JP2004100569A - Exhaust emission control device of internal combustion engine - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve exhaust emission control performance by allowing a second catalyst to function effectively. <P>SOLUTION: The exhaust emission control device comprises: a first catalyst 53 that is arranged at an exhaust passage; a first catalyst downstream air/fuel ratio sensor 66, a second catalyst 54, and an electric control apparatus 70. The electric control apparatus incorporates a catalyst model for virtually dividing the second catalyst 54 into a plurality of blocks along the flow direction of an exhaust gas and for calculating physical quantity (for example, oxygen concentration flowing out of the same block) related to the cleaning of the exhaust gas to each block. Then, the electric control apparatus estimates the physical quantity of the middle block (a block at the upstream of a block at the lowest downstream) in the second catalyst by using the output of the first catalyst downstream air/fuel sensor and the catalyst model, and controls the air/fuel ratio in a mixed air to be supplied to an engine so that the physical quantity reaches a specific value. As a result, the state of the second catalyst can be rapidly acquired, thus appropriately maintaining the state of the second catalyst regardless of feedback control delay. <P>COPYRIGHT: (C)2004,JPO

Description

【００４５】
いま、時刻ｔ〜ｔ＋Δｔの所与の期間における特定領域での化学種の収支を考えると、図８に示したように、特定領域の排ガス相（単に、「ガス相」とも称呼する。）における化学種の変化量ΔＭは、下記の（１）式に示したとおり、同特定領域に流入した同化学種の量Ｍｉｎから、同特定領域から流出した同化学種の量Ｍｏｕｔと同特定領域のコート層に奪われた同化学種の量Ｍｃｏａｔとを減算した量と等しい。このように、触媒モデルは各特定領域における特定成分の物質収支に基づいて構築される。
【００４６】
【数１】

【００４７】
以下、（１）式の各項について個別に検討する。先ず、（１）式の左辺にある化学種の変化量ΔＭは、下記（２）式により求めることができる。（２）式は、上記所与の期間における化学種の濃度変化量（化学種の濃度Ｃｇの時間変化量を所与の期間に渡り積分した量）に微小体積σ・ｄＡ・ｄｘを乗じた値を着目しているブロック（特定領域）の全体に渡って軸方向に積分したものである。
【００４８】
【数２】

【００４９】
（１）式の右辺第１項のＭｉｎは、単位時間あたりに特定領域に流入する排ガスの体積に相当する値である「特定領域に流入する排ガスの流速ｖｇｉｎと同特定領域の断面積ｄＡの積ｖｇｉｎ・ｄＡ（実際には、断面積ｄＡで開口率σの触媒内に流速ｖｇｉｎの排ガスが流れ込むので、触媒内部での排ガスの流速はｖｇｉｎ／σとなり、この実際の流速ｖｇｉｎ／σと触媒の実質的な断面積σ・ｄＡの積）」に同流入する排ガス中の化学種の濃度Ｃｇｉｎを乗じた値Ｃｇｉｎ・ｖｇｉｎ・ｄＡを所与の期間に渡り積分した値である。また、（１）式の右辺第２項のＭｏｕｔは、特定領域から流出する排ガスの流速ｖｇｏｕｔと同特定領域の断面積ｄＡの積ｖｇｏｕｔ・ｄＡ（実際には、排ガスの流速ｖｇｏｕｔ／σと実質的な断面積σ・ｄＡの積）に同流出する排ガス中の前記化学種の濃度Ｃｇｏｕｔを乗じた値Ｃｇｏｕｔ・ｖｇｏｕｔ・ｄＡを所与の期間に渡り積分した値である。即ち、上記（１）式の右辺第１項及び第２項は下記（３）式のように記述することができる。
【００５０】
【数３】

【００５１】
ところで、特定領域に流入する排ガスの流速ｖｇｉｎと同特定領域から流出する排ガスの流速ｖｇｏｕｔとの間に大きな差異はないので、ｖｇ＝ｖｇｉｎ＝ｖｇｏｕｔとおくと、（３）式は、下記（４）式のように変形される。
【００５２】
【数４】

【００５３】
次に、（１）式の右辺第３項のコート層に伝達される（移動する）化学種の量Ｍｃｏａｔについて検討する。幾何学的表面積Ｓｇｅｏは触媒の単位体積あたりの化学種の反応に寄与する表面積であるから、特定領域において化学種の反応に寄与する表面積はＳｇｅｏ・ｄＡ・ｄｘであり、同特定領域の単位長あたりに同反応に寄与する面積はＳｇｅｏ・ｄＡとなる。また、コート層に伝達される化学種の量は、フィックの法則から、排ガス相の化学種の濃度Ｃｇとコート層の化学種の濃度Ｃｗとの差に比例すると考えることができる。これらから、下記の（５）式が得られる。なお、ｈ_Ｄは比例定数であるが、上記の表１に示したように、物質伝達率と称呼される値である。
【００５４】
【数５】

【００５５】
従って、上記（１），（２），（４）式、及び（５）式から、以下の（６）式が得られる。
【００５６】
【数６】

【００５７】
この（６）式に準定常（ｑｕａｓｉ　ｓｔａｔｅ）近似を適用すると、（６）式の左辺は「０」（∂Ｃｇ／∂ｔ＝０）であると考えることができるから（即ち、濃度Ｃｇは瞬間的に定常値に至ると考えられるから）、下記の（７）式が得られる。
【００５８】
【数７】

【００５９】
ここで、見かけの拡散速度（実質的な拡散速度）Ｒ_Ｄを（８）式のようにおけば、（７）式は（９）式に書き直される。
【００６０】
【数８】

【００６１】
【数９】

【００６２】
次に、特定領域のコート層における化学種の収支（特定成分の物質収支）を上記と同様に考えると、下記（１０）式に示したように、コート層内における化学種の時間的変化量（単位時間あたりの変化量）ΔＭｃは、単位時間あたりに排ガス相からコート層へ伝達される同化学種の量Ｍｄから、同単位時間あたりにコート層にて反応により消費される同化学種の量Ｍｒを減じた量である。
【００６３】
【数１０】

【００６４】
（１０）式の左辺（コート層内における化学種の時間的変化量）ΔＭｃは、下記（１１）式に示したように、化学種の濃度変化（∂Ｃｗ／∂ｔ）に体積（（１−σ）・ｄＡ・ｄｘ）を乗じることにより求められ、右辺第１項（単位時間あたりに排ガス相からコート層へ伝達される化学種の量Ｍｄ）は（５）式で説明した理由と同じ理由により、即ち、フィックの法則から考えると、下記（１２）式のように記述することができる。
【００６５】
【数１１】

【００６６】
【数１２】

【００６７】
また、（１０）式の右辺第２項（単位時間あたりにコート層にて反応により消費される化学種の量Ｍｒ）は、コート層での化学種の消費速度Ｒを用いた下記（１３）式により求められる。
【００６８】
【数１３】

【００６９】
従って、（１０）〜（１３）式から、下記の（１４）式が得られる。
【００７０】
【数１４】

【００７１】
この（１４）式に準定常（ｑｕａｓｉ　ｓｔａｔｅ）近似を適用すると（∂Ｃｗ／∂ｔ＝０）、下記の（１５）式が得られる。
【００７２】
【数１５】

【００７３】
ここで、（１５）式に（８）式を適用すれば、下記の（１６）式が得られる。
【００７４】
【数１６】

【００７５】
以上を要約すると、（９）式及び（１６）式が触媒モデルの基本式である。（９）式は、ある化学種の「特定領域への流入量」と「排ガス相からコート層への拡散量＋特定領域からの流出量」とが釣り合っていることを示し、（１６）式は、同化学種の「排ガス相からコート層への拡散量」と「コート層での消費量」とが釣り合っていることを示している。
【００７６】
次に、かかる触媒モデルを使用して特定領域から流出する特定の化学種ｉの濃度Ｃｇｏｕｔを実際に算出するための方法について説明する。先ず、（９）式を離散化すると、下記（１７）式が得られる。なお、以下においては上記ｄｘをＬとして表す。
【００７７】
【数１７】

【００７８】
ここで、図９に概念的に示したように、特定領域Ｉから流出する化学種の濃度Ｃｇｏｕｔは同特定領域Ｉの化学種の濃度Ｃｇ（Ｉ）の影響を強く受けると考えられるので、下記の（１８）式のように置くことができる。かかる考え方は「風上法」と称呼される。換言すると、風上法とは、「特定領域Ｉに隣接する上流側の領域（Ｉ−１）における濃度Ｃｇ（Ｉ−１）の化学種が、特定領域Ｉに流入する。」という考え方であり、下記（１９）式のように記述することもできる。
【００７９】
【数１８】

【００８０】
【数１９】

【００８１】
ところで、反応速度論に基けば、ある化学種の消費速度Ｒは、その化学種のコート層の平均濃度Ｃｗの関数ｆｃｗ（例えば、Ｃｗのｎ乗に比例する関数）となるので、この関数ｆｃｗを最も簡便となるようにＣｗに比例すると設定すれば、消費速度Ｒは（２０）式にて示したように置くことができる。なお、以下において、（２０）式中のＲ＊を便宜上「消費速度定数」と称呼する。
【００８２】
【数２０】

【００８３】
この（２０）式を上記（１６）式（Ｒ＝Ｒ_Ｄ・（Ｃｇ−Ｃｗ）…（１６））に適用すると下記（２１）式が得られ、同（２１）式を変形することにより下記（２２）式が得られる。
【００８４】
【数２１】

【００８５】
【数２２】

【００８６】
また、上述した風上法によれば、Ｃｇ＝Ｃｇｏｕｔであるから、（２２）式は下記（２３）式に書き換えられる。
【００８７】
【数２３】

【００８８】
そして、Ｃｇ＝Ｃｇｏｕｔなる関係を上記（１７）式に適用してＣｇを消去するとともに、同（１７）式と上記（２３）式とからＣｗを消去すると、下記（２４）式が得られる。
【００８９】
【数２４】

【００９０】
そこで、値ＳＰを下記（２５）式のようにおけば、（２４）式は（２６）式のように書き直すことができる。値ＳＰは、見かけの拡散速度Ｒ_Ｄと消費速度定数Ｒ＊のうちの小さい方の値に強い影響を受ける値であるから、Ｃｇｏｕｔの変化が物質の伝達（Ｒ_Ｄ）又は化学的反応（Ｒ＊）の何れにより律速されているかを示す値となっており、従って、「反応律速因子」と呼ぶこともできる。
【００９１】
【数２５】

【００９２】
【数２６】

【００９３】
以上のことから、消費速度定数Ｒ＊と見かけの拡散速度Ｒ_Ｄとを決定できれば、特定領域に流入する化学種濃度Ｃｇｉｎを与えることにより、（２５）式と（２６）式とに基づいて同特定領域から流出する化学種の濃度Ｃｇｏｕｔを求めることができる。また、これにより、次の特定領域に流入する化学種濃度Ｃｇｉｎが定まるので、同次の特定領域の化学種の濃度Ｃｇｏｕｔを算出することが可能となる。以上が、化学種の濃度Ｃｇｏｕｔを算出する触媒モデルの基本的考え方である。
【００９４】
次に、上記消費速度定数Ｒ＊と見かけの拡散速度Ｒ_Ｄを決定するとともに、特定領域から流出する化学種濃度Ｃｇｏｕｔを求める際のより具体的な方法の一例について説明する。この例（触媒モデル）では、触媒での酸化・還元反応である三元反応は瞬時に且つ完全に終了するものと仮定し、その結果としての酸素の過不足に基く酸素の吸蔵・放出反応に着目することとする。なお、この仮定（触媒モデル）は、現実的であり且つ精度の良いものである。
【００９５】
この場合、着目する化学種ｉは、例えば、酸素Ｏ_２や窒素酸化物の一つである一酸化窒素ＮＯのように酸素を生成する（酸素をもたらす）化学種（ストレージ・エージェント）、及び、一酸化炭素ＣＯや炭化水素ＨＣのように酸素を消費する化学種（リダクション・エージェント）から選ばれた化学種である。
【００９６】
また、以下において、ストレージ・エージェントの化学種ｉ（この場合、化学種ｉはＯ_２又はＮＯ）のＣｇｏｕｔをＣｇｏｕｔ，ｓｔｏｒ，ｉ、同化学種ｉのＣｗをＣｗ，ｓｔｏｒ，ｉ、同化学種ｉのＣｇｉｎをＣｇｉｎ，ｓｔｏｒ，ｉ、同化学種ｉの見かけの拡散速度Ｒ_ＤをＲ_Ｄ，ｉ、同化学種ｉの消費速度をＲｓｔｏｒ，ｉ、同化学種ｉの消費速度定数をＲ＊ｓｔｏｒ，ｉ、及び同化学種ｉの反応律速因子ＳＰｓｔｏｒ，ｉと表す。
【００９７】
同様に、リダクション・エージェントの化学種ｉ（この場合、化学種ｉはＣＯ又はＨＣ等）のＣｇｏｕｔをＣｇｏｕｔ，ｒｅｄｕｃ，ｉ、同化学種ｉのＣｗをＣｗ，ｒｅｄｕｃ，ｉ、同化学種ｉのＣｇｉｎをＣｇｉｎ，ｒｅｄｕｃ，ｉ、同化学種ｉの見かけの拡散速度Ｒ_ＤをＲ_Ｄ，ｉ、同化学種ｉの消費速度をＲｒｅｄｕｃ，ｉ、同化学種ｉの消費速度定数をＲ＊ｒｅｄｕｃ，ｉ、及び同化学種ｉの反応律速因子ＳＰｒｅｄｕｃ，ｉと表す。このように各値を表すと、上記（２０），（２３），（２５），（２６）式から以下の（２７）〜（３４）式が得られる。
【００９８】
【数２７】

