathrm{amount}\left(T_2\left(t\right),t\right)\left[g\right]=\{\begin{array}{cc}0& \left(T_2\left(t\right)<\mathrm{TL}\right)\\ {}_{T1}^{T2\left(t\right)}{\mathrm{SO}}_3\mathrm{distribution}\mathrm{after}\mathrm{adsorption}\left(t\right){\mathrm{dT}}_1& \left(T_2\left(t\right)\mathrm{TL}\right)\end{array}& \left(21\right)\end{array}$

(66) The estimating section M5 substitutes the calculated total desorbable SO.sub.2 amount into formula (22) as follows, and calculates an amount of SO.sub.2 that newly desorbs from the DOC 22a in the t.sup.th cycle, that is, a newly desorbing SO.sub.2 amount. Further, the estimating section M5 substitutes the calculated total desorbable SO.sub.3 amount into formula (23) as follows, and calculates an amount of SO.sub.3 that newly desorbs from the DOC 22a in the t.sup.th cycle, that is, a newly desorbing SO.sub.3 amount. For desorption rates in formulae (22) and (23), set values are used, and can be stored in the ROM of the ECU 30, for example.
Newly desorbing SO.sub.2 amount(T.sub.2(t),t) [g]=total desorbable SO.sub.2 amount [g]desorption rate(22)
Newly desorbing SO.sub.3 amount(T.sub.2(t),t) [g]=total desorbable SO.sub.3 amount [g]desorption rate(23)

(67) Returning to FIG. 3, the estimating section M6 reflects the newly desorbing SOx amount which is estimated in the estimating section M5 in the SOx distribution after adsorption, and estimates a final adsorbed SOx distribution.

(68) The estimating section M6 specifically assumes that SOx desorbs by the amount corresponding to the newly desorbing SOx amount estimated in the estimating section M5, and a shape of the SOx distribution after adsorption changes, and estimates the final adsorbed SOx distribution (a SOx distribution after desorption). A relation between the final adsorbed SOx distribution and the SOx distribution after adsorption will be described with reference to FIG. 11 with SO.sub.2 as an example. FIG. 11 is a diagram for describing a relation between a final desorbed SOx distribution and the SOx distribution after adsorption. Note that TL and TH in a horizontal axis of FIG. 11 respectively correspond to the lower limit temperature and the upper limit temperature described above. As shown in FIG. 11, a distribution which remains after an area of the SO.sub.2 distribution after adsorption at the time of an integral value of the SO.sub.2 distribution after adsorption from the lower limit temperature TL corresponding to the newly desorbing SO.sub.2 amount, that is, an area from the lower limit temperature TL to a temperature Tdso.sub.2 is removed from the SOx distribution after adsorption becomes the final adsorbed SO.sub.2 distribution.

(69) In a case where the temperature Tdso.sub.2 in FIG. 11 exceeds the bed temperature T.sub.1, the case means that SO.sub.2 is totally desorbed from the DOC 22a. Considering this, the final adsorbed SO.sub.2 distribution in the t.sup.th cycle is expressed by formula (24) as follows having the bed temperature T.sub.1 as a variable, and the final adsorbed SO.sub.3 distribution in the t.sup.th cycle is expressed by formula (25) as follows. A temperature Tdso.sub.3 in formula (25) corresponds to a floor temperature T.sub.1 at a time of an integral value from the lower limit temperature TL, of the SO.sub.3 distribution after adsorption corresponding to the newly desorbing SO.sub.3 amount.

(70) $\begin{array}{cc}\mathrm{Final}\mathrm{absorbed}{\mathrm{SO}}_2\mathrm{distribution}\left(T_1,t\right)\left[g\right]=\{\begin{array}{cc}0& \left(T_1\left(t\right)<{\mathrm{Td}}_{\mathrm{SO}2}\right)\\ {\mathrm{SO}}_2\mathrm{distribution}\mathrm{after}\mathrm{adsorption}& \left(T_1\left(t\right){\mathrm{Td}}_{\mathrm{SO}2}\right)\end{array}& \left(24\right)\\ \mathrm{Final}\mathrm{absorbed}{\mathrm{SO}}_3\mathrm{distribution}\left(T_1,t\right)\left[g\right]=\{\begin{array}{cc}0& \left(T_1\left(t\right)<{\mathrm{Td}}_{\mathrm{SO}3}\right)\\ {\mathrm{SO}}_3\mathrm{distribution}\mathrm{after}\mathrm{adsorption}& \left(T_1\left(t\right){\mathrm{Td}}_{\mathrm{SO}3}\right)\end{array}& \left(25\right)\end{array}$

