Method and system of controlling exhaust after-treatment apparatus for vehicle

A system and method for controlling an exhaust after-treatment apparatus for vehicle are provided. The method includes detecting, by a controller, signals from a front lambda sensor and a rear lambda sensor of a Lean NOx Trap (LNT), when an engine is driven in a rich mode and acquiring, by the controller, a temperature of exhaust gas detected by a temperature sensor, when the engine is driven in a rich mode. Further the method includes comparing, by the controller, the signals from the front lambda sensor and the rear lambda sensor to detect a breakthrough time when a breakthrough occurs between the signals from the front lambda sensor and the rear lambda sensor. In addition, the controller is configured to determine an additional rich time period based on the breakthrough time and the temperature of exhaust gas.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims under 35 U.S.C. §119(a) the benefit of Korean Patent Application No. 10-2014-0049098 filed on Apr. 24, 2014, the entire contents of which are incorporated herein by reference.

BACKGROUND

Technical Field

The present disclosure relates to a method for controlling an exhaust after-treatment apparatus for a vehicle and more particularly, a method for controlling an exhaust after-treatment apparatus for a vehicle that improves exhaust after-treatment performance by controlling an amount of ammonia (NH3) generated by a Lean NOx Trap (NLT).

Background Art

With the strengthening of vehicle emission regulations, a DeNOx catalyst technique (e.g., Lean NOx Trap (LNT), Selective Catalytic Reduction (SCR) and the like) has been applied to an after-treatment apparatus to reduce nitrogen oxides (NOx) in exhaust gas.

The DeNOx catalyst is a type of catalyst converter that removes NOx included in exhaust gas. The DeNOx catalyst causes an oxidation-reduction reaction between NOx and a reducing agent (e.g., urea, ammonia (NH3), carbon monoxide (CO), or hydrocarbon (HC)), to reduce NOx by the oxidation-reduction reaction with the reducing agent.

Recently, a LNT (or referred to as a LNT catalyst) has been used as an after-treatment apparatus to remove NOx from exhaust gas ingredients generated when a lean-burn engine operates. The LNT absorbs or occludes NOx included in exhaust gas in a lean environment, and desorbs the absorbed or occluded NOx in a rich environment.

A SCR system may effectively reduce NOx by supplying a reducing agent to a SCR catalyst. The SCR system supplies a reducing agent to exhaust gas to reduce NOx, unlike an Exhaust Gas Recirculation (EGR) apparatus of reducing NOx by recirculating exhaust gas to lower the combustion temperature of a combustion chamber. “Selective Catalyst Reduction (SCR)” means making a reducing agent, such as urea, NH3, CO, HC, and the like, react with NOx among oxygen and NOx.

A Diesel Oxidation Catalyst (DOC), a Diesel Particulate Filter (DPF), and a Catalyzed Particulate Filter (CPF) have been developed and used within vehicles to reduce particulates from exhaust gas. Recently, a SCR on Diesel Particulate Filter (SDPF) that collects particulates and reduces NOx has been used.

The SDPF, which is manufactured by coating a porous DPF with a SCR catalyst, causes NH3to react with NOx in exhaust gas within the SCR catalyst to generate water and nitrogen (N2), while collecting particulates in the exhaust gas though the filter function, that is, the DPF function. Accordingly, although various after-treatment apparatuses are used to meet vehicle emission regulation, strengthening of the vehicle emission regulations requires an after-treatment apparatus with greater optimal performance. Meanwhile, in the LNT catalyst, a NOx absorbing catalyst and a Diesel Oxidation Catalyst (DOC) are included within a carrier. When the engine is driven in a lean mode, NOx is absorbed by a catalyst washcoat, and when the engine is driven in a rich mode, diesel fuel is used as a reducing agent to reduce the absorbed NOx to nitrogen (N2).