【００９９】
【数２８】

【０１００】
【数２９】

【０１０１】
【数３０】

【０１０２】
【数３１】

【０１０３】
【数３２】

【０１０４】
【数３３】

【０１０５】
【数３４】

【０１０６】
これらの式に基づいて、Ｃｇｏｕｔ，ｓｏｔｒ，ｉ（具体的には、特定領域から流出する酸素の濃度Ｃｇｏｕｔ，Ｏ２、特定領域から流出する一酸化窒素の濃度Ｃｇｏｕｔ，ＮＯ）及びＣｇｏｕｔ，ｒｅｄｕｃ，ｉ（具体的には、特定領域から流出する一酸化炭素の濃度Ｃｇｏｕｔ，ＣＯ、特定領域から流出する炭化水素の濃度Ｃｇｏｕｔ，ＨＣ）を求めるため、先ず、消費速度定数Ｒ＊ｓｔｏｒ，ｉ及び消費速度定数Ｒ＊ｒｅｄｕｃ，ｉを求める。
【０１０７】
ところで、反応速度論によれば、特定領域のコート層で酸素が吸蔵される速度（酸素の吸蔵速度）である酸素の消費速度Ｒｓｔｏｒ，ｉは、同コート層のストレージ・エージェント（Ｏ_２、ＮＯｘ等）の濃度Ｃｗ，ｓｔｏｒ，ｉ（例えば、Ｃｗ，Ｏ２、Ｃｗ，ＮＯ）の関数ｆ１（Ｃｗ，ｓｔｏｒ，ｉ）の値に比例するとともに、特定領域のコート層の最大酸素吸蔵密度と実際の酸素吸蔵密度との差（Ｏｓｔｍａｘ−Ｏｓｔ）の関数ｆ２（Ｏｓｔｍａｘ−Ｏｓｔ）の値とに比例すると考えられる。この最大酸素吸蔵密度と酸素吸蔵密度との差（Ｏｓｔｍａｘ−Ｏｓｔ）は、着目している特定領域における酸素吸蔵余裕量を表す。
【０１０８】
そこで、簡単のために関数ｆ１（ｘ）＝ｆ２（ｘ）＝ｘとすると、下記の（３５）式が得られる。下記（３５）式のｋｓｔｏｒ，ｉは酸素吸蔵速度係数（吸蔵側反応速度係数，ストレージ・エージェントの消費速度係数）であって、よく知られたアレニウスの式で表される温度に依存して変化する係数であり、別途検出又は推定される触媒温度Ｔｅｍｐと所定の関数（酸素吸蔵速度係数ｋｓｔｏｒ，ｉと触媒温度Ｔｅｍｐとの間の関係を規定したマップでも良い。）とに基づいて求めることができる。なお、酸素吸蔵速度係数ｋｓｔｏｒ，ｉは、触媒劣化程度に応じても変化するので、同触媒劣化程度に応じて求めてもよい。
【０１０９】
【数３５】

【０１１０】
従って、（２７）式と（３５）式とから、消費速度定数Ｒ＊ｓｔｏｒ，ｉは下記（３６）式により求めることができる。
【０１１１】
【数３６】

【０１１２】
また、酸素の吸蔵（吸着）と放出のみに着目しているこの触媒モデルにおいては、還元剤であるリダクション・エージェントはコート層に吸蔵されている酸素の放出のみに使用されるから、同リダクション・エージェントの消費速度Ｒｒｅｄｃｕ，ｉはコート層に吸蔵されている酸素が放出される速度（酸素の放出速度）Ｒｒｅｌ，ｉと等しい。
【０１１３】
そこで、酸素の放出速度Ｒｒｅｌ，ｉについて検討すると、同放出速度Ｒｒｅｌ，ｉは、酸素の吸蔵速度Ｒｓｔｏｒ，ｉと同様に反応速度論に基き、同コート層において酸素を消費する化学種（例えば、ＣＯ，ＨＣ）の濃度Ｃｗ，ｒｅｄｕｃ，ｉ（例えば、Ｃｗ，ＣＯ、Ｃｗ，ＨＣ）の関数ｇ１（Ｃｗ，ｒｅｄｕｃ，ｉ）の値に比例するとともに、酸素吸蔵密度Ｏｓｔの関数ｇ２（Ｏｓｔ）の値とに比例すると考えられる。
【０１１４】
そこで、簡単のために関数ｇ１（ｘ）＝ｇ２（ｘ）＝ｘとすると、下記の（３７）式が得られる。下記（３７）式のｋｒｅｌ，ｉは酸素放出速度係数（吸脱側反応速度係数）であって、酸素吸蔵速度係数ｋｓｔｏｒ，ｉと同様にアレニウスの式で表される温度に依存して変化する係数であり、別途検出又は推定される触媒温度Ｔｅｍｐに基づいて所定の関数（酸素放出速度係数ｋｒｅｌ，ｉと触媒温度Ｔｅｍｐとの間の関係を規定したマップでも良い。）に基づいて求めることができる。なお、酸素放出速度係数ｋｒｅｌ，ｉは、触媒劣化程度に応じても変化するので、同触媒劣化程度に応じて求めてもよい。
【０１１５】
【数３７】

【０１１６】
この結果、上述したようにリダクション・エージェントの消費速度Ｒｒｅｄｃｕ，ｉはコート層の酸素の放出速度Ｒｒｅｌ，ｉと等しいから、消費速度定数Ｒ＊ｒｅｄｕｃ，ｉは（３１）式と（３７）式とを比較することにより得られる下記（３８）式に基づいて求めることができる。
【０１１７】
【数３８】

【０１１８】
以上のことから、酸素吸蔵密度Ｏｓｔが求められれば（酸素吸蔵密度Ｏｓｔの求め方については、後述する。）、（３６）式から消費速度定数Ｒ＊ｓｔｏｒ，ｉ（例えば、Ｒ＊Ｏ２）を求めることができる。一方、見かけの拡散速度Ｒ_Ｄ，ｉ（例えば、Ｒ_Ｄ，Ｏ２）は（８）式のようにＳｇｅｏ・ｈ_Ｄ，ｉであるから、温度と流量の関数（触媒の温度と同触媒を通過する排ガスの流量の関数）として実験的に求めておくことができる。この結果、（２９）式からＳＰｓｔｏｒ，ｉ（例えば、ＳＰｓｔｏｒ，Ｏ２）が決定されるので、境界条件としてＣｇｉｎ，ｓｔｏｒ，ｉ（例えば、Ｃｇｉｎ，Ｏ２）が与えられるとき、（３０）式からＣｇｏｕｔ，ｓｔｏｒ，ｉ（例えば、Ｃｏｕｔ，Ｏ２）が求められる。そして、新たなＣｗ，ｓｔｏｒ，ｉ（例えば、Ｃｗ，Ｏ２）が（２８）式により求められる。
【０１１９】
同様に、酸素吸蔵密度Ｏｓｔが求められれば、（３８）式から消費速度定数Ｒ＊ｒｅｄｕｃ，ｉ（例えば、Ｒ＊ｒｅｄｕｃ，ＣＯ）を求めることができる。一方、見かけの拡散速度Ｒ_Ｄ，ｉ（例えば、Ｒ_Ｄ，ＣＯ）は（８）式のようにＳｇｅｏ・ｈ_Ｄ，ｉであるから、温度と流量の関数（触媒の温度と同触媒を通過する排ガスの流量の関数）として実験的に求めておくことができる。この結果、（３３）式からＳＰｒｅｄｕｃ，ｉ（例えば、ＳＰｒｅｄｕｃ，ＣＯ）が決定されるので、境界条件としてＣｇｉｎ，ｒｅｄｕｃ，ｉ（例えば、Ｃｇｉｎ，ＣＯ）が与えられるとき、（３４）式からＣｇｏｕｔ，ｒｅｄｕｃ，ｉ（例えば、Ｃｇｏｕｔ，ＣＯ）が求められる。そして、新たなＣｗ，ｒｅｕｄｃ，ｉ（例えば、Ｃｗ，ＣＯ）が（３２）式により求められる。
【０１２０】
次に、Ｃｇｏｕｔ，ｓｔｏｒ，ｉ、Ｃｇｏｕｔ，ｒｅｄｕｃ，ｉを求めるために必要となる酸素吸蔵密度Ｏｓｔの求め方について説明する。
【０１２１】
先ず、コート層での化学種としての酸素の収支について着目すると、同収支はコート層での酸素の吸蔵分と酸素の放出分の差であるから、下記（３９）式により記述される。（３９）式でｄＡ・Ｌは特定領域の体積ｄＶである。
【０１２２】
【数３９】

【０１２３】
この（３９）式を変形すると、下記（４０）式が得られる。
【０１２４】
【数４０】

【０１２５】
この（４０）式を、（３５）式と（３７）式とを用いながら離散化すると、下記の（４１）式が得られる。
【０１２６】
【数４１】

【０１２７】
この（４１）式を変形すると、下記（４２）式〜（４４）式が得られ、これらから酸素吸蔵密度Ｏｓｔを求めること（更新して行くこと）ができる。
【０１２８】
【数４２】

【０１２９】
【数４３】

【０１３０】
【数４４】

【０１３１】
このように、式（４２）〜（４４）式から酸素吸蔵密度Ｏｓｔが求められるので、上述したようにＣｇｏｕｔ，ｓｔｏｒ，ｉ、Ｃｇｏｕｔ，ｒｅｄｕｃ，ｉを求めることができる。また、酸素吸蔵密度Ｏｓｔが求められるから、下記（４５）式に基づいて特定領域の酸素吸蔵量ＯＳＡを求めることができる。
【数４５】