(71) A relation between the newly desorbing SO.sub.2 amount and the temperature Tdso.sub.2 can be expressed by formula (26) as follows, and a relation between the newly desorbing SO.sub.3 amount and the temperature Tdso.sub.3 can be expressed by formula (27) as follows.
.sub.TL.sup.TdSO2SO.sub.2 distribution after adsorption(T.sub.1,t) [g/ C.]dT.sub.1=Newly desorbing SO.sub.2 amount(t) [g](26)
.sub.TL.sup.TdSO3SO.sub.3 distribution after adsorption(T.sub.1,t) [g/ C.]dT.sub.1=Newly desorbing SO.sub.3 amount(t) [g](27)

(72) Returning to FIG. 3, the estimating section M7 estimates an amount of SOx (hereinafter, also referred to as a passing SO.sub.3 amount) to be converted to SO.sub.3 in the aforementioned passing SOx.

(73) As described in FIG. 2, in the DOC 22a, a part of SO.sub.2 that is adsorbed to the precious metal 22d is converted into SO.sub.3. Assuming that the conversion also occurs to SO.sub.2 in the passing SOx, the rate at which passing SOx converts to SO.sub.3 depends on the present bed temperature T.sub.2 and the exhaust flow rate (gas flow rate) GA of engine 10. The estimating section M7 estimates the passing SO.sub.3 amount in the t.sup.th cycle by formula (28) as follows having a passing amount, the present bed temperature T.sub.2, and gas flow rate GA as variables. An amount of SO.sub.2 (hereinafter, also referred to as a passing SO.sub.2 amount) that is not converted to SO.sub.3 in the passing SOx can be expressed by formula (29) as follows.
Passing SO.sub.3 amount(passing amount(t),T.sub.2(t)) [g/s]=Passing SOx amount(t) [g]SO.sub.3 conversion rate map(T.sub.2(t))SO.sub.3 conversion rate correction map(GA(t))(28)
Passing SO.sub.2 amount(passing amount(t),T.sub.2(t)) [g/s]=Passing SOx amount(t) [g]{1SO.sub.3 conversion rate map(T.sub.2(t))}{1SO.sub.3 conversion rate correction map(GA(t))}(29)

(74) The SO.sub.3 conversion rate map (T.sub.2(t)) in formulae (28) and (29) is a map which is created on the basis of a characteristic that a ratio (that is, the SO.sub.3 conversion rate) of SOx discharged in the state of SO.sub.3 from the DOC 22a of the SOx flowing into the DOC 22a in the t.sup.th cycle varies in accordance with the present bed temperature T.sub.2 of the DOC 22a. FIG. 12 is a diagram for describing an SO.sub.3 conversion rate map. For example, the characteristic of the SO.sub.3 conversion rate map is such that as shown in FIG. 12, when the present bed temperature T.sub.2 is in a certain temperature range , the SO.sub.3 conversion rate is high, and at a side of lower temperatures than the temperature range , conversion to SO.sub.3 from SO.sub.2 hardly occurs. The map like this can be stored in the ROM of the ECU 30, for example, and can be properly read in accordance with the present bed temperature T.sub.2.

(75) The SO.sub.3 conversion rate correction map (GA(t)) in formulae (28) and (29) is a map which is created on the basis of a characteristic that a conversion rate of SO.sub.3 in the t.sup.th cycle varies in accordance with a gas flow rate GA. FIG. 13 is a diagram for describing an SO.sub.3 conversion rate correction map. For example, the characteristic of the SO.sub.3 conversion rate correction map is such that as shown in FIG. 13, when the gas flow rate GA is in a certain gas flow rate range , the SO.sub.3 conversion rate is high, and at a side of higher flow rates than the gas flow rate range , the higher the gas flow rate GA becomes, the harder conversion to SO.sub.3 from SO.sub.2 hardly occurs. The map like this can be stored in the ROM of the ECU 30, for example, and can be properly read in accordance with the gas flow rate GA. As the gas flow rate GA, a detection value of the airflow meter 32 can be used, for example.

(76) Returning to FIG. 3, the estimating section M8 estimates a ratio of reduction of SO.sub.3 to SO.sub.2 (hereinafter, also referred to as a SO.sub.2 reduction rate) in the DOC 22a among the passing SOx described above.