Generally, a diesel engine is driven in a lean mode, in which an amount of air that enters the engine is more than that of an equivalence ratio, and NOx generated when the diesel engine is driven in the lean mode is absorbed within a LNT catalyst, which is a NOx Storage Catalyst (NSC). To reduce the NOx absorbed in the LNT catalyst to nitrogen (N2), a throttle valve is closed by a predetermined amount to reduce inflowing air, and post combustion is induced to switch the lean mode to the rich mode.

For driving in the lean mode and the rich mode, signals from lambda sensors or NOx sensors installed before and after the LNT catalyst are used. However, since NOx sensors are expensive, lambda sensors are generally used. When NOx absorbed within the LNT catalyst reaches a predetermined level, the lean mode is switched to the rich mode to commence NOx regeneration control from a predetermined level (e.g., a level ranging from about 0.92 to about 0.94) based on a signal from the lambda sensor installed before the LNT catalyst, and a reducing agent generated by driving in the rich mode, acts to reduce NOx absorbed within the LNT catalyst to N2.

In the LNT catalyst, the amount of the absorbed NOx is gradually reduced, and as the rich mode continues while reactants decrease, an amount of slipped reducing agents increases. Accordingly, a value detected by the lambda sensor installed after the LNT catalyst gradually converges to a value detected by the lambda sensor installed before the LNT catalyst, which represents that reducing agents are slipped after the LNT catalyst.

SUMMARY

The present disclosure provides a method for controlling an exhaust after-treatment apparatus for a vehicle that may improve exhaust after-treatment performance by providing an additional rich-mode driving time period after a time (e.g., a breakthrough time) when a signal from a front lambda sensor is substantially similar (e.g., about the same value) to a signal from a rear lambda sensor to limit an amount of ammonia (NH3) generated by a Lean NOx Trap (LNT).

In one aspect, the present invention provides a method for controlling an exhaust after-treatment apparatus that may include: detecting signals from a front lambda sensor and a rear lambda sensor of a Lean NOx Trap (LNT); acquiring a temperature of exhaust gas detected by a temperature sensor, when an engine is driven in a rich mode; comparing the signals from the front lambda sensor and the rear lambda sensor to detect a breakthrough time when a breakthrough occurs between the signals from the front lambda sensor and the rear lambda sensor; and determining an additional rich time period based on the breakthrough time and the temperature of exhaust gas. The engine may continue to be driven in the rich mode for the additional rich time period after the breakthrough time. Further, the breakthrough time may be a time when the signal from the front lambda sensor is about the same as the signal from the rear lambda sensor, when the engine is driven in the rich mode.

The determination of the additional rich time period may include: determining the additional rich time period as a, when the temperature of exhaust gas is less than T1and the breakthrough time is earlier (e.g., less) than t1; determining the additional rich time period as a+β, when the temperature of exhaust gas is less than T1and the breakthrough time is later than (e.g., greater than) or equal to t1and earlier than (e.g., less than) t2; and determining the additional rich time period as a+γ, when the temperature of exhaust gas is less than T1and the breakthrough time is later than or equal to t2, wherein β<γ, t1<t2, and b>c>a when T1is less than or equal to about 250° C.

In addition, the determination of the additional rich time period may include: determining the additional rich time period as b, when the temperature of exhaust gas is greater than or equal to T1and less than T2, and the breakthrough time is earlier than t1; determining the additional rich time period as b+β, when the temperature of exhaust gas is greater than or equal to T1and less than T2, and the breakthrough time is later than or equal to t1and earlier than t2; and determining the additional rich time period as b+γ, when the temperature of exhaust gas is greater than or equal to T1and less than T2, and the breakthrough time is later than or equal to t2, wherein β<γ, t1<t2, T1<T2, and b>c>a when T1is less than or equal to about 250° C. and T2is greater than or equal to about 350° C.

Further, the determination of the additional rich time period may include: determining the additional rich time period as c, when the temperature of exhaust gas is greater than or equal to T2, and the breakthrough time is earlier than t1; determining the additional rich time period as c+β, when the temperature of exhaust gas is greater than or equal to T2, and the breakthrough time is later than or equal to t1and earlier than t2; and determining the additional rich time period as c+γ, when the temperature of exhaust gas is greater than or equal to T2, and the breakthrough time is later than or equal to t2, wherein β<γ, t1<t2, and b>c>a when T2is greater than or equal to about 350° C.