【０１３２】
従って、触媒に流入する化学種濃度Ｃｇｉｎ，ｉが境界条件として与えられたとき、触媒上流のブロック（特定領域）から、順次、（４５）式を用いて各ブロックの酸素吸蔵量ＯＳＡを求めることができ、これにより、触媒内部の酸素吸蔵量の分布が精度良く推定される。また、各ブロックの酸素吸蔵量ＯＳＡを触媒全体について積算すれば、同触媒全体の酸素吸蔵量についても精度良く推定することができる。以上が、本排気浄化装置が使用する触媒モデルであり、同排気浄化装置は係る触媒モデルにより推定される第２触媒５４のブロックｉから流出する酸素の濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞を用いて空燃比制御を行う。
【０１３３】
（実際の作動）
次に、上記排気浄化装置の実際の作動について、ＣＰＵ７１が実行するルーチンを示したフローチャートを参照しながら説明する。なお、本排気浄化装置の触媒モデルは、酸素をストレージエージェントとして考慮し、一酸化炭素及び炭化水素をリダクションエージェントとして考慮している。これに対し、更に、窒素酸化物をストレージエージェントとして考慮してもよいし、一酸化炭素のみでリダクションエージェントを代表させてもよい。
【０１３４】
ＣＰＵ７１は、各気筒のクランク角が各吸気上死点前の所定クランク角度（例えば、ＢＴＤＣ９０°ＣＡ）となる毎に、図１０に示したルーチンを繰り返し実行するようになっている。従って、任意の気筒のクランク角度が前記所定クランク角度になると、ＣＰＵ７１はステップ１０００から処理を開始してステップ１００５に進み、エアフローメータ６１により計測された吸入空気量ＡＦＭと、エンジン回転速度ＮＥとに基いて、機関に供給される混合気の空燃比を理論空燃比とするための基本燃料噴射量Ｆｂａｓｅをマップから求める。
【０１３５】
次いで、ＣＰＵ７１はステップ１０１０に進み、基本燃料噴射量Ｆｂａｓｅに後述する空燃比フィードバック補正量ＤＦｉを加えた値を最終燃料噴射量Ｆｉとして設定するとともに、続くステップ１０１５にて同最終燃料噴射量Ｆｉの燃料を噴射するための指示をインジェクタ３９に対して行い、ステップ１０９５に進んで本ルーチンを一旦終了する。以上により、フィードバック補正された最終燃料噴射量Ｆｉの燃料が吸気行程を迎える気筒に対して噴射される。
【０１３６】
次に、上記空燃比フィードバック補正量ＤＦｉの算出について説明すると、ＣＰＵ７１は図１１に示したルーチンを所定時間の経過毎に繰り返し実行している。従って、所定のタイミングになると、ＣＰＵ７１はステップ１１００から処理を開始し、ステップ１１０５に進んで空燃比フィードバック制御条件が成立しているか否かを判定する。空燃比フィードバック制御条件は、例えば、機関の冷却水温ＴＨＷが第１所定温度以上であり、機関の一回転当りの吸入空気量（負荷）が所定値以下であり、第１触媒下流空燃比センサ６６が正常であるときに成立する。
【０１３７】
いま、空燃比フィードバック制御条件が成立し、且つ、後述する第２触媒５４のブロックｉから流出する酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が正の閾値Ｃｒｅｆｐｌｓより小さい状態から大きい状態へと変化したとして説明を続ける。この場合、ＣＰＵ７１はステップ１１０５にて「Ｙｅｓ」と判定してステップ１１１０に進み、ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が正の閾値Ｃｒｅｆｐｌｓより大きいか否かを判定する。前述の仮定に従えば、ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞は正の閾値Ｃｒｅｆｐｌｓより大きいので、ＣＰＵ７１はステップ１１１０にて「Ｙｅｓ」と判定してステップ１１１５に進み、同ステップ１１１５にて本ルーチンを前回実行したときの（前回の）ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が閾値Ｃｒｅｆｐｌｓより小さいか否かを判定する。前述の仮定に従えば、前回のＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞は正の閾値Ｃｒｅｆｐｌｓより小さいので、ＣＰＵ７１はステップ１１１５にて「Ｙｅｓ」と判定してステップ１１２０に進み、同ステップ１１２０にて空燃比フィードバック補正量ＤＦｉに正の値βを設定し、ステップ１１９５に進んで本ルーチンを一旦終了する。
【０１３８】
このように、本排気浄化装置は、酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が正の閾値Ｃｒｅｆｐｌｓより小さい状態から大きい状態へと変化したとき、空燃比フィードバック補正量ＤＦｉを正の値βとし、これにより、機関に供給される混合気の空燃比（従って、第１触媒５３に流入する空燃比）を理論空燃比よりもリッチ（理論空燃比−α＝理論空燃比−α２）とする。この結果、第２触媒５４にもリッチな空燃比の排ガスが流入するようになり、図４の時刻ｔ２〜ｔ３に示したように、酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が略「０」に維持されるようになる。
【０１３９】
なお、今回及び前回の酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が正の閾値Ｃｒｅｆｐｌｓより大きいとき、ＣＰＵ７１はステップ１１１０にて「Ｙｅｓ」、ステップ１１１５にて「Ｎｏ」と判定し、そのままステップ１１９５に進んで本ルーチンを一旦終了する。この結果、空燃比フィードバック補正量ＤＦｉは正の値βに維持され、機関に供給される混合気の空燃比も理論空燃比よりリッチな空燃比（理論空燃比−α）に維持される。
【０１４０】
一方、空燃比フィードバック制御条件が成立し、且つ、第２触媒５４のブロックｉから流出する酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が負の閾値Ｃｒｅｆｍｎｓより大きい状態から小さい状態へと変化したとして説明を続ける。この場合、ＣＰＵ７１はステップ１１０５にて「Ｙｅｓ」、ステップ１１１０にて「Ｎｏ」と判定してステップ１１２５に進み、ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が負の閾値Ｃｒｅｆｍｎｓより小さいか否かを判定する。前述の仮定に従えば、ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞は負の閾値Ｃｒｅｆｍｎｓより小さいので、ＣＰＵ７１はステップ１１２５にて「Ｙｅｓ」と判定してステップ１１３０に進み、同ステップ１１３０にて本ルーチンを前回実行したときの（前回の）ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が閾値Ｃｒｅｆｍｎｓより大きいか否かを判定する。前述の仮定に従えば、前回のＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞は閾値Ｃｒｅｆｍｎｓより大きいので、ＣＰＵ７１はステップ１１３０にて「Ｙｅｓ」と判定してステップ１１３５に進み、同ステップ１１３５にて空燃比フィードバック補正量ＤＦｉに正の値βの符号をマイナスにした値（−β）を設定し、ステップ１１９５に進んで本ルーチンを一旦終了する。
【０１４１】
このように、本排気浄化装置は、酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が負の閾値Ｃｒｅｆｍｎｓより大きい状態から小さい状態へと変化したとき、空燃比フィードバック補正量ＤＦｉを負の値−βとし、これにより、機関に供給される混合気の空燃比（従って、第１触媒５３に流入する空燃比）を理論空燃比よりもリーン（理論空燃比＋α＝理論空燃比＋α１）とする。この結果、第２触媒５４にもリーンな空燃比の排ガスが流入するようになり、図４の時刻ｔ１〜ｔ２及び時刻ｔ３〜ｔ４に示したように、酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が略「０」に維持されるようになる。
【０１４２】
なお、今回及び前回の酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が負の閾値Ｃｒｅｆｍｎｓより小さいとき、ＣＰＵ７１はステップ１１１０にて「Ｎｏ」、ステップ１１２５にて「Ｙｅｓ」、ステップ１１３０にて「Ｎｏ」と判定し、そのままステップ１１９５に進んで本ルーチンを一旦終了する。この結果、空燃比フィードバック補正量ＤＦｉは負の値−βに維持され、機関に供給される混合気の空燃比も理論空燃比よりリーンな空燃比（理論空燃比＋α）に維持される。
【０１４３】
また、空燃比フィードバック制御条件が成立してなければ、ＣＰＵ７１はステップ１１０５にて「Ｎｏ」と判定してステップ１１４０に進み、同ステップ１１４０にて空燃比フィードバック補正量ＤＦｉに「０」を設定し、次いでステップ１１９５に進んで本ルーチンを一旦終了する。以上のように、空燃比フィードバック補正量ＤＦｉは、酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が正の閾値Ｃｒｅｆｐｌｓと負の閾値Ｃｒｅｆｍｎｓとの間の所定値になるように決定される。
【０１４４】
次に、上記空燃比フィードバック補正量ＤＦｉの決定に使用する第２触媒５４のＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞を求めるとともに、第１触媒５３から流出する酸素の濃度であるＣｇｏｕｔＳＣ，Ｏ２＜ｒ＞を求め、同酸素濃度ＣｇｏｕｔＳＣ，Ｏ２＜ｒ＞と第１触媒下流空燃比センサ６６の出力との比較結果に基づいて同第１触媒５３及び同第２触媒５４に対する各触媒モデルの修正を行うための実際の作動について説明する。
【０１４５】
ＣＰＵ７１は図１２にフローチャートにより示したルーチンを所定時間の経過毎に繰り返し実行している。従って、所定のタイミングになると、ＣＰＵ７１はステップ１２００から処理を開始し、ステップ１２０５に進んで第１触媒５３用の酸素吸蔵速度係数ｋｓｔｏｒＳＣ＜ｊ＞，Ｏ２（ｋ）、係数ｋｒｅｌＳＣ，ＣＯ（ｋ）＜ｊ＞、及び係数ｋｒｅｌＳＣ，ＨＣ（ｋ）＜ｊ＞を、第１触媒５３の温度ＴｅｍｐＳＣと同第１触媒５３の劣化程度を表す劣化指標値ＲＥＫＫＡＳＣと図１７に示したようなマップ（ルックアップテーブル）とから決定する。なお、例えば、ｋｓｔｏｒＳＣ，Ｏ２（ｋ）＜ｊ＞のように、ＳＣが付与されている値は第１触媒用の値であることを意味し、＜ｊ＞が付与されている値はブロックｊ（ｊ番目のブロック）に対する値であることを意味する（以下、同じ。）。
【０１４６】
上記触媒温度ＴｅｍｐＳＣ及び後述する第２触媒５４の触媒温度ＴｅｍｐＵＦは、機関１０の運転状態（例えば、吸入空気量Ｇａとエンジン回転速度ＮＥ）に応じて推定される。上記第１触媒５３の劣化指標値ＲＥＫＫＡＳＣ及び第２触媒触媒５４の劣化指標値ＲＥＫＫＡＵＦは、第１触媒５３の最大酸素吸蔵量ＣｍａｘＳＣ及び第２触媒５４の最大酸素吸蔵量ＣｍａｘＵＦに応じてそれぞれ求められる。例えば、劣化指標値ＲＥＫＫＡＳＣは最大酸素吸蔵量ＣｍａｘＳＣが減少するほと増大する値として、劣化指標値ＲＥＫＫＡＵＦは最大酸素吸蔵量ＣｍａｘＵＦが減少するほと増大する値として求められる。
【０１４７】
また、最大酸素吸蔵量ＣｍａｘＳＣ，ＣｍａｘＵＦは、次のようにして求められる。即ち、機関１０が所定の定常運転状態にある場合に、第１触媒下流空燃比センサ６６及び第２触媒下流空燃比センサ６７が理論空燃比よりリーンな空燃比を検出しているとき、第１触媒５３に流入する排ガスの空燃比（機関に供給される混合気の空燃比）を所定のリッチ空燃比に維持し、これにより第１触媒５３及び第２触媒５４のそれぞれに貯蔵されている酸素を総べて消費する。この結果、先ず、第１触媒下流空燃比センサ６６が理論空燃比よりリーンな空燃比に対応する値から理論空燃比よりリッチな空燃比に対応する値を出力し、次いで、第２触媒下流空燃比センサ６７が理論空燃比よりリーンな空燃比に対応する値から理論空燃比よりリッチな空燃比に対応する値を出力する。この時点を時点Ｔ１０とする。
【０１４８】
次に、時点Ｔ１０から第１触媒５３に流入する排ガスの空燃比を所定のリーン空燃比に設定する。これにより、第１触媒５３に酸素が吸蔵され始め、やがて最大酸素吸蔵量ＣｍａｘＳＣに到達する。このとき、第１触媒下流空燃比センサ６６は理論空燃比よりリッチな空燃比に対応する値から理論空燃比よりリーンな空燃比に対応する値を出力する。この時点を時点Ｔ２０とする。
【０１４９】
ＣＰＵ７１は、上記時点Ｔ１０〜時点Ｔ２０において、第１触媒５３に流入する排ガス中に含まれる酸素の量を下記（４６）式、及び（４７）式に基づいて求める。（４６）式における排ガスの空燃比ＡＦは、エアフローメータ６１が計測する単位時間あたりの吸入空気質量Ｇａを最終燃料噴射量Ｆｉとエンジン回転速度ＮＥとに基づいて求められる単位時間あたりの供給燃料質量Ｇｆで除することにより求められる。下記（４７）式により求められる積算値Ｏ２ｓｔｏｒａｇｅが最大酸素吸蔵量ＣｍａｘＳＣである。
【０１５０】
【数４６】

【０１５１】
【数４７】

【０１５２】
次に、時点Ｔ２０以降も第１触媒５３に流入する排ガスの空燃比を前記所定のリーン空燃比に維持する。これにより第１触媒５３からリーン空燃比の排ガスが流出するので、同時点Ｔ２０から第２触媒５４に酸素が吸蔵され始め、所定時間が経過すると第２触媒５４の酸素吸蔵量が最大酸素吸蔵量ＣｍａｘＵＦに達する。この結果、第２触媒下流空燃比センサ６７が理論空燃比よりリッチな空燃比に対応する値から理論空燃比よりリーンな空燃比に対応する値を出力する。この時点を時点Ｔ３０とする。
【０１５３】
ＣＰＵ７１は、上記時点Ｔ２０〜時点Ｔ３０において、第１触媒５３に流入する排ガス中に含まれる酸素の量を上記（４６）式、及び（４７）式に基づいて求める。なお、この場合、上記（４７）式の積分区間はＴ２０〜時点Ｔ３０である。この（４７）式により求められる積算値Ｏ２ｓｔｏｒａｇｅが最大酸素吸蔵量ＣｍａｘＵＦである。
【０１５４】
再び、図１２を参照すると、ＣＰＵ７１は、ステップ１２１０に進んで第１触媒５３の各特定成分のＣｇｏｕｔＳＣを算出するサブルーチンを実行する。このサブルーチンは図１３〜図１５のフローチャートにより示されていて、ＣＰＵ７１はこれらのルーチンを実行することで第１触媒５３から流出する酸素濃度ＣｇｏｕｔＳＣ，Ｏ２＜ｒ＞、一酸化炭素濃度ＣｇｏｕｔＳＣ，ＣＯ＜ｒ＞、及び炭化水素濃度ＣｇｏｕｔＳＣ，ＨＣ＜ｒ＞を算出する。なお、前述したように、触媒モデルは、第１触媒５３をｒ個のブロックに分けて各特定成分を求めるようになっている。
【０１５５】
ここで、ステップ１２１０における具体的処理内容を説明すると、ＣＰＵ７１は同ステップ１２１０に進んだとき図１３のステップ１３００から処理を開始し、ステップ１３０５に進んで変数ｊの値を「０」に設定する。この変数ｊは、以下において何番目のブロックについての演算を行うのかを決定する変数である。次いで、ＣＰＵ７１は、ステップ１３１０にて変数ｊの値を「１」だけ増大するとともに、ステップ１３１５にて変数ｊの値がｒ＋１と等しくなったか否か、即ち、総べてのブロックについて各特定成分の算出が終了したか否かを判定する。
【０１５６】
現段階での変数ｊの値は「１」であるから、ＣＰＵ７１はステップ１３１５にて「Ｎｏ」と判定してステップ１３２０に進み、前回の本ルーチンの演算時において後述するステップ１３５５にて算出されたｊ番目のブロック（ブロックｊ）のコート層の酸素濃度ＣｗＳＣ，Ｏ２（ｋ＋１）＜ｊ＞を今回のコート層の酸素濃度ＣｗＳＣ，Ｏ２（ｋ）＜ｊ＞に設定し、続くステップ１３２５にて前回の本ルーチンの演算時において後述する図１６のステップ１６１５にて算出された酸素吸蔵密度ＯｓｔＳＣ（ｋ＋１）＜ｊ＞を今回の酸素吸蔵密度Ｏｓｔの値ＯｓｔＳＣ（ｋ）＜ｊ＞に設定する。なお、今回の演算が機関１０の始動後初めてである場合、上記各値には適当な初期値が与えられる。
【０１５７】
次いで、ＣＰＵ７１は、ステップ１３３０にて同ステップ１３３０内に記載した式（上記（３６）式を参照。）に従って酸素の消費速度定数Ｒ＊ｓｔｏｒＳＣ，Ｏ２（ｋ）＜ｊ＞を求める。ステップ１３３０にて用いる最大酸素吸蔵密度ＯｓｔＳＣｍａｘ＜ｊ＞は、一定値としてもよいが、前記触媒劣化指標値ＲＥＫＫＡＳＣ（又は、最大酸素吸蔵量ＣｍａｘＳＣ）に応じて決定されることが望ましい（以下、同じ。）。その後、ＣＰＵ７１はステップ１３３５にて見かけの拡散速度Ｒ_ＤＳＣ，Ｏ２（ｋ）＜ｊ＞を触媒温度ＴｅｍｐＳＣとマップＭａｐＲ_ＤＳＣＯ２とから決定する。
【０１５８】
続いて、ＣＰＵ７１はステップ１３４０にて酸素の反応律速因子ＳＰｓｔｏｒＳＣ，Ｏ２＜ｊ＞を同ステップ１３４０内に記載した式（上記（２９）式を参照。）により求め、ステップ１３４５にてブロックｊよりも前の（即ち、上流の）ブロックｊ−１から流出する酸素濃度ＣｇｏｕｔＳＣ，Ｏ２（ｋ）＜ｊ−１＞をブロックｊに流入する酸素濃度ＣｇｉｎＳＣ，Ｏ２（ｋ）＜ｊ＞として取り込む。
【０１５９】
この段階でｊの値は「１」であるから、ブロックｊは第１触媒５３の最も上流のブロックであって、それより前の（上流の）ブロックｊ−１は存在しない。従って、ステップ１３４５における前のブロックのＣｇｏｕｔＳＣ，Ｏ２（ｋ）＜ｊ−１＞は、同第１触媒５３に流入する排ガスの酸素濃度ＣｇｉｎＳＣ，Ｏ２である。この第１触媒５３に流入する排ガスの酸素濃度ＣｇｉｎＳＣ，Ｏ２（＝Ｃｇｉｎ，Ｏ２）は、同第１触媒５３に流入する排ガスの空燃比と同排ガスの流量とに基く関数ｆＯ２により求められる。下記の（４８）式の右辺は、この関数ｆＯ２の具体例である。（４８）式で用いられる排ガスの空燃比ＡＦは、エアフローメータ６１が計測する単位時間あたりの吸入空気質量Ｇａを最終燃料噴射量Ｆｉとエンジン回転速度ＮＥとに基づいて求められる単位時間あたりの供給燃料質量Ｇｆで除することにより求められる。
【０１６０】
【数４８】

【０１６１】
上記（４８）式の導出過程を簡単に述べると、第１触媒５３に流入する排ガスの空燃比ＡＦはＧａ／Ｇｆであり、Ｇｆに対して理論空燃比を得るために必要な空気質量をＧａｓｔｏｉｃｈとすると、理論空燃比ＡＦｓｔｏｉｃｈはＧａｓｔｏｉｃｈ／Ｇｆとなる。一方、供給燃料質量がＧｆであるときに空燃比がＡＦとなったとき、理論空燃比ＡＦｓｔｏｉｃｈを得るために必要な空気質量に対する過剰な空気質量はＧａ−Ｇａｓｔｏｉｃｈであるから、酸素の質量をＭａｓｓＯ２とおくと、下記（４９）式が得られ、この（４９）式から上記（４８）式が得られる。
【０１６２】
【数４９】