(77) In the DOC 22a, part of SO.sub.3 is converted to SO.sub.2 by reduction reaction. The reduction reaction to SO.sub.2 is influenced by the reducing atmosphere of the DOC 22a. The estimating section M8 estimates the SO.sub.2 reduction rate in the t.sup.th cycle by formula (30) as follows having a ratio F/A of the exhaust emission addition amount to the exhaust flow rate (gas flow rate) GA as variable.
SO.sub.2 reduction rate(F/A(t)) []=SO.sub.2 reduction rate map(F/A(t))(30)

(78) The SO.sub.2 reduction rate map (F/A(t)) in formula (30) is a map which is created on the basis of a characteristic that a SO.sub.2 reduction rate in the t.sup.th cycle varies in accordance with the F/A indicating the strength of the reducing atmosphere of the DOC 22a. FIG. 14 is a diagram for describing the SO.sub.2 reduction rate map. For example, as shown in FIG. 14, the characteristic of the SO.sub.2 reduction rate map shows a tendency that as the F/A increases from 0, that is, as the reducing atmosphere becomes stronger, the SO.sub.2 reduction rate gradually increases from 0 to 1 and thereafter is maintained in the vicinity of 1. The map like this can be stored in the ROM of the ECU 30, for example, and can be properly read in accordance with the F/A. The F/A in the t.sup.th cycle can be calculated by the formula (31) having the passing amount and the gas flow rate GA flowing into the DOC 22a as variables.
F/A(passing amount(t),GA(t))=exhaust emission addition amount(t)/1000light oil specific gravity [g/cm.sup.3]/GA[g/s](31)

(79) Returning to FIG. 3, the calculating section M9 calculates an amount of SO.sub.3 (hereinafter, also referred to as an allowable desorption SO.sub.3 amount) that may be desorbed from the DOC 22a during increase of the bed temperature of the DOC 22a. The allowable desorption SO.sub.3 amount will be described with reference to FIG. 15. FIG. 15 is a view for describing an allowable desorption SO.sub.3 amount. A constrained SO.sub.3 amount shown in FIG. 15 corresponds to a constraint concerning sulfate white smoke, and in FIG. 14, a sum of the passing SO.sub.3 amount and the allowable desorption SO.sub.3 amount is equal to the constrained SO.sub.3 amount. The sum of the passing SO.sub.3 amount and the allowable desorption SO.sub.3 amount is an amount of SO.sub.3 at a downstream side of the DOC 22a. Therefore, if the sum becomes the constraint SO.sub.3 amount, the constrained is satisfied.

(80) However, a part of the sum of the passing SO.sub.3 amount and the allowable desorption SO.sub.3 amount is reduced to SO.sub.2 in the course of flowing through the DOC 22a. Therefore, if allowable desorption SO.sub.3 amount satisfies the following formula (32) with constrained SO.sub.3 amount, passing SO.sub.3 amount, and SO.sub.2 reduction rate as variables, the constraint is satisfied.
Allowable desorption SO.sub.3 amount(constraint SO.sub.3 amount(gas flow rate(t)),passing SO.sub.3 amount(t),SO.sub.2 reduction rate(F/A(t))) [g/s]=constrained SO.sub.3 amount(gas flow rate(t)) [g/s]/(1SO.sub.2 reduction rate) []passing SO.sub.3 amount(t) [g/s](32)

(81) In the following explanation, the allowable desorption SO.sub.3 amount (constraint SO.sub.3 amount (gas flow rate (t)), passing SO.sub.3 amount (t), SO.sub.2 reduction rate (F/A(t))) will be also simply referred to as the allowable desorption SO.sub.3 amount (t).

(82) Returning to FIG. 3, the calculation section M10 calculates a target bed temperature Ttrg in the t.sup.th cycle for restraining generation of sulfate white smoke under PM regeneration control. The target bed temperature Ttrg will be described with reference to FIG. 16. FIG. 16 is a diagram for describing a target bed temperature Ttrg. Note that TL and TH in a horizontal axis in FIG. 16 respectively correspond to the lower limit temperature and the upper limit temperature described above. As shown in FIG. 16, a bed temperature T.sub.1 corresponds to the target bed temperature Ttrg. The bed temperature T.sub.1 is a temperature at a time in which a value, which is obtained by multiplying an integral value from the low temperature side of the final adsorbed SO.sub.3 distribution by a desorption rate, corresponds to the allowable desorption SO.sub.3 amount calculated in the calculating section M9.

(83) A relation between the allowable desorption SO.sub.3 amount in the t.sup.th cycle and the target temperature Ttrg can be expressed by formula (33) as follows. A set value is used as the desorption rate in formula (33), and can be stored in the ROM of the ECU, for example.
.sub.TL.sup.TtrgFinal adsorbed SO.sub.3 distribution(T.sub.1,t) [g/ C.]dT.sub.1desorption rate=allowable desorption SO.sub.3 amount(t) [g](33)

(84) In this way, according to the system of the first embodiment, it is possible to improve the estimation accuracy of the amount of SO.sub.3 discharged from the DOC 22a by modeling the reduction reaction of SO.sub.3 at the DOC 22a. This makes it possible to raise the target bed temperature Ttrg while satisfying the constrained SO.sub.3 amount. As a result, generation of PM can be completed at an early stage while suppressing white smoke, so that deterioration in fuel consumption can be suppressed.