Reference numerals set forth in the Drawings includes reference to the following elements as further discussed below:1: engine2: LNT3: SCR (SDPF)4: DPF5: SCR6: front lambda sensor7,7-1,7-2,7-3: rear lambda sensor8,9,10: temperature sensor

It should be understood that the appended drawings are not necessarily to scale, presenting a somewhat simplified representation of various features illustrative of the basic principles of the invention. The specific design features of the present invention as disclosed herein, including, for example, specific dimensions, orientations, locations, and shapes will be determined in part by the particular intended application and use environment. In the figures, reference numbers refer to the same or equivalent parts of the present invention throughout the several figures of the drawing.

DETAILED DESCRIPTION

Exemplary embodiments of the present disclosure relate to a combination system of a Lean NOx Trap (LNT) and a passive Selective Catalyst Recirculation (SCR) to meet strengthened emission regulation, and provide a method that controls an amount of ammonia (NH3) generated by the LNT.

FIG. 1is an exemplary block diagram illustrating a configuration of an exhaust after-treatment apparatus according to an exemplary embodiment of the present disclosure. Referring toFIG. 1, a LNT (e.g., a LNT catalyst)2and a zeolite type SCR (e.g., a zeolite type SCR catalyst)3may be arranged as shown based on flow of exhaust gas to allow exhaust gas discharged from an engine1to pass through the LNT2and the SCR3. In other words, the LNT2may be disposed after the engine1, and the SCR3may be disposed after the LNT2.

The SCR3may be a SCR on Diesel Particulate Filter (SPDF) that collects particulates and reduces NOx. The SDPF, which may be manufactured by coating a porous DPF with a SCR catalyst, may cause ammonia (NH3) to react with NOx within exhaust gas in the SCR catalyst to generate water and nitrogen (N2), while collecting particulates in the exhaust gas. The combination of the SDPF3and the LNT2may form a passive SCR to desorb NOx absorbed in the LNT2in a rich environment to generate ammonia (NH3) as a by-product, and to cause NH3to react with NOx in exhaust gas in the SDPF2, which reduces the NOx.

FIG. 2is an exemplary block diagram illustrating a configuration of an exhaust after-treatment apparatus according to an exemplary embodiment of the present disclosure. Referring toFIG. 2, a LNT2, a H2S reduction type Diesel Particulate Filter (DPF)4, and a zeolite type SCR5may be disposed as shown based on flow of exhaust gas so exhaust gas discharged from an engine1may pass through the LNT2, the DPF4, and the SCR5. In other words, the LNT2may be disposed after the engine1, and the DPF4may be disposed between the LNT2and the SCR5.

In the exemplary embodiments shown inFIGS. 1 and 2, a front lambda sensor6may be configured to detect a density of oxygen in exhaust gas and may be disposed between the engine1and the LNT2and a rear lambda sensor7may be disposed after the LNT2. In addition, the front lambda sensor may be disposed before the LNT2. In particular, as shown inFIG. 1, the rear lambda sensor7or7-1may be disposed after the SDPF3, in other words, after the LNT2or after the SDPF3. Further, as shown inFIG. 2, the rear lambda sensor7,7-2, or7-3may be disposed after the LNT2, after the DPF4, or after the SCR5.

In addition, the exhaust after-treatment apparatus may include at least one temperature sensor configured to detect a temperature of exhaust gas. In particular, as shown inFIG. 1, temperature sensors8and9may be disposed after the LNT2and after the SDPF3, respectively, and shown inFIG. 2, temperature sensors8,9, and10may be disposed after the LNT2, after the DPF4, and after the SCR5, respectively. In the exhaust after-treatment apparatus configured as shown inFIGS. 1 and 2, when the engine1is operated in a rich mode, the LNT2may generate NH3, and the SCR5or the SDPF3(hereinafter, collectively referred to as a SCR) causes the NH3to react with NOx, which may reduce nitrogen oxides in exhaust gas.