【０１６３】
次に、ＣＰＵ７１はステップ１３５０に進み、同ステップ１３５０に記述した式（上記（３０）式を参照。）に従ってＣｇｏｕｔＳＣ，Ｏ２（ｋ＋１）＜ｊ＞を求める。ｖｇの値はエアフローメータ１３が検出した吸入空気流量ＡＦＭ（＝Ｇａ）とする。このように、ステップ１３５０では、対象としているブロックｊから流出する酸素濃度ＣｇｏｕｔＳＣ，Ｏ２を新たに算出する。次いで、ＣＰＵ７１はステップ１３５５に進み、同ステップ１３５５に記述した式（上記（２８）式を参照。）に従ってＣｗＳＣ，Ｏ２（ｋ＋１）＜ｊ＞を求める。即ち、ＣＰＵ７１は、ステップ１３５５にて対象としているブロックｊのコート層の酸素濃度ＣｗＳＣ，Ｏ２を新たに算出し、ステップ１３６０を経由して図１４に示したステップ１４００に進む。このように、図１３により示したルーチンは、第１触媒５３のブロックｊ（特定領域ｊ）における排ガス相の酸素濃度推定手段、及びコート層の酸素濃度推定手段を構成している。
【０１６４】
次に、ＣＰＵ７１はステップ１４００からステップ１４０５に進んで、前回の本ルーチンの演算時において後述するステップ１４３５にて算出されたコート層の一酸化炭素ＣｗＳＣ，ＣＯ（ｋ＋１）＜ｊ＞を今回のコート層の一酸化炭素濃度ＣｗＳＣ，ＣＯ＜ｊ＞（ｋ）に設定する。なお、今回の演算が機関１０の始動後初めてである場合、上記ＣｗＳＣ，ＣＯ＜ｊ＞（ｋ）には適当な初期値が与えられる。
【０１６５】
次に、ＣＰＵ７１は、ステップ１４１０にて同ステップ１４１０内に記載した式（上記（３８）式を参照。）に従って消費速度定数Ｒ＊ｒｅｄｕｃＳＣ，ＣＯ（ｋ）＜ｊ＞を求め、その後、ステップ１４１５にて見かけの拡散速度Ｒ_ＤＳＣ，ＣＯ（ｋ）＜ｊ＞を触媒温度ＴｅｍｐＳＣとマップＭａｐＲ_ＤＳＣＣＯとから決定する。
【０１６６】
続いて、ＣＰＵ７１はステップ１４２０にて一酸化炭素の反応律速因子ＳＰｒｅｄｕｃＳＣ，ＣＯ＜ｊ＞を同ステップ１４２０内に記載した式（上記（３３）式を参照。）により求め、ステップ１４２５にて、ブロックｊよりも前の（即ち、上流の）ブロックｊ−１から流出する一酸化炭素濃度ＣｇｏｕｔＳＣ，ＣＯ（ｋ）＜ｊ−１＞を、ブロックｊに流入する一酸化炭素濃度ＣｇｉｎＳＣ，ＣＯ（ｋ）＜ｊ＞として取り込む。
【０１６７】
この段階でｊの値は「１」であるから、対象としているブロックｊは第１触媒５３の最も上流のブロックであって、それより上流のブロックｊ−１は存在しない。従って、ステップ１４２５における前のブロックのＣｇｏｕｔＳＣ，ＣＯ（ｋ）＜ｊ−１＞は、同第１触媒５３に流入する排ガスの一酸化炭素濃度ＣｇｉｎＳＣ，ＣＯである。この場合、第１触媒５３に流入する排ガスの空燃比Ａ／Ｆ（「Ｇａ／Ｇｆ」として計算により求められる。）と一酸化炭素濃度ＣｇｉｎＳＣ，ＣＯとの関係は図１８のグラフに示したようであるから、この関係を予め実験により求めてマップとして記憶しておき、計算により求められる実際の排ガスの空燃比Ａ／Ｆと同マップとから一酸化炭素濃度ＣｇｉｎＳＣ，ＣＯを求める。
【０１６８】
次に、ＣＰＵ７１はステップ１４３０に進み、同ステップ１４３０に記述した式（上記（３４）式を参照。）に従ってＣｇｏｕｔＳＣ，ＣＯ（ｋ＋１）＜ｊ＞を求める。即ち、ブロックｊから流出する一酸化炭素濃度ＣｇｏｕｔＳＣ，ＣＯを新たに算出する。次いで、ＣＰＵ７１はステップ１４３５に進み、同ステップ１４３５に記述した式（上記（３２）式を参照。）に従ってＣｗＳＣ，ＣＯ（ｋ＋１）＜ｊ＞を求める。即ち、ＣＰＵ７１は、ステップ１４３５にて対象としているブロックｊのコート層の一酸化炭素濃度ＣｗＳＣ，ＣＯを新たに算出し、ステップ１４９５を経由して図１５に示したステップ１５００に進む。このように、図１４により示したルーチンは、第１触媒５３のブロックｊにおける排ガス相の一酸化炭素濃度推定手段、及びコート層の一酸化炭素濃度推定手段を構成している。
【０１６９】
図１５に示したルーチンは、炭化水素ＨＣについての演算を行うルーチンであり、一酸化炭素ＣＯについての演算を行うための先に説明した図１４のルーチンと同様なルーチンである。
【０１７０】
簡単に説明すると、ＣＰＵ７１はステップ１５００からステップ１５０５に進んで、前回の本ルーチンの演算時において後述するステップ１５３５にて算出されたコート層の一酸化炭素ＣｗＳＣ，ＨＣ（ｋ＋１）＜ｊ＞を今回のコート層の一酸化炭素濃度Ｃｗ，ＨＣの値であるＣｗＳＣ，ＨＣ（ｋ）＜ｊ＞に設定する。なお、今回の演算が機関１０の始動後初めてである場合、上記各値には適当な初期値が与えられる。
【０１７１】
次に、ＣＰＵ７１は、ステップ１５１０にて同ステップ１５１０内に記載した式（上記（３８）式を参照。）に従って消費速度定数Ｒ＊ｒｅｄｕｃＳＣ，ＨＣ（ｋ）＜ｊ＞を求め、その後、ステップ１５１５にて見かけの拡散速度Ｒ_ＤＳＣ，ＨＣ（ｋ）＜ｊ＞を触媒温度ＴｅｍｐＳＣとマップＭａｐＲ_ＤＳＣＨＣとから決定する。
【０１７２】
続いて、ＣＰＵ７１はステップ１５２０にて炭化水素の反応律速因子ＳＰｒｅｄｕｃＳＣ，ＨＣ＜ｊ＞を同ステップ１５２０内に記載した式（上記（３３）式を参照。）により求め、ステップ１５２５にて、ブロックｊよりも前の（即ち、上流の）ブロックｊ−１から流出する炭化水素濃度ＣｇｏｕｔＳＣ，ＨＣ（ｋ）＜ｊ−１＞をブロックｊに流入する炭化水素濃度Ｃｇｉｎ，ＨＣ（ｋ）＜ｊ＞として取り込む。
【０１７３】
この段階でｊの値は「１」であるから、ブロックｊは第１触媒５３の最も上流のブロックであって、それより上流のブロックｊ−１は存在しない。従って、ステップ１５２５におけるＣｇｏｕｔ，ＨＣ（ｋ）＜ｊ−１＞は、同第１触媒５３に流入する排ガスの炭化水素濃度Ｃｇｉｎ，ＨＣである。この場合、第１触媒５３に流入する排ガスの空燃比Ａ／Ｆ（「Ｇａ／Ｇｆ」として計算により求められる。）と炭化水素濃度Ｃｇｉｎ，ＨＣとの関係は図１９のグラフに示したようであるから、この関係を予め実験により求めてマップとして記憶しておき、計算により求められる実際の排ガスの空燃比Ａ／Ｆと同マップとから炭化水素濃度Ｃｇｉｎ，ＨＣを求める。
【０１７４】
次に、ＣＰＵ７１はステップ１５３０に進み、同ステップ１５３０に記述した式（上記（３４）式を参照。）に従ってＣｇｏｕｔＳＣ，ＨＣ（ｋ＋１）＜ｊ＞を求める。即ち、ブロックｊから流出する炭化水素濃度ＣｇｏｕｔＳＣ，ＨＣを新たに算出する。次いで、ＣＰＵ７１はステップ１５３５に進み、同ステップ１５３５に記述した式（上記（３２）式を参照。）に従ってＣｗＳＣ，ＨＣ（ｋ＋１）＜ｊ＞を求める。即ち、ＣＰＵ７１は、ステップ１５３５にてブロックｊのコート層の炭化水素濃度Ｃｗ，ＨＣを新たに算出し、ステップ１５９５を経由して図１６に示したステップ１６００に進む。このように、図１５により示したルーチンは、ブロックｊ（特定領域ｊ）における排ガス相の炭化水素濃度推定手段、及びコート層の炭化水素濃度推定手段を構成している。
【０１７５】
次に、ＣＰＵ７１は、ステップ１６００からステップ１６０５に進み、上記（４３）式に基く同ステップ１６０５内に記述した式により係数Ｐ＜ｊ＞を求めるとともに、続くステップ１６１０にて上記（４４）式に基く同ステップ１６１０に記述した式により係数Ｑ＜ｊ＞を求める。次いで、ＣＰＵ７１はステップ１６１５にて上記（４２）式に基く同ステップ１６１５に記述した式により酸素吸蔵密度ＯｓｔＳＣ（ｋ＋１）＜ｊ＞を求め、次のステップ１６２０にて上記（４５）式に基づく同ステップ１６２０に記述した式によりこのブロックｊの酸素吸蔵量ＯｓｔＳＣ（ｋ＋１）＜ｊ＞・ｄＡ・Ｌをブロック１〜ブロックｊ−１までの酸素吸蔵量ＯＳＡＳＣ（ｊ−１）に加えることにより、ブロック１〜ブロックｊまでの酸素吸蔵量ＯＳＡＳＣ（ｊ）を求め、ステップ１６９５を経由して図１３のステップ１３１０に戻る。なお、酸素吸蔵量ＯＳＡＳＣ（０）の値は「０」に設定してある。このように、図１６に示したルーチンは、第１触媒５３のブロックｊの酸素吸蔵密度算出手段、及びブロック１〜ブロックｊまでの酸素吸蔵量算出手段を構成している。
【０１７６】
ステップ１３１０に戻ったＣＰＵ７１は、変数ｊの値を「１」だけ増大するから、上述と同様にして次に下流にあるブロックの各種値が順次演算されて行く。そして、ブロックｒまでの各種値が演算されると、変数ｊの値はステップ１３１０にてｒ＋１と等しくされるので、ＣＰＵ７１はステップ１３１５にて「Ｙｅｓ」と判定し、ステップ１３９５を経由して図１２のステップ１２１５へと進む。
【０１７７】
ＣＰＵ７１は、ステップ１２１５にて第１触媒下流空燃比センサ６６の出力ｖａｂｙｆｓと図２に示したマップＭａｐＡＦとから第１触媒５３下流の排気通路を流れる排ガスの実際の空燃比（検出空燃比）ＡＦＳＣｄｗｎ，ａｃｔを求め、続くステップ１２２０にて先に触媒モデルにより求めた第１触媒５３から流出する酸素濃度ＣｇｏｕｔＳＣ，Ｏ２＜ｒ＞と下記（５０）式とに基づいて、第１触媒５３下流の排気通路を流れる排ガスの推定空燃比ＡＦＳＣｄｗｎ，ｅｓｔを求める。この（５０）式は、上述した（４６）式から導かれる。
【０１７８】
【数５０】