(85) In the aforementioned embodiment, the estimating section M1 corresponds to inflow SOx amount estimating section of the present disclosure. The estimating sections M2, M2 and M3 correspond to passing SO.sub.3 amount estimating section of the present disclosure. The estimating sections M5 and M6 correspond to final adsorbed SOx distribution estimating section of the present disclosure. The estimating section M8 corresponds to SO.sub.2 reduction rate estimating section of the present disclosure. The calculating section M9 corresponds to allowable desorption SO.sub.3 amount calculating section of the present disclosure. The calculating section M10 corresponds to target temperature calculating section of the present disclosure.

(86) Further, in the aforementioned embodiment, the present bed temperature T.sub.2 corresponds to the representative temperature of the present disclosure.

(87) Incidentally, in the aforementioned embodiment, PM regeneration control is performed by addition of fuel from the fuel adding valve 24. However, the PM regeneration control may be performed by injection of fuel from the injector 12 (more specifically, sub injection (for example, post injection) later than main injection). In this case, the exhaust emission addition amount in formula (1) can be replaced with a sub injection amount from the injector 12.

(88) Further, in the aforementioned embodiment, the target temperature of the bed temperature of the DOC 22a is calculated with the period under PM regeneration control as an example. However, when control of desorbing SOx from the DOC 22a is performed in combination with PM regeneration control, the target temperature of the bed temperature of the DOC 22a may be calculated by the aforementioned method during the desorption control. In this way, the calculation method of the target temperature described above can be applied to control in general that increases the bed temperature of the DOC 22a to the temperature range in which SOx desorbs from the DOC 22a.

(89) Further, in the aforementioned embodiment, the exhaust emission purifying device 22 including the DOC 22a and the DPF 22b is described as an example. However, the function of oxidizing HC and the like in the DOC 22a is given to the DPF 22b, and the DOC 22a may be omitted from the exhaust emission purifying device 22. In this case, an effect similar to the aforementioned embodiment can be obtained by applying the calculation method of the target temperature described above to the DPF 22b which is given the oxidizing function.

(90) Further, although in the aforementioned embodiment, the engine 10 includes the turbocharger 16, the engine 10 does not have to include the turbocharger 16. That is, the calculation method of the target temperature described above can be also applied to the system of a non-turbocharging diesel engine.

(91) Furthermore, the ECU 30 that the system of the first embodiment is equipped with may be configured as follows. FIG. 17 is a diagram illustrating an example of a hardware configuration of the ECU included in the system of the embodiment. The respective functions of the ECU 30 may be realized by a processing circuit. According to the example shown in FIG. 17, the processing circuit of the ECU 30 includes at least one processor 301 and at least one memory 302.

(92) In a case where the processing circuit includes at least one processor 301 and at least one memory 302, the respective functions of the ECU 30 may be realized by software, firmware or a combination of software and firmware. At least one of the software and the firmware may be described as a program. At least one of the software and the firmware may be stored in at least one memory. At least one processor 301 may realize the respective functions of the ECU 30 by reading out a program stored in at least one memory 302 and executing the program. At least one processor 301 may be, for example, CPU (Central Processing Unit), processing unit, arithmetic unit, micro processing unit, microcomputer, or DSP (Digital Signal Processor). At least one memory 302 may include a non-volatile or volatile semiconductor memory, for example, RAM (Random Access Memory), EPROM (Erasable Programmable Read Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory) or the like, magnetic disk, flexible disk, optical disk or the like.

(93) FIG. 18 is a diagram illustrating another example of a hardware configuration of the ECU included in the system of the embodiment. According to the example shown in FIG. 18, the processing circuit of the ECU 30 includes at least one piece of dedicated hardware 303.

(94) In a case where the processing circuit includes at least one piece of dedicated hardware 303, the processing circuit may be, for example, a single circuit, a composite circuit, a programmed processor, a parallel-programmed processor, an ASIC (Application Specific Integrated Circuit), a FPGA (Field-Programmable Gate Array) or any combination thereof. The functions of each part of the ECU 30 may be realized by respective processing circuits. Further, the functions of each part of the ECU 30 may be realized by collectively by a processing circuit.

(95) With regard to the respective functions of the ECU 30, one part thereof may be realized with dedicated hardware 303, and another part may be realized with software or firmware. The processing circuit may realize the respective functions of the ECU 3.0 by means of hardware 303, software, firmware or any combination thereof.