In the exhaust after-treatment apparatus, as a rich-mode driving time period (e.g., a rich time period) when the engine1is driven in the rich mode increases, NH3and hydro carbon (HC)/carbon monoxide (CO) may also increase. However, to optimally adjust the rich time period, the rich time period may be set and adjusted based on driving conditions of the engine.

When a determined rich time period is longer than (e.g., greater than) a time period (e.g., an optimal rich time period) for optimal adjusting of the rich time period, the slip of CO/HC may increase while a generated amount of NH3may not substantially increase, which may decrease fuel efficiency. When the determined rich time period is shorter than (e.g., less than) the optimal rich time period for optimal adjustment, the contribution degree of the SCR3or5to purification of NOx may decrease since the generation amount of NH3is minimal although the slip of CO/HC decreases. Accordingly, the exhaust after-treatment apparatus according to the exemplary embodiment of the present disclosure may optimally adjust a rich time period based on driving conditions of the engine1to optimize a generated amount of NH3of the LNT2, which may cause the SCR3or5to efficiently purify NOx.

The exhaust after-treatment apparatus may be configured to determine an optimal rich time period based on driving conditions of the engine1when a rich environment is periodically formed to reduce NOx absorbed and stored within the LNT2, which may increase a generated amount of NH3, increase a purification rate of NOx of the SCR3or5, decrease the slip of CO/HC, and preventing a decrease in fuel efficiency.

When a breakthrough time when a signal from the front lambda sensor6, located before the LNT2, is about the same as a signal from the rear lambda sensor7,7-1,7-2or7-3, located after the LNT2, the engine1is driven in the rich mode, the signal from the front lambda sensor6to be similar to the signal from the rear lambda sensor7,7-1,7-2, or7-3, a generated amount of NH3may increase by lengthening the rich time period by a predetermined period of time α. When the engine1enters the rich mode may be denoted by tbt, and a time period taken for the signal from the front lambda sensor6to be similar to the signal from the rear lambda sensor7,7-1,7-2, or7-3may be denoted by t.

However, the slip of CO/HC may also increase. Accordingly, a time period α (e.g., an additional rich time period) may need to be optimized after the breakthrough time tbtbased on driving conditions of the engine1. To optimize the additional rich time period α, main factors that influence generation of NH3, such as a temperature and flow of exhaust gas, a degree of catalyst aging, and a time period t taken to reach the breakthrough time tbtwhen the engine1is driven in the rich mode, which may be engine/catalyst conditions, an engine lambda value (e.g., an air fuel ratio) may be set to a substantially constant value.

The additional rich time period α may be determined based on a temperature T of exhaust gas and a breakthrough time tbtwhen a signal from the front lambda sensor6is about the same as a signal from the rear lambda sensor7,7-1,7-2, or7-3after the engine1enters the rich mode, and the factors that influence the generation of NH3(e.g., as a temperature and flow of exhaust gas, a degree of catalyst aging, and a time period t taken to reach the breakthrough time tbt).

FIG. 3is an exemplary view for describing NH3generation mechanism of the LNT2according to an exemplary embodiment of the present disclosure. The top graph ofFIG. 3shows exemplary signals (e.g., lambda values) from the front lambda sensor7and the rear lambda sensor7,7-1,7-2, or7-3, the middle graph ofFIG. 3shows an exemplary temperature of exhaust gas before the LNT2, and the bottom graph ofFIG. 3shows exemplary densities of NH3and CO after the LNT2.