【０１７９】
次いで、ＣＰＵ７１はステップ１２２５に進み、上記検出空燃比ＡＦＳＣｄｗｎ，ａｃｔと上記推定空燃比ＡＦＳＣｄｗｎ，ｅｓｔの差の絶対値が閾値ＡＦｔｈより小さいか否かを判定する。つまり、第１触媒５３についての触媒モデル誤差が小さいか否かを判定する。そして、触媒モデル誤差が大きいとき、ＣＰＵ７１はステップ１２２５にて「Ｎｏ」と判定してステップ１２３０に進み、同ステップ１２３０にて第１触媒５３に対する触媒モデルを修正するために酸素吸蔵速度係数ｋｓｔｏｒＳＣ，Ｏ２（ｋ）＜ｊ＞、係数ｋｒｅｌＳＣ，ＣＯ（ｋ）＜ｊ＞、及び係数ｋｒｅｌＳＣ，ＨＣ（ｋ）＜ｊ＞を、例えば、所定量だけ変化（増大又は減少）することで修正し、その後、ステップ１２１０に戻って第１触媒５３の各特定成分のＣｇｏｕｔＳＣを再び算出する。
【０１８０】
このような処理が繰り返し行われると、第１触媒５３の触媒モデル誤差が小さくなるので、上記検出空燃比ＡＦＳＣｄｗｎ，ａｃｔと上記推定空燃比ＡＦＳＣｄｗｎ，ｅｓｔの差の絶対値が閾値ＡＦｔｈより小さくなる。この結果、ＣＰＵ７１は、ステップ１２２５にて「Ｙｅｓ」と判定してステップ１２３５に進み、同ステップ１２３５にてブロック毎に求められた係数ｋｓｔｏｒＳＣ，Ｏ２（ｋ）＜ｊ＞の平均値をｋｓｔｏｒＳＣ，Ｏ２ａｖｅ、ｋｒｅｌＳＣ，ＣＯ（ｋ）＜ｊ＞の平均値をｋｒｅｌＳＣ，ＣＯａｖｅ、及び係数ｋｒｅｌＳＣ，ＨＣ（ｋ）＜ｊ＞の平均値をｋｒｅｌＳＣ，ＨＣａｖｅとして求める。、
【０１８１】
次に、ＣＰＵはステップ１２４０に進み、同ステップ１２４０にて第２触媒５４の触媒モデルの修正係数を同第２触媒５４のブロック毎に求める。なお、上述したように、触媒モデルは第２触媒５４をｍ個のブロックに分けて各特定成分を求めるようになっている。ステップ１２４０での処理について具体的に述べると、ＣＰＵ７１はブロックｊ毎に定められている所定の変換マップＭａｐｋｓｔｏｒＯ２＜ｊ＞と上記平均値ｋｓｔｏｒＳＣ，Ｏ２ａｖｅとから第２触媒５４のブロックｊのための修正係数ｃｏｅｆ，ｋｓｔｏｒＵＦ，Ｏ２＜ｊ＞を求め、同様に、ブロックｊ毎に定められている所定の変換マップＭａｐｋｒｅｌＣＯ＜ｊ＞と上記平均値ｋｒｅｌＳＣ，ＣＯａｖｅとからブロックｊのための修正係数ｃｏｅｆ，ｋｓｔｏｒＵＦ，ＣＯ＜ｊ＞を求め、ブロックｊ毎に定められている所定の変換マップＭａｐｋｒｅｌＨＣ＜ｊ＞と上記平均値ｋｒｅｌＳＣ，ＨＣａｖｅとから第２触媒５４のブロックｊのための修正係数ｃｏｅｆ，ｋｒｅｌＵＦ，ＨＣ＜ｊ＞を求める。
【０１８２】
次いで、ＣＰＵ７１はステップ１２４５に進み、第２触媒５４用の酸素吸蔵速度係数基本値ｋｓｔｏｒＵＦｏｒｇ，Ｏ２（ｋ）＜ｊ＞、基本係数ｋｒｅｌＵＦｏｒｇ，ＣＯ（ｋ）＜ｊ＞、及び基本係数ｋｒｅｌＵＦｏｒｇ，ＨＣ（ｋ）＜ｊ＞を、第２触媒５４の温度ＴｅｍｐＵＦと同触媒５４の劣化程度を表す劣化指標値ＲＥＫＫＡＵＦと図１７に示したマップと同様なマップとから決定する。なお、例えば、ｋｓｔｏｒＵＦｏｒｇ，Ｏ２（ｋ）＜ｊ＞のようにＵＦが付与されている値は、第２触媒用の値であることを意味する（以下、同じ。）。
【０１８３】
次に、ＣＰＵ７１はステップ１２５０に進み、第２触媒５４用の各ブロックｊについての酸素吸蔵速度係数ｋｓｔｏｒＵＦ，Ｏ２（ｋ）＜ｊ＞を上記酸素吸蔵速度係数基本値ｋｓｔｏｒＵＦｏｒｇ，Ｏ２（ｋ）＜ｊ＞に上記修正係数ｃｏｅｆ，ｋｓｔｏｒＵＦ，Ｏ２＜ｊ＞を乗じることにより求め、同様に、係数ｋｒｅｌＵＦ，ＣＯ（ｋ）＜ｊ＞を基本係数ｋｒｅｌＵＦｏｒｇ，ＣＯ（ｋ）＜ｊ＞に上記修正係数ｃｏｅｆ，ｋｒｅｌＵＦ，ＣＯ＜ｊ＞を乗じることにより求めるとともに、係数ｋｒｅｌＵＦ，ＨＣ（ｋ）＜ｊ＞を上記基本係数係数ｋｒｅｌＵＦｏｒｇ，ＨＣ（ｋ）＜ｊ＞に上記修正係数ｃｏｅｆ，ｋｒｅｌＵＦ，ＨＣ＜ｊ＞を乗じることにより求める。
【０１８４】
そして、ＣＰＵ７１はステップ１２５５に進んで第２触媒５４の各特定成分のＣｇｏｕｔＵＦを算出するサブルーチンを実行する。このサブルーチンは図１３〜図１６のフローチャートに示されたルーチンとそれぞれ同様の図２０〜図２３のフローチャートにより示されていて、ＣＰＵ７１はこれらのルーチンを実行することで第２触媒５４の各ブロックｊから流出する酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｊ＞、一酸化炭素濃度ＣｇｏｕｔＵＦ，ＣＯ＜ｊ＞、及び炭化水素濃度ＣｇｏｕｔＵＦ，ＨＣ＜ｊ＞を算出する。
【０１８５】
以下、簡単に説明すると、ＣＰＵ７１はステップ２０００に続くステップ２００５にて変数ｊの値を「０」に設定し、ステップ２０１０にて変数ｊの値を「１」だけ増大するとともに、ステップ２０１５にて変数ｊの値がｍ＋１と等しくなったか否か、即ち、総べてのブロックについて各特定成分の算出が終了したか否かを判定する。
【０１８６】
現段階での変数ｊの値は「１」であるから、ＣＰＵ７１はステップ２０１５にて「Ｎｏ」と判定してステップ２０２０に進み、前回の本ルーチンの演算時において算出されたブロックｊのコート層の酸素濃度ＣｗＵＦ，Ｏ２（ｋ＋１）＜ｊ＞を今回のコート層の酸素濃度ＣｗＵＦ，Ｏ２（ｋ）＜ｊ＞に設定し、続くステップ２０２５にて前回の本ルーチンの演算時において算出された酸素吸蔵密度ＯｓｔＵＦ（ｋ＋１）＜ｊ＞を今回の酸素吸蔵密度Ｏｓｔの値ＯｓｔＵＦ（ｋ）＜ｊ＞に設定する。なお、今回の演算が機関１０の始動後初めてである場合、上記各値には適当な初期値が与えられる。
【０１８７】
次いで、ＣＰＵ７１は、ステップ２０３０にて酸素の消費速度定数Ｒ＊ｓｔｏｒＵＦ，Ｏ２（ｋ）＜ｊ＞を求め、続くステップ２０３５にて見かけの拡散速度Ｒ_ＤＵＦ，Ｏ２（ｋ）＜ｊ＞を触媒温度ＴｅｍｐＵＦとマップＭａｐＲ_ＤＵＦＯ２とから決定する。続いて、ＣＰＵ７１はステップ２０４０にて酸素の反応律速因子ＳＰｓｔｏｒＵＦ，Ｏ２＜ｊ＞を求め、ステップ２０４５にてブロックｊよりも上流のブロックｊ−１から流出する酸素濃度ＣｇｏｕｔＵＦ，Ｏ２（ｋ）＜ｊ−１＞をブロックｊに流入する酸素濃度ＣｇｉｎＵＦ，Ｏ２（ｋ）＜ｊ＞として取り込む。
【０１８８】
この段階でｊの値は「１」であるから、ブロックｊは第２触媒５４の最も上流のブロックであって、それより上流のブロックｊ−１は存在しない。従って、ステップ２０４５における前のブロックのＣｇｏｕｔＵＦ，Ｏ２（ｋ）＜ｊ−１＞は、同第２触媒５４に流入する排ガスの酸素濃度ＣｇｉｎＵＦ，Ｏ２である。この第２触媒５４に流入する排ガスの酸素濃度ＣｇｉｎＵＦ，Ｏ２は上記（４８）式に基づいて求められる。このとき、ＣＰＵ７１は、（４８）式で使用される排ガスの空燃比ＡＦを、第１触媒下流空燃比センサ６６の出力ｖａｂｙｆｓと図２に示したマップとから取得する。即ち、この場合、第２触媒５４に流入する排ガスの酸素濃度ＣｇｉｎＵＦ，Ｏ２（＝ＣｇｉｎＵＦ，Ｏ２（ｋ）＜１＞）が第１触媒下流空燃比センサ６６の出力（検出空燃比）に基づいて決定・取得される。
【０１８９】
次に、ＣＰＵ７１はステップ２０５０に進んでブロックｊから流出する酸素濃度ＣｇｏｕｔＵＦ，Ｏ２（ｋ＋１）＜ｊ＞を求め、続くステップ２０５５にてブロックｊのコート層の酸素濃度ＣｗＵＦ，Ｏ２（ｋ＋１）＜ｊ＞を求める。そして、ＣＰＵ７１はステップ２０６０を経由して図２１に示したステップ２１００に進む。このように、図２０により示したルーチンは、第２触媒５４のブロックｊ（特定領域ｊ）における排ガス相の酸素濃度推定手段、及びコート層の酸素濃度推定手段を構成している。
【０１９０】
次に、ＣＰＵ７１はステップ２１０５に進んで、前回の本ルーチンの演算時において算出されたコート層の一酸化炭素ＣｗＵＦ，ＣＯ（ｋ＋１）＜ｊ＞を今回のコート層の一酸化炭素濃度ＣｗＵＦ，ＣＯ＜ｊ＞（ｋ）に設定する。なお、今回の演算が機関１０の始動後初めてである場合、上記ＣｗＵＦ，ＣＯ＜ｊ＞（ｋ）には適当な初期値が与えられる。
【０１９１】
次に、ＣＰＵ７１は、ステップ２１１０〜ステップ２１２０にて、消費速度定数Ｒ＊ｒｅｄｕｃＵＦ，ＣＯ（ｋ）＜ｊ＞を求め、見かけの拡散速度Ｒ_ＤＵＦ，ＣＯ（ｋ）＜ｊ＞を触媒温度ＴｅｍｐＵＦとマップＭａｐＲ_ＤＵＦＣＯとから決定し、一酸化炭素の反応律速因子ＳＰｒｅｄｕｃＵＦ，ＣＯ＜ｊ＞を求める。そして、ステップ２１２５にて、ブロックｊよりも前の（即ち、上流の）ブロックｊ−１から流出する一酸化炭素濃度ＣｇｏｕｔＵＦ，ＣＯ（ｋ）＜ｊ−１＞を、ブロックｊに流入する一酸化炭素濃度ＣｇｉｎＵＦ，ＣＯ（ｋ）＜ｊ＞として取り込む。
【０１９２】
この段階でｊの値は「１」であるから、対象としているブロックｊは第２触媒５４の最も上流のブロックであって、それより上流のブロックｊ−１は存在しない。従って、ステップ２１２５における前のブロックのＣｇｏｕｔＵＦ，ＣＯ（ｋ）＜ｊ−１＞は、同第２触媒５４に流入する排ガスの一酸化炭素濃度ＣｇｉｎＵＦ，ＣＯである。この場合、第２触媒５４に流入する排ガスの空燃比Ａ／Ｆと一酸化炭素濃度ＣｇｉｎＵＦ，ＣＯとの関係は図１８のグラフに示したようであるから、この関係を予め実験により求めてマップとして記憶しておき、第１触媒下流空燃比センサ６６の出力ｖａｂｙｆｓと図２に示したマップとから求められる実際の排ガスの空燃比Ａ／Ｆ（検出空燃比）と同記憶したマップとから一酸化炭素濃度ＣｇｉｎＵＦ，ＣＯ（＝ＣｇｉｎＵＦ，ＣＯ（ｋ）＜１＞）を求める。
【０１９３】
次に、ＣＰＵ７１はステップ２１３０に進みブロックｊから流出する一酸化炭素濃度ＣｇｏｕｔＵＦ，ＣＯ（ｋ＋１）＜ｊ＞を求め、ステップ２１３５にてブロックｊのコート層の一酸化炭素濃度ＣｗＵＦ，ＣＯ（ｋ＋１）＜ｊ＞を求め、その後、ステップ２１９５を経由して図２２に示したステップ２２００に進む。このように、図２１により示したルーチンは、第２触媒５４のブロックｊにおける排ガス相の一酸化炭素濃度推定手段、及びコート層の一酸化炭素濃度推定手段を構成している。
【０１９４】
図２２に示したルーチンは、炭化水素ＨＣについての演算を行うルーチンであり、一酸化炭素ＣＯについての演算を行うための先に説明した図２１のルーチンと同様なルーチンである。
【０１９５】
簡単に説明すると、ＣＰＵ７１はステップ２２００からステップ２２０５に進んで、前回の本ルーチンの演算時において算出されたコート層の一酸化炭素ＣｗＵＦ，ＨＣ（ｋ＋１）＜ｊ＞を今回のコート層の一酸化炭素濃度ＣｗＵＦ，ＨＣ（ｋ）＜ｊ＞に設定する。なお、今回の演算が機関１０の始動後初めてである場合、上記各値には適当な初期値が与えられる。
【０１９６】
次に、ＣＰＵ７１は、ステップ２２１０にて消費速度定数Ｒ＊ｒｅｄｕｃＵＦ，ＨＣ（ｋ）＜ｊ＞を求め、その後、ステップ２２１５にて見かけの拡散速度Ｒ_ＤＵＦ，ＨＣ（ｋ）＜ｊ＞を触媒温度ＴｅｍｐＵＦとマップＭａｐＲ_ＤＵＦＨＣとから決定し、続くステップ２２２０にて炭化水素の反応律速因子ＳＰｒｅｄｕｃＵＦ，ＨＣ＜ｊ＞を求める。そして、ステップ２２２５にて、ブロックｊよりも前の（即ち、上流の）ブロックｊ−１から流出する炭化水素濃度ＣｇｏｕｔＵＦ，ＨＣ（ｋ）＜ｊ−１＞をブロックｊに流入する炭化水素濃度Ｃｇｉｎ，ＨＣ（ｋ）＜ｊ＞として取り込む。
【０１９７】
この段階でｊの値は「１」であるから、ブロックｊは第２触媒５４の最も上流のブロックであって、それより上流のブロックｊ−１は存在しない。従って、ステップ２２２５におけるＣｇｏｕｔＵＦ，ＨＣ（ｋ）＜ｊ−１＞は、同第２触媒５４に流入する排ガスの炭化水素濃度ＣｇｉｎＵＦ，ＨＣである。この場合、第２触媒５４に流入する排ガスの空燃比Ａ／Ｆと炭化水素濃度Ｃｇｉｎ，ＨＣとの関係は図１９のグラフに示したようであるから、この関係を予め実験により求めてマップとして記憶しておき、第１触媒下流空燃比センサ６６の出力ｖａｂｙｆｓと図２に示したマップとから求められる実際の排ガスの空燃比Ａ／Ｆ（検出空燃比）と同記憶したマップとから炭化水素濃度ＣｇｉｎＵＦ，ＨＣ（＝ＣｇｉｎＵＦ，ＨＣ（ｋ）＜１＞）を求める。
【０１９８】
次に、ＣＰＵ７１はステップ２２３０に進みブロックｊから流出する一酸化炭素濃度ＣｇｏｕｔＵＦ，ＨＣ（ｋ＋１）＜ｊ＞を求め、ステップ２２３５にてブロックｊのコート層の一酸化炭素濃度ＣｗＵＦ，ＨＣ（ｋ＋１）＜ｊ＞を求め、ステップ２２９５を経由して図２３に示したステップ２３００に進む。このように、図２２により示したルーチンは、第２触媒５４のブロックｊ（特定領域ｊ）における排ガス相の炭化水素濃度推定手段、及びコート層の炭化水素濃度推定手段を構成している。
【０１９９】
次に、ＣＰＵ７１は、ステップ２３００からステップ２３０５に進んで係数Ｐ＜ｊ＞を求めるとともに、続くステップ２３１０にて係数Ｑ＜ｊ＞を求める。次いで、ＣＰＵ７１はステップ２３１５にて上記（４２）式に基く同ステップ２３１５に記述した式により酸素吸蔵密度ＯｓｔＵＦ（ｋ＋１）＜ｊ＞を求め、次のステップ２３２０にて上記（４５）式に基づいて求められるブロックｊの酸素吸蔵量（＝ＯｓｔＵＦ（ｋ＋１）＜ｊ＞・ｄＡ・Ｌ）をブロック１〜ブロックｊ−１までの酸素吸蔵量ＯＳＡＵＦ（ｊ−１）に加えることによりブロック１〜ブロックｊまでの酸素吸蔵量ＯＳＡＵＦ＜ｊ＞を求め、ステップ２３９５を経由して図１３のステップ２０１０に戻る。なお、酸素吸蔵量ＯＳＡＵＦ（０）の値は「０」に設定してある。このように、図２３に示したルーチンは、第２触媒５４のブロックｊの酸素吸蔵密度算出手段、及びブロック１〜ブロックｊまでの酸素吸蔵量算出手段を構成している。なお、酸素吸蔵量ＯＳＡＵＦ＜ｊ＞は総べてＲＡＭ７３内に格納されて行く。従って、ブロック１〜ブロックｉまでの酸素吸蔵量ＯＳＡＵＦ＜ｉ＞もＲＡＭ内に格納される。
【０２００】
ステップ２０１０に戻ったＣＰＵ７１は、変数ｊの値を「１」だけ増大するから、上述と同様にして次に下流にあるブロックの各種値が順次演算されて行く。従って、変数ｊの値が値ｉとなったとき、上記空燃比フィードバック補正量を決定する際に使用される酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞（＝ＣｇｏｕｔＵＦ，Ｏ２（ｋ＋１）＜ｉ＞）が求められる。そして、ブロックｍまでの各種値が演算されると、変数ｊの値はステップ２０１０にてｍ＋１と等しくされるので、ＣＰＵ７１はステップ２０１５にて「Ｙｅｓ」と判定し、ステップ２０９５を経由して図１２のステップ１２９５へと進む。
【０２０１】
このように、ＣＰＵ７１は触媒モデルを使用し、第２触媒５４の排ガス浄化に関する状態である「第２触媒５４のブロックｉから流出する特定成分の量に関する値である酸素の濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞」を第１触媒下流空燃比センサ６６の出力を用いた演算により推定・取得し、同酸素の濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞が所定の値（「０」より小さいＣｒｅｆｍｎｓと「０」より大きいＣｒｅｆｐｌｓの間の値）となるように機関に供給される混合気の空燃比（従って、第２触媒５４に流入する排ガスの空燃比）を制御する。
【０２０２】
従って、本排気浄化装置は、第２触媒５４の下流に設けられるＯ２センサの出力変化よりも早い時点で同第２触媒５４の排ガス浄化に関する状態（この場合、ＣｇｏｕｇＵＦ，Ｏ２＜ｉ＞）を取得することができ、この取得した状態に基づいて機関１０に供給される混合気の空燃比を制御することにより同第２触媒５４に流入する排ガスの空燃比を適切に制御することができる。この結果、本排気浄化装置は、有害成分の排出量を一層低減することができる。
【０２０３】
また、本排気浄化装置は、中間ブロック（ブロックｉ）から流出する特定成分の量に関する値を空燃比制御に用い、同特定成分を第２触媒５４の中間ブロックまでで略「０」とする制御を行うので、空燃比の制御誤差や空燃比のフィードバック制御の不可避的な遅れのため、同中間ブロックより同特定成分が流出したとしても、同中間ブロックよりも下流のブロックによりこれを浄化することができる。換言すると、少なくとも第２触媒５４の中間ブロックよりも下流側に位置するブロックを排ガス浄化のための予備的な触媒（バッファ的な触媒）として備えておくことができるので、有害排気成分の排出量をより低減し得る。
【０２０４】
更に、本実施形態においては、第２触媒５４の上流に配設され同第２触媒５４に流入する排ガスの空燃比を直接検出できる第１触媒下流空燃比センサ６６の出力を演算に用いることにより同第２触媒５４の特定成分の量に関する値ＣｇｏｕｔＵＦ，Ｘ（ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞）を求めている。従って、例えば、第１触媒５３の上流に備えた空燃比センサの出力に基づいて第２触媒５４の特定成分の量に関する値ＣｇｏｕｔＵＦ，Ｘを求める場合に比較して、より精度良く同第２触媒５４の特定成分の量に関する値ＣｇｏｕｔＵＦ，Ｘを求めることができる。
【０２０５】
＜第１実施形態の変形例＞
第１実施形態の変形例に係る排気浄化装置は、第２触媒５４の最下流のブロックｍ（第２触媒５４の流出口）から流出する濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｍ＞を上記閾値Ｃｒｅｆｍｎｓと上記閾値Ｃｒｅｆｐｌｓの間の値）となるように、機関１０に供給される混合気の空燃比を制御するものである。具体的に述べると、係る変形例のＣＰＵ７１は、図１１のステップ１１１０，１１１５，１１２５，１１３０における酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞を酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｍ＞に置換したルーチンを実行する。
【０２０６】