Referring to the top graph ofFIG. 3, before a breakthrough time when signals from the front lambda sensor6and the rear lambda sensor7-1,7-2, or7-3may intersect with each other to cause the lambda values to become about the same, NOx may be stored and absorbed in the LNT2in the lean mode, and the absorbed NOx may be broken down into nitrogen (N2) and purified in the rich mode. This process may be expressed as Reaction Equation 1 below.
Ba(NO3)2+3CO→2NO+2CO2+BaCO3
2NO+2CO→N2+2CO2Reaction Equation 1

In addition, after the breakthrough time, H2may react with NO to generate NH3for the additional rich time period α when the engine1continues to be driven in the rich mode. This process may be expressed as Reaction Equation 2 below.
CO+H2O→CO2+H2
3HC+3H2O→3CO+6H2
5H2+2NO→2NH3+2H2O  Reaction Equation 2

NH3may be generated from the LNT2, starting from when oxygen stored within an oxygen storage material of the LNT2and NOx stored within a NOx absorbing material of the LNT2may be consumed. Accordingly, by providing the additional rich time period α, the LNT2may be operated to emit a substantial amount of NH3.

FIG. 4is an exemplary graph showing a generation amount of NH3of the LNT2with respect to the temperature of exhaust gas in an exhaust after-treatment apparatus according to an exemplary embodiment of the present disclosure. As shown inFIG. 4, NH3may be generated at a low temperature around 200° C., a largest amount of NH3may be generated at a temperature around 300° C., and even at a substantial temperature above about 350° C., NH3may still be generated. The generation amount of NH3may be based on the engine lambda value (e.g., the air-fuel ratio), flow of exhaust gas, and density of exhaust gas.

Referring to the lower graph ofFIG. 3, since a largest amount of NH3may be generated at the breakthrough time tbt, a generated amount of NH3may be increased by maintaining the rich mode of the engine1for an additional rich time period α after the breakthrough time tbtat which the largest amount of NH3is generated. However, when the additional rich time period α is substantially short (e.g., less than a predetermined rich time period), a generated amount of NH3may decrease. In addition, when the additional rich time period α is substantially long (e.g., greater than a predetermined rich time period), an amount of CO may substantially increase although a generated amount of NH3may increase, which may decrease fuel efficiency. Accordingly, the additional rich time period α may need to be optimally determined. Further, as shown inFIG. 3, for the additional rich time period α, a rate of generation of NH3per second may decrease gradually.

FIG. 5is an exemplary graph showing generation amounts of NH3of the LNT2with respect to the temperature of exhaust gas based on different breakthrough times tbt. As shown inFIG. 5, a largest amount of NH3may be generated when the temperature of exhaust gas is around 300° C. Further, when the temperature of exhaust gas is less than or greater than 300° C., a generated amount of NH3may decrease.

In addition, as the breakthrough time tbtincrease (e.g., the longer a breakthrough time tbt), the greater an increase in the amount of NH3. Accordingly, by determining an additional rich time period α based on a temperature of exhaust gas and a breakthrough time tbt, the LNT2may emit a maximum amount of NH3, which may increase a purification ratio of NOx.

As shown inFIG. 4, when the temperature of exhaust gas is within the range of about 275° C. to about 325° C., a maximum amount of NH3may be generated, and as the temperature of exhaust gas decrease from about 275° C. to about 225° C. or increase from about 325° C. to about 375° C., the amount of NH3generated may decrease. When the temperature of exhaust gas exceeds about 375° C., the amount of NH3generated may substantially decrease. Further, as shown inFIG. 5, as a time period t taken to reach the breakthrough time tbtdecreases, the generated amount of NH3may decrease, and accordingly, an additional rich time period α may also decrease.

FIG. 6is an exemplary graph showing the densities of NH3discharged from the LNT2over time, when different breakthrough times tbt(e.g., times at which breakthroughs occur between signals from the front lambda sensor6and the rear lambda sensor7,7-1,7-2, or7-3) and different temperatures of exhaust gas are used as control factors.
tbt=tbt1(tbt1>tbt2>tbt3)& temperature of exhaust gas=about 300° C.  Condition 1
tbt=tbt2(tbt1>tbt2>tbt3)& temperature of exhaust gas=about 350° C.  Condition 2
tbt=tbt3(tbt1>tbt2>tbt3)& temperature of exhaust gas=about 400° C.  Condition 3

InFIG. 6, a first graph may be obtained when the condition 1 is selected as control factors, a second graph may be obtained when the condition 2 is selected as control factors, and a third graph may be obtained when the condition 3 is selected as control factors. As shown inFIG. 6, since different breakthrough times tbtand different temperatures of exhaust gas are used as control factors, the density peak values of NH3may appear at different time. As seen from the first, second, and third graphs, the density peak values of NH3may decrease in order, and the emission amounts of NH3may also decrease in order. The graphs show a similar pattern of emission density of NH3although different conditions are selected as control factors.

InFIG. 6, time periods tp1, tp2, and tp3may represent time periods from an arbitrary time tato times tbt1, tbt2, and tbt3at which the densities of NH3reach peak values, respectively. The time periods tp1, tp2, and tp3may be respectively determined as additional rich time periods a for the respective conditions 1, 2, and 3. In other words, a time difference between an arbitrary reference time taand a breakthrough time tbt(tbt1, tbt2, tbt3) may be determined as an additional rich time period α. Accordingly, by using a temperature of exhaust gas and a breakthrough time tbtas control factors for determining an additional rich time period α, and determining an additional rich time period α after the breakthrough time tbtbased on the temperature of exhaust gas and the breakthrough time tbt, a generated amount of NH3may be effectively increased.

FIG. 7is an exemplary graph showing the densities of NH3discharged from the LNT2over time, according to the conditions 1, 2, and 3 described above with reference toFIG. 6. In the graphs ofFIG. 7, tp1, tp2, and tp3may represent time periods from an arbitrary time tato times at which the densities of NH3reach peak values, respectively, and β1, β2, and β3may represent time periods for which the rich mode is maintained after the times tbt1, tbt2, and tbt3, respectively. In particular, tp1+β1, tp2+β2, and tp3+β3may be respectively determined as additional rich times periods a for the respective conditions 1, 2, and 3. In other words, a time difference between an arbitrary reference time taand a time tbt+β(tbt1+β, tbt2+β, tbt3+β) may be determined as an additional rich time period α.

As the value of β1, β2, or β3increases, a generated amount of NH3of the LNT2may also increase. However, since the slip amount of CO/HC also increases, the value of β1, β2, or β3may be preferably set to about 2 seconds or less. The additional rich time period α may be determined by a main controller of a vehicle, and an engine controller may be configured to operate the engine1based on the additional rich time period α based on a signal transferred from the main controller.

Accordingly, to determine an additional rich time period α based on a temperature of exhaust gas and a breakthrough time tbtand adjust a generated amount of NH3based on the additional control time period α, the main controller may be configured to determine the additional rich time period α and lengthen the rich mode of the engine1, using a process as follows. The main controller may be configured to determine whether a driving mode of the engine1is in the rich mode and detect signals from the front lambda sensor6and the rear lambda sensor7,7-1,7-2, or7-3when the engine1is driven in the rich mode.

In addition, the main controller may be configured to compare the signals from the front lambda sensor6and the rear lambda sensor7,7-1,7-2, or7-3to detect a breakthrough time at which a breakthrough occurs between the signals from the front lambda sensor6and the rear lambda sensor7,7-1,7-2, or7-3, determine an additional rich time period α based on the breakthrough time and a temperature of exhaust gas detected using the temperature sensor8or9, and maintain the rich mode of the engine1for the additional rich time period α after the breakthrough time. The breakthrough time may be a time when the signal (e.g., a lambda value) from the front lambda sensor6is about the same as the signal (e.g. a lambda value) from the rear lambda sensor7,7-1,7-2, or7-3when the engine1is driven in the rich mode. In particular, when a lambda value is determined to be less than 1 based on signal information from the rear lambda sensor6and/or the rear lambda sensor7,7-1,7-2, or7-3, the main controller may be configured to determine the engine1is driven (e.g., operated) in the rich mode. As described above, an additional rich time period α for lengthening the rich mode may be determined to optimally increase a generated amount of NH3of the LNT2, wherein factors for determining the additional rich time period α may be a temperature of exhaust gas and a breakthrough time tbt.