このように、第１実施形態の変形例は、最下流のブロック（第２触媒５４の流出口）から流出する濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｍ＞を空燃比のフィードバック制御に用いているが、第１実施形態の排気浄化装置と同様、第１触媒下流空燃比センサ６６の出力を演算に用いることにより同第２触媒５４の特定成分の量に関する値ＣｇｏｕｔＵＦ，Ｏ２，＜ｍ＞を求めているので、第２触媒５４の下流の空燃比センサ出力に基づく空燃比フィードバック制御よりも迅速な制御が可能であり、且つ、第１触媒５３の上流に備えた空燃比センサの出力に基づいて第２触媒５４の特定成分の量に関する値ＣｇｏｕｔＵＦ，Ｏ２，＜ｍ＞を求める場合に比較して、より精度良く同第２触媒５４の特定成分の量に関する値ＣｇｏｕｔＵＦ，Ｏ２＜ｍ＞を求めることができる。
【０２０７】
＜第２実施形態＞
次に、本発明による排気浄化装置の第２実施形態について説明すると、この排気浄化装置は、第２触媒５４のブロックｉから流出する酸素の濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞に代えて同第２触媒５４のブロック１〜ブロックｉまでの酸素吸蔵量ＯＳＡＵＦ＜ｉ＞（即ち、第２触媒５４を排ガスの流れ方向に沿って複数のブロックに分割したときの最上流に位置するブロックから、最下流に位置するブロックよりも上流に位置する中間ブロックまでのブロックにより構成される部分の酸素吸蔵量）が所定の値（この場合、ＯＳＡｒｅｆｌｏｗ〜ＯＳＡｒｅｆｈｉｇｈの値）となるように、機関１０に供給される混合気の空燃比を制御する点においてのみ、上記第１実施形態の排気浄化装置と異なっている。従って、以下、かかる相違点を中心として説明する。
【０２０８】
（第２実施形態の空燃比制御）
先ず、第２実施形態に係る排気浄化装置の空燃比制御について説明する。図２４は、かかる空燃比制御におけるタイムチャートであり、（Ａ）は機関１０に供給される混合気の空燃比（従って、第１触媒上流の排ガスの空燃比）を示し、（Ｂ）は上述した触媒モデルにより算出される第２触媒５４の１番目のブロックからｉ番目のブロック（ブロック１〜ブロックｉ）までの部分において貯蔵された酸素吸蔵量ＯＳＡＵＦ＜ｉ＞を示している。
【０２０９】
本排気浄化装置は、触媒モデルにより上記酸素吸蔵量ＯＳＡＵＦ＜ｉ＞を求め、同酸素吸蔵量ＯＳＡＵＦ＜ｉ＞が第２触媒５４の最大酸素吸蔵量ＣｍａｘＵＦの略半分程度の量となるように機関１０に供給される混合気の空燃比を制御する。より具体的に述べると、本排気浄化装置は、酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がロー側閾値ＯＳＡｒｅｆｌｏｗより小さくなったとき、第２触媒５４の酸素吸蔵量が過小になる恐れがあると考えられるので、機関１０に供給される混合気の空燃比を理論空燃比よりも所定値α１だけリーンに設定する（時刻ｔ１１，ｔ１３を参照。）。
【０２１０】
これに対し、酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がハイ側閾値ＯＳＡｒｅｆｈｉｇｈより大きくなったとき、第２触媒５４の酸素吸蔵量が過大になる恐れがあると考えられるので、機関１０に供給される混合気の空燃比を理論空燃比よりも所定値α２だけリッチに設定する（時刻ｔ１２を参照。）。なお、所定値α１と所定値α２とは異なる値でもよく、等しい値であってもよい。以下、α１とα２は互いに等しく、値αであるとして説明する。
【０２１１】
また、前記ロー側閾値ＯＳＡｒｅｆｌｏｗとハイ側閾値ＯＳＡｒｅｆｈｉｇｈは、第２触媒の最大酸素吸蔵量ＣｍａｘＵＦの半分の量（ＣｍａｘＵＦ／２）を同第２触媒の全体の容量Ｖａｌｌと中間ブロックまでの容量（ブロック１〜ブロックｉまでの容量）Ｖｐａｒｔで比例配分した量Ｃｍｉｄ＝（ＣｍａｘＵＦ・Ｖｐａｒｔ）／（２・Ｖａｌｌ）を挟むように設定してある。即ち、ＯＳＡｒｅｆｌｏｗ＜Ｃｍｉｄ＜ＯＳＡｒｅｆｈｉｇｈである。
【０２１２】
（実際の作動）
次に、上記排気浄化装置の実際の作動について、ＣＰＵ７１が実行するルーチンを示したフローチャートを参照しながら説明する。本排気浄化装置のＣＰＵ７１は、図１１に代わる図２５にフローチャートにより示したルーチンを実行する点を除き、第１実施形態に係る排気浄化装置のＣＰＵ７１と同一のルーチンを実行する。従って、以下、図２５に示したルーチンに基づく作動を中心として説明する。なお、図２５において図１１と同一のステップには同一の符号を付し、その詳細な説明を省略する。
【０２１３】
ＣＰＵ７１は、図２５に示したルーチンを所定時間の経過毎に実行する。従って、所定のタイミングになると、ＣＰＵ７１はステップ２５００から処理を開始し、ステップ１１０５に進んで空燃比フィードバック制御条件が成立しているか否かを判定する。
【０２１４】
いま、空燃比フィードバック制御条件が成立しているとして説明を続けると、第２触媒５４のブロックｉまでの酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がハイ側閾値ＯＳＡｒｅｆｈｉｇｈより小さい状態から大きい状態へと変化したとき、ＣＰＵ７１は、酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がハイ側閾値ＯＳＡｒｅｆｈｉｇｈより大きいか否かを判定するステップ２５１０にて「Ｙｅｓ」と判定するとともに、本ルーチンを前回実行したときの（前回の）酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がハイ側閾値ＯＳＡｒｅｆｈｉｇｈより小さいか否かを判定するステップ２５１５にて「Ｙｅｓ」と判定してステップ１１２０に進み、同ステップ１１２０にて空燃比フィードバック補正量ＤＦｉに正の値βを設定し、その後、ステップ２５９５に進んで本ルーチンを一旦終了する。これにより、機関に供給される混合気の空燃比（従って、第１触媒５３に流入する空燃比）が理論空燃比よりもリッチ（理論空燃比−α＝理論空燃比−α２）となるので、第２触媒５４にもリッチな空燃比の排ガスが流入するようになり、図２４の時刻ｔ１２〜ｔ１３に示したように、酸素吸蔵量ＯＳＡＵＦ＜ｉ＞が減少する。
【０２１５】
これに対し、今回及び前回の酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がハイ側閾値ＯＳＡｒｅｆｈｉｇｈより大きいとき、ＣＰＵ７１はステップ２５１０にて「Ｙｅｓ」、ステップ２５１５にて「Ｎｏ」と判定し、そのままステップ２５９５に進んで本ルーチンを一旦終了する。この結果、空燃比フィードバック補正量ＤＦｉは正の値βに維持され、機関に供給される混合気の空燃比も理論空燃比よりリッチな空燃比（理論空燃比−α）に維持される。
【０２１６】
一方、空燃比フィードバック制御条件が成立している場合に第２触媒５４のブロックｉまでの酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がロー側閾値ＯＳＡｒｅｆｌｏｗより大きい状態から小さい状態へと変化すると、ＣＰＵ７１は、酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がロー側閾値ＯＳＡｒｅｆｌｏｗより小さいか否かを判定するステップ２５２５にて「Ｙｅｓ」と判定するとともに、前回の酸素吸蔵量ＯＳＡＵＦ＜ｉ＞がロー側閾値ＯＳＡｒｅｆｌｏｗより大きいか否かを判定するステップ２５３０にて「Ｙｅｓ」と判定してステップ１１３５に進み、同ステップ１１３５にて空燃比フィードバック補正量ＤＦｉに負の値−βを設定し、その後、ステップ２５９５に進んで本ルーチンを一旦終了する。これにより、機関に供給される混合気の空燃比が理論空燃比よりもリーン（理論空燃比＋α＝理論空燃比＋α１）となるので、第２触媒５４にもリーンな空燃比の排ガスが流入するようになり、図４の時刻ｔ１１〜ｔ１２に示したように、酸素吸蔵量ＯＳＡＵＦ＜ｉ＞が増大する。
【０２１７】
なお、今回及び前回の酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞がロー側閾値ＯＳＡｒｅｆｌｏｗよりも小さいとき、ＣＰＵ７１はステップ２５１０にて「Ｎｏ」、ステップ２５２５にて「Ｙｅｓ」、ステップ２５３０にて「Ｎｏ」と判定し、そのままステップ２５９５に進んで本ルーチンを一旦終了する。この結果、空燃比フィードバック補正量ＤＦｉは負の値−βに維持され、機関に供給される混合気の空燃比も理論空燃比よりリーンな空燃比（理論空燃比＋α）に維持される。
【０２１８】
また、空燃比フィードバック制御条件が成立していなければ、ＣＰＵ７１はステップ１１０５にて「Ｎｏ」と判定してステップ１１４０に進み、同ステップ１１４０にて空燃比フィードバック補正量ＤＦｉに「０」を設定し、次いでステップ２５９５に進んで本ルーチンを一旦終了する。
【０２１９】
このように、第２実施形態に係る排気浄化装置は、第２触媒５４の排ガス浄化に関する状態を示す物理量である「第２触媒５４のブロック１〜ブロックｉからなる同第２触媒５４の部分（上流部）の酸素吸蔵量ＯＳＡＵＦ＜ｉ＞」を第１触媒下流空燃比センサ６６の出力を用いた演算により推定・取得し、同酸素吸蔵量ＯＳＡＵＦ＜ｉ＞が所定の値（ロー側閾値ＯＳＡｒｅｆｌｏｗとハイ側閾値ＯＳＡｒｅｆｈｉｇｈの間の値）となるように機関に供給される混合気の空燃比を制御することで、同第２触媒５４に流入する排ガスの空燃比を制御する。
【０２２０】
従って、本排気浄化装置は、第２触媒５４の下流に設けられるＯ２センサの出力変化よりも早い時点で同第２触媒５４の排ガス浄化に関する状態を取得することができ、この取得した状態に基づいて機関１０に供給される混合気の空燃比を制御するので、フィードバック制御の制御遅れに関わらず、同第２触媒５４の状態を良好な状態に維持できる。この結果、本排気浄化装置は、有害成分の排出量を一層低減することができる。
【０２２１】
また、本排気浄化装置は、第２触媒５４の最上流のブロック（ブロック１）から、最下流に位置するブロック（ブロックｍ）よりも上流に位置する中間ブロック（ブロックｉ）までの同第２触媒の部分（上流部分）の酸素吸蔵量ＯＳＡＵＦ＜ｉ＞が、第２触媒の最大酸素吸蔵量ＣｍａｘＵＦの半分の量（ＣｍａｘＵＦ／２）を同第２触媒の全体の容量Ｖａｌｌと中間ブロックまでの容量Ｖｐａｒｔで比例配分した量Ｃｍｉｄ＝（ＣｍａｘＵＦ・Ｖｐａｒｔ）／（２・Ｖａｌｌ）を挟む範囲（ＯＳＡｒｅｆｌｏｗ〜ＯＳＡｒｅｆｈｉｇｈ）となるように制御されるので、同第２触媒５４は酸素吸蔵機能による浄化作用を有している状態に維持される可能性が高い。
【０２２２】
また、空燃比フィードバック制御遅れにより、中間ブロックまでで排ガスを浄化できない場合（つまり、中間ブロックまでの酸素吸蔵量が「０」又は最大酸素吸蔵量に到達した場合）であっても、少なくとも同中間ブロックよりも下流に位置するブロック（ブロックｉ＋１〜ブロックｍ）を排ガス浄化のための予備的な触媒として使用できるので、有害排気成分の排出量を低減できる可能性が高くなる。
【０２２３】
更に、本実施形態においても、第２触媒５４の上流に配設され同第２触媒５４に流入する排ガスの空燃比を直接検出できる第１触媒下流空燃比センサ６６の出力を演算に用いることにより同第２触媒５４の酸素吸蔵量ＯＳＡＵＦ＜ｉ＞を求めている。従って、例えば、第１触媒５３の上流に備えた空燃比センサの出力に基づいて酸素吸蔵量ＯＳＡＵＦ＜ｉ＞を求める場合に比較して、より精度良く酸素吸蔵量ＯＳＡＵＦ＜ｉ＞を求めることができる。
【０２２４】
＜第２実施形態の変形例＞
第２実施形態の変形例は、中間ブロックｉまでの酸素吸蔵量ＯＳＡＵＦ＜ｉ＞に代わり、第２触媒５４の全体の酸素吸蔵量ＯＳＡＵＦ＜ｍ＞が所定の値（ＯＳＡｒｅｆｌｏｗ〜ＯＳＡｒｅｆｈｉｇｈ）となるように、機関１０に供給する混合気の空燃比を制御するものである。具体的に述べると、係る変形例のＣＰＵ７１は、図２５のステップ２５１０，２５１５，２５２５，２５３０における酸素吸蔵量ＯＳＡＵＦ＜ｉ＞を酸素吸蔵量ＯＳＡＵＦ＜ｍ＞に置換したルーチンを実行する。
【０２２５】
このように、第２実施形態の変形例は、第２触媒５４の全体の酸素吸蔵量ＯＳＡＵＦ＜ｍ＞を空燃比のフィードバック制御に用いているが、第２実施形態の排気浄化装置と同様、第１触媒下流空燃比センサ６６の出力を演算に用いることにより同酸素吸蔵量ＯＳＡＵＦ＜ｍ＞を求めているので、第２触媒５４の下流の空燃比センサ出力に基づく空燃比フィードバック制御よりも迅速な制御が可能であり、且つ、第１触媒５３の上流に備えた空燃比センサの出力に基づいて酸素吸蔵量ＯＳＡＵＦ＜ｍ＞を求める場合に比較して、より精度良く同酸素吸蔵量ＯＳＡＵＦ＜ｍ＞を求めることができる。
【０２２６】
＜第３実施形態＞
次に、本発明による排気浄化装置の第３実施形態について説明すると、この排気浄化装置は、第１触媒下流空燃比センサ６６の出力が現時点から所定時間だけ同現時点の出力を継続すると仮定して同所定時間後のブロックｉから流出する酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞を予測・推定し、その推定値が所定の値（この場合、Ｃｒｅｆｍｎｓ〜Ｃｒｅｆｐｌｓの値）となるように、機関１０に供給される混合気の空燃比を制御する点においてのみ、上記第１実施形態の排気浄化装置と異なっている。従って、以下、かかる相違点を中心として説明する。
【０２２７】
上記相違点は、第３実施形態に係る排気浄化装置のＣＰＵ７１が、図２６にフローチャートにより示したルーチンを第１実施形態に係る排気浄化装置のＣＰＵ７１が実行するルーチンに加えて所定時間の経過毎に実行することにより生じる。
【０２２８】
具体的に説明すると、ＣＰＵ７１は所定のタイミングにてステップ２６００から処理を開始し、ステップ２６０５に進んで変数ｎの値を「０」に設定するとともに、ステップ２６１０にて同変数ｎの値を「１」だけ増大し、続くステップ２６１５にて同変数ｎの値が「１」より大きい所定値ｎｍａｘより小さいか否かを判定する。この場合、ｎの値は「１」であるからＣＰＵ７１はステップ２６１５にて「Ｙｅｓ」と判定してステップ２６２０に進み、ＣｇｏｕｔＵＦ，Ｘ（ｋ）＜０＞（ＣｇｏｕｔＵＦ，Ｏ２（ｋ）＜０＞，ＣｇｏｕｔＵＦ，ＣＯ（ｋ）＜０＞，ＣｇｏｕｔＵＦ，ＨＣ（ｋ）＜０＞）を現時点の第１触媒下流空燃比センサ６６の出力により決定し、同決定した値を保持する。即ち、第２触媒５４に流入する各濃度ＣｇｉｎＵＦ，Ｏ２（ｋ）＜１＞，ＣｇｉｎＵＦ，ＣＯ（ｋ）＜１＞，ＣｇｉｎＵＦ，ＨＣ（ｋ）＜１＞を、第１触媒下流空燃比センサ６６の出力と前述した記憶されているマップとにより決定し、その値を保持する。
【０２２９】
そして、ＣＰＵ７１はステップ２６２５に進み、同ステップ２６２５にてステップ２０００〜２０９５を実行することにより、ＣｇｏｕｔＵＦ，Ｘ（ｋ）＜ｊ＞（ＣｇｏｕｔＵＦ，Ｏ２（ｋ）＜ｊ＞，ＣｇｏｕｔＵＦ，ＣＯ（ｋ）＜ｊ＞，ＣｇｏｕｔＵＦ，ＨＣ（ｋ）＜ｊ＞）（ｊ＝１〜ｍ）を求め、再び、ステップ２６１０に戻る。このとき、ＣｇｉｎＵＦ，Ｏ２（ｋ）＜１＞，ＣｇｉｎＵＦ，ＣＯ（ｋ）＜１＞，ＣｇｉｎＵＦ，ＨＣ（ｋ）＜１＞には、上記保持した値を使用する。このようにして、ＣＰＵ７１は、変数ｎの値が所定値ｎｍａｘとなるまで、第１触媒下流空燃比センサ６６の出力が現時点の出力に維持される（変化しない）と仮定してＣｇｏｕｔＵＦ，Ｘ（ｋ）＜ｊ＞を繰り返し計算する。
【０２３０】
また、ＣＰＵ７１は、図１１に示したルーチンを実行するとき、ステップ１１１０及びステップ１１２５のＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞として、図２６に示したルーチンにおける変数ｎの値が（ｎｍａｘ−１）であるときに求められたＣｇｏｕｔＵＦ，Ｏ２＜ｍ＞を採用し、ステップ１１１５及びステップ１１３０のＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞として、図２６に示したルーチンにおける変数ｎの値が（ｎｍａｘ−２）であるときに求められたＣｇｏｕｔＵＦ，Ｏ２＜ｍ＞を採用する。
【０２３１】
以上により、変数ｎの値がｎｍａｘ−１となるまで、即ち、現時点から所定時間だけ第１触媒下流空燃比センサ６６の出力が現時点の出力に維持される（変化しない）と仮定して計算された第２触媒５４の最下流のブロックｍから流出する酸素濃度ＣｇｏｕｔＵＦ，Ｏ２（ｋ）＜ｍ＞に基づく空燃比制御が行われる。
【０２３２】
この第３実施形態によれば、時間的に先の（将来の）第２触媒５４の状態が予測され、その予測値ＣｇｏｕｔＵＦ，Ｏ２（ｋ）＜ｍ＞に基づいて機関に供給される混合気の空燃比がフィードバック制御されるので、同フィードバック制御に内在する不可避的な制御遅れに関わらず、排ガスをより一層効果的に浄化することができる。
【０２３３】
＜第４実施形態＞
次に、本発明による排気浄化装置の第４実施形態について説明すると、この排気浄化装置は、第１触媒下流空燃比センサ６６の出力が現時点から所定時間だけ同現時点の出力を継続すると仮定して同所定時間後の第２触媒５４全体の酸素吸蔵量ＯＳＡＵＦ＜ｍ＞を予測・推定し、その推定値が所定の値（この場合、ＯＳＡｒｅｆｌｏｗ〜ＯＳＡｒｅｆｈｉｇｈの値）となるように、機関１０に供給される混合気の空燃比を制御する点においてのみ、上記第２実施形態の排気浄化装置と異なっている。従って、以下、かかる相違点を中心として説明する。
【０２３４】
上記相違点は、第４実施形態の排気浄化装置のＣＰＵ７１が、第２実施形態の排気浄化装置のＣＰＵ７１が実行する各ルーチンに加えて図２６にフローチャートにより示したルーチンを追加的に実行することにより生じる。即ち、ＣＰＵ７１は、図２６のルーチンを実行することで、現時点から所定時間だけ第１触媒下流空燃比センサ６６の出力が現時点の出力に維持される（変化しない）と仮定して第２触媒５４の全体の酸素吸蔵量ＯＳＡＵＦ＜ｍ＞を求める。
【０２３５】
また、ＣＰＵ７１は、図２５に示したルーチンを実行するとき、ステップ２５１０及びステップ２５２５のＯＳＡＵＦ＜ｉ＞として、図２６に示したルーチンにおける変数ｎの値が（ｎｍａｘ−１）であるときに求められたＯＳＡＵＦ＜ｍ＞を採用し、ステップ２５１５及びステップ２５３０のＯＳＡＵＦ＜ｉ＞として、図２６に示したルーチンにおける変数ｎの値が（ｎｍａｘ−２）であるときに求められたＯＳＡＵＦ＜ｍ＞を採用する。
【０２３６】