FIG. 8and Table 1 show an additional rich time period α that is determined based on a temperature T of exhaust gas and a breakthrough time tbt.

As shown inFIG. 8and Table 1, when the rich mode for DeNOx is applied to the engine1, the additional rich time period α may be determined to be a when a temperature T of exhaust gas is less than T1(T<T1) and the breakthrough time tbtis earlier than (e.g., less than) t1(tbt<t1), the additional rich time period α may be determined to be a+β when the temperature T of exhaust gas is less than T1(T<T1) and the breakthrough time tbtis later than (e.g., greater than) or equal to t1and earlier than t2(t1≦tbt<t2), and the additional rich time period α may be determined to be a+γ when the temperature T of exhaust gas is less than T1(T<T1) and the breakthrough time tbtis later than or equal to t2(tbt≧t2), wherein β<γ and t1<t2.

In addition, the additional rich time period α may be determined to be b when the temperature T of exhaust gas is greater than or equal to T1and less than T2(T1≦T<T2) and the breakthrough time tbtis earlier than t1(tbt<t1), the additional rich time period α may be determined to b+β when the temperature T of exhaust gas is greater than or equal to T1and less than T2(T1≦T<T2) and the breakthrough time tbtis later than or equal to t1and earlier than t2(t1≦tbt<t2), and the additional rich time period α may be determined to be b+γ when the temperature T of exhaust gas is greater than or equal to T1and lower than T2(T1≦T<T2) and the breakthrough time tbtis later than or equal to t2(tbt>t2), wherein β<γ and t1<t2.

Further, the additional rich time period α may be determined to be c when the temperature T of exhaust gas is greater than or equal to T2(T≧T2) and the breakthrough time tbtis earlier than t1(tbt<t1), the additional rich time period α may be determined to be c+β when the temperature T of exhaust gas is greater than or equal to T2(T≧T2) and the breakthrough time tbtis later than or equal to t1and earlier than t2(t1≦tbt<t2), and the additional rich time period α may be determined to be c+γ when the temperature T of exhaust gas is greater than or equal to T2(T≧T2) and the breakthrough time tbtis later than or equal to t2(tbt≧t2), wherein β<γ and t1<t2. Herein, T1may be less than T2. For example, T1may be set to about 250° C. or less, and T2may be set to about 350° C. or greater.

Since a largest amount of NH3may be emitted from the LNT2when the temperature T of exhaust gas is about 300° C., the values a, b, and c representing the additional rich time period α may satisfy b>c>a when 300° C. is between T1and T2. The LNT2may have a later breakthrough time tbtand generate a greater amount of NH3since the LNT2has a greater storage amount of NOx and a lower deterioration of catalyst. In addition, as described above, the generated amount of NH3may decrease when the temperature of exhaust gas is less than or greater than 300° C.

Accordingly, the additional rich time period α after the breakthrough time tbtmay be determined based on the temperature of exhaust gas and the breakthrough time tbt, using a 3×3 matrix similar to Table 1. However, the additional rich time period α after the breakthrough time tbtmay also be determined using a 2×2 matrix or a 4×4 matrix, according to different combinations of conditions, such as the temperature of exhaust gas and the breakthrough time tbt, instead of the 3×3 matrix. Additionally, the additional rich time period α after the breakthrough time tbtmay be determined using any other method based on the temperature of exhaust gas and the breakthrough time tbt.

As described above, by determining an additional rich time period α based on a temperature of exhaust gas and a breakthrough time tbtto adjust a generated amount of NH3, a generated amount of NH3may be effectively increased, a SCR located after a LNT may be configured reduce a large amount of NOx, the slip of CO/HC may be reduced, and a decrease in fuel efficiency may be prevented. In addition, future emission regulations may be effectively satisfied.