以上により、変数ｎの値がｎｍａｘ−１となるまで、即ち、現時点から所定時間だけ第１触媒下流空燃比センサ６６の出力が現時点の出力に維持される（変化しない）と仮定して計算された第２触媒５４全体の酸素吸蔵量ＯＳＡＵＦ＜ｍ＞に基づく空燃比制御が行われる。
【０２３７】
この第４実施形態によれば、時間的に先の（将来の）第２触媒５４の状態である酸素吸蔵量が予測され、その予測値ＯＳＡＵＦ＜ｍ＞に基づいて機関に供給される混合気の空燃比がフィードバック制御されるので、同フィードバック制御に内在する不可避的な制御遅れに関わらず、排ガスをより一層効果的に浄化することができる。
【０２３８】
以上、説明したように、本発明の各実施形態によれば、第１触媒下流空燃比センサ６６の出力と触媒モデルとによって、第２触媒５４の排気浄化に関連する物理量（第２触媒５４の所定のブロックから流出する酸素濃度や第２触媒５４全体の酸素吸蔵量又は同第２触媒５４の上流側部分の酸素吸蔵量等）が時間遅れなく推定され、同物理量が所望の量となるように第２触媒５４に流入する排ガスの空燃比が制御されるので、同第２触媒５４を排気浄化を良好に行うことができる状態に維持しておくことが可能となる。その結果、各排気浄化装置は、有害成分の排出量をより効果的に低減することができる。更に、第１触媒５３に対する触媒モデルのモデル誤差が、第１触媒下流空燃比センサ６６の出力に基づいて低減されるとともに、その結果が、第２触媒５４の触媒モデルの修正にも反映される。従って、第２触媒５４の排気浄化に関連する物理量をより一層精度良く推定することもできる。
【０２３９】
なお、本発明は上記実施形態に限定されることはなく、本発明の範囲内において種々の変形例を採用することができる。例えば、上記空燃比制御における理論空燃比からの振幅（α１，α２，αにより表される。）は、図２７に示したように、第２触媒５４の温度ＴｅｍｐＵＦ、吸入空気量Ｇａ、及び第２触媒５４の劣化指標値ＲＥＫＫＡＵＦ等の少なくとも一つに応じて可変としてもよい。これによれば、第２触媒５４の酸素による一次被毒を適切に解消して、同第２触媒５４の状態をより良好に維持することが可能となる。また、第１触媒下流空燃比センサ６６は、ＣＯ濃度、ＨＣ濃度、及びＮＯｘ濃度の少なくとも一つ（好ましくは、総べて）を検出し得る排ガス特性検出センサに置換してもよい。
【０２４０】
更に、上記第１実施形態及び第３実施形態等においては酸素濃度ＣｇｏｕｔＵＦ，Ｏ２＜ｉ＞を空燃比制御の指標値としているが、他の特定成分である一酸化炭素濃度ＣｇｏｕｔＵＦ，ＣＯ＜ｉ＞、炭化水素濃度ＣｇｏｕｔＵＦ，ＨＣ＜ｉ＞等を制御の指標値としてもよい。
【図面の簡単な説明】
【図１】本発明の第１実施形態に係る排気浄化装置を搭載した内燃機関の概略図である。
【図２】図１に示した第１触媒下流空燃比センサの出力と空燃比との関係を示したグラフである。
【図３】図１に示した第２触媒下流空燃比センサの出力と空燃比との関係を示したグラフである。
【図４】図１に示した排気浄化装置による空燃比制御を説明するためのタイムチャートである。
【図５】触媒モデルを説明するための触媒の模式図である。
【図６】図１に示した触媒の外観図である。
【図７】図６に示した触媒の部分断面図である。
【図８】触媒モデルを説明するための模式図である。
【図９】触媒モデルで使用する風上法を説明するための模式図である。
【図１０】図１に示したＣＰＵが実行する燃料噴射量計算のためのルーチンを示したフローチャートである。
【図１１】図１に示したＣＰＵが実行する空燃比フィードバック補正量を計算するためのルーチンを示したフローチャートである。
【図１２】触媒中の特定ガス成分濃度を算出するとともに触媒モデルの修正を行うために図１に示したＣＰＵが実行するルーチンを示したフローチャートである。
【図１３】触媒モデルにしたがって第１触媒内部における酸素濃度を求めるためのルーチンを示したフローチャートである。
【図１４】触媒モデルにしたがって第１触媒内部における一酸化炭素濃度を求めるためのルーチンを示したフローチャートである。
【図１５】触媒モデルにしたがって第１触媒内部における炭化水素濃度を求めるためのルーチンを示したフローチャートである。
【図１６】触媒モデルにしたがって第１触媒の酸素吸蔵密度と酸素吸蔵量を求めるためのルーチンを示したフローチャートである。
【図１７】触媒劣化度と触媒温度とから触媒モデルにて使用する各係数（各乗数）を求めるためのマップである。
【図１８】触媒に流入する一酸化炭素濃度を決定するために使用される排ガスの空燃比と同一酸化炭素濃度との関係を規定したマップである。
【図１９】触媒に流入する炭化水素濃度を決定するために使用される排ガスの空燃比と同炭化水素濃度との関係を規定したマップである。
【図２０】触媒モデルにしたがって第２触媒内部における酸素濃度を求めるためのルーチンを示したフローチャートである。
【図２１】触媒モデルにしたがって第２触媒内部における一酸化炭素濃度を求めるためのルーチンを示したフローチャートである。
【図２２】触媒モデルにしたがって第２触媒内部における炭化水素濃度を求めるためのルーチンを示したフローチャートである。
【図２３】触媒モデルにしたがって第２触媒の酸素吸蔵密度と酸素吸蔵量を求めるためのルーチンを示したフローチャートである。
【図２４】本発明の第２実施形態に係る排気浄化装置による空燃比制御を説明するためのタイムチャートである。
【図２５】第２実施形態に係る排気浄化装置のＣＰＵが実行する空燃比フィードバック補正量を計算するためのルーチンを示したフローチャートである。
【図２６】第３実施形態に係る排気浄化装置のＣＰＵが酸素濃度の予測値（将来値）を計算するために実行するルーチンを示したフローチャートである。
【図２７】各実施形態の空燃比制御における空燃比の制御幅を示したグラフである。
【符号の説明】
１０…内燃機関、５３…第１触媒、５４…第２触媒、６６…第１触媒下流空燃比センサ（第１触媒下流排ガス特性検出センサ）、７０…電気制御装置、７１…ＣＰＵ。[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an exhaust purification device for an internal combustion engine in which a catalyst is disposed in an exhaust passage.
[0002]
[Prior art]
The three-way catalyst oxidizes unburned components (HC, CO) in the exhaust gas and reduces nitrogen oxides (NOx) at the same time when the air-fuel ratio of the exhaust gas of the internal combustion engine flowing into the catalyst is approximately the stoichiometric air-fuel ratio. (This is referred to as “catalytic function” or “redox function”). On the other hand, recently, in order to further purify exhaust gas of an internal combustion engine, a three-way catalyst (hereinafter, referred to as a "first catalyst") called a start converter is disposed in an exhaust passage of the engine. An exhaust gas purifying apparatus is used in which a three-way catalyst called an under-floor converter (hereinafter, referred to as a "second catalyst") is provided in the exhaust passage downstream of the first catalyst. In this case, the first catalyst is disposed at a position closer to the exhaust port of the engine than the second catalyst, and the exhaust gas having a high temperature flows therein. Demonstrate. On the other hand, the second catalyst takes a longer time to warm up than the first catalyst, but after warming up once, exhibits an excellent exhaust purification function in cooperation with the first catalyst.
[0003]
In addition, the three-way catalyst is used to store (store) oxygen. ₂ It has a storage function (hereinafter, this function is referred to as “oxygen storage function”, and the amount of oxygen stored in the three-way catalyst is referred to as “oxygen storage amount”). Is rich, the stored oxygen oxidizes unburned components such as HC and CO, and when the inflowing exhaust gas has a lean air-fuel ratio, oxygen and nitrogen oxides (NOx) in the exhaust gas The oxygen obtained by reducing is stored inside. Thus, the three-way catalyst can effectively purify unburned HC, CO, and NOx even when the air-fuel ratio of the engine deviates from the stoichiometric air-fuel ratio to some extent.
[0004]
By the way, since the operating state of the internal combustion engine changes every moment, the air-fuel ratio of the exhaust gas becomes rich or lean. On the other hand, the oxygen storage amount of the three-way catalyst varies from “0” to the maximum amount of oxygen storage that the catalyst can store (hereinafter referred to as “maximum oxygen storage amount”). Therefore, if the exhaust gas with a rich air-fuel ratio flows into the three-way catalyst when the oxygen storage amount in the three-way catalyst is “0”, the catalyst will remove unburned CO and HC using the stored oxygen. Oxidation cannot be performed. Conversely, if exhaust gas with a lean air-fuel ratio flows into the three-way catalyst when the amount of oxygen stored in the three-way catalyst is the maximum oxygen storage amount, the catalyst cannot afford to deprive NOx of oxygen. Cannot be reduced. From the above, it is preferable that the oxygen storage amount in the three-way catalyst is maintained at about half of the maximum oxygen storage amount.
[0005]
Patent Literature 1 discloses an exhaust gas purifying apparatus that includes the first catalyst and the second catalyst based on the above-described viewpoint, and further performs an exhaust gas purifying performance by performing control in consideration of an oxygen storage amount of both the catalysts. Is disclosed. More specifically, this exhaust gas purification device estimates the oxygen storage amount of the first catalyst based on the air-fuel ratio of the exhaust gas flowing into the first catalyst, and the estimated oxygen storage amount of the first catalyst is set to a target value. The air-fuel ratio of the engine is controlled so as to obtain the amount. At the same time, when the O2 sensor (exhaust gas characteristic detection sensor) provided downstream of the second catalyst detects that the exhaust characteristic flowing out of the second catalyst is in a lean state, the exhaust gas purification device detects the oxygen storage amount. The target amount is reduced, and when the O2 sensor provided downstream of the second catalyst detects that the exhaust characteristic flowing out of the second catalyst is in a rich state, the target amount of the oxygen storage amount is increased. ing. Patent Literature 1 describes that such a configuration prevents the atmosphere in the second catalyst from being biased to lean or rich, so that the conversion efficiency can be kept high.
[0006]
[Patent Document 1]
JP 2001-234787 A
[0007]
[Problems to be solved by the invention]
In the above-described conventional exhaust gas purification apparatus, the target amount of oxygen storage amount of the first catalyst is changed based on the output of an O2 sensor provided downstream of the second catalyst. That is, in the exhaust gas purification device, the oxygen storage amount of the second catalyst substantially becomes the maximum oxygen storage amount, and the exhaust gas containing a large amount of oxygen starts to flow out of the second catalyst, or The oxygen storage amount becomes substantially “0” and the exhaust gas containing a large amount of unburned components starts flowing out of the second catalyst, and the exhaust gas flowing out reaches the O2 sensor a predetermined time after the time, Thereafter, the target amount is changed when the O2 sensor generates an output corresponding to the exhaust gas that has arrived after a predetermined response delay time. For this reason, the second catalyst is in a state where the oxygen storage amount is substantially the maximum oxygen storage amount or “0”, that is, the second catalyst cannot perform the exhaust gas purification by the oxygen storage function well. The vehicle will be left in the state for a relatively long time, and as a result, a large amount of harmful components may be discharged depending on the operation state.
[0008]
Summary of the Invention
Therefore, one of the objects of the present invention is to quickly determine the internal state of the second catalyst based on the output of the first catalyst downstream exhaust gas characteristic detection sensor disposed in the exhaust passage between the first catalyst and the second catalyst. By controlling the air-fuel ratio of the exhaust gas flowing into the second catalyst based on the estimated internal state of the second catalyst, the state of the second catalyst is made more suitable from the viewpoint of exhaust gas purification. An object of the present invention is to provide an exhaust purification device that can be maintained.
[0009]
An exhaust gas purifying apparatus for an internal combustion engine according to the present invention for achieving the above object is provided with a first catalyst disposed in an exhaust passage and disposed in the exhaust passage downstream of the first catalyst. A first catalyst downstream exhaust gas characteristic detection sensor for detecting a characteristic of exhaust gas in the exhaust passage in the portion, and a second catalyst disposed in the exhaust passage downstream of the first catalyst downstream exhaust gas characteristic detection sensor. ing. And an exhaust gas purification related physical quantity estimating means for estimating a physical quantity related to exhaust gas purification inside the second catalyst by at least an operation using an output of the first catalyst downstream exhaust gas characteristic detection sensor; Air-fuel ratio control means for controlling the air-fuel ratio of the exhaust gas flowing into the second catalyst so that the estimated physical quantity related to the purification of the exhaust gas becomes a predetermined value.
[0010]
In this case, the “physical quantity related to exhaust gas purification inside the second catalyst” estimated by the exhaust gas purification related physical quantity estimating means is a value related to the amount of a specific component in exhaust gas passing through the second catalyst (for example, The concentration of the specific component, the absolute amount of the specific component, etc.), or a value relating to the oxygen storage amount of the second catalyst (eg, the oxygen storage amount of the entire second catalyst, or the oxygen storage amount of the upstream portion of the second catalyst) Quantity etc.). The specific component is, for example, a component to be purified by a catalyst such as carbon monoxide CO, hydrocarbon HC, nitrogen oxide NOx, oxygen O 2 ₂ And so on.
[0011]
Further, the air-fuel ratio control means for controlling the air-fuel ratio of the exhaust gas flowing into the second catalyst so that the estimated physical quantity related to the purification of the exhaust gas becomes a predetermined value is, for example, a mixture of the air-fuel mixture supplied to the engine. A means for controlling the air-fuel ratio may be used, or the air-fuel ratio may be controlled by controlling the air-fuel ratio of the air-fuel mixture taken into the engine and supplying air or fuel from a nozzle or the like provided in an exhaust passage upstream of the second catalyst. By doing so, means for controlling the air-fuel ratio of the exhaust gas flowing into the second catalyst may be used. If the air-fuel ratio of the air-fuel mixture supplied to the engine is controlled, the air-fuel ratio of the exhaust gas flowing into the first catalyst can be controlled, and as a result, the air-fuel ratio of the exhaust gas flowing into the second catalyst can be controlled. You can also.
[0012]
According to this, a physical quantity related to exhaust gas purification inside the second catalyst is estimated at least by calculation using an output of the first catalyst downstream exhaust gas characteristic detection sensor, and the estimated physical quantity related to exhaust gas purification is calculated. The air-fuel ratio of the exhaust gas flowing into the second catalyst is controlled to have a predetermined value. Therefore, the present exhaust gas purification apparatus can acquire information on the state of the second catalyst relating to exhaust gas purification at a time earlier than the output change of the O2 sensor provided downstream of the second catalyst, and flows into the second catalyst. The air-fuel ratio of the exhaust gas can be appropriately controlled. As a result, the present exhaust gas purifying apparatus can set the second catalyst in a more suitable state from the viewpoint of exhaust gas purification (for example, a state where the oxygen storage amount of the second catalyst is about half of the maximum oxygen storage amount, or Since the specific component of the exhaust gas can be maintained at “0” at the outlet position of the exhaust gas of the catalyst or at a position upstream of the same outlet), the emission amount of harmful components can be further reduced.
[0013]
In this case, the exhaust gas purification-related physical quantity estimating means may include an intermediate block located upstream of a block located most downstream when the second catalyst is virtually divided into a plurality of blocks along the flow direction of the exhaust gas. It is preferable to estimate a value related to the amount of the specific component in the exhaust gas flowing out of the exhaust gas as a physical quantity related to the exhaust gas purification.
[0014]
According to this, for example, by setting the predetermined value to “0” or a value (range) near “0”, the specific component in the exhaust gas is made substantially “0” up to the intermediate block of the second catalyst. be able to. Therefore, even if the specific component flows out of the intermediate block due to an unavoidable control delay of the air-fuel ratio feedback control, the amount of the specific component flowing out is very small, so that the specific component is purified by a block located downstream of the intermediate block. Therefore, the discharge amount of the specific component flowing out of the second catalyst can be further reduced. In other words, a block downstream of the intermediate block can function as a preliminary catalyst.
[0015]
Further, the exhaust gas purification related physical quantity estimating means may include one or more of the second catalyst located upstream of a most downstream block when the second catalyst is virtually divided into a plurality of blocks along the flow direction of the exhaust gas. It is preferable that the oxygen storage amount of the portion of the second catalyst composed of the block is estimated as a physical quantity related to the exhaust gas purification. In this case, the one or more blocks include all blocks from the block located at the most upstream position of the second catalyst to the intermediate block located at the upstream of the block located at the most downstream position. The (upstream side) portion of the second catalyst, the second catalyst portion composed of the intermediate block and a part of the block upstream of the intermediate block, or the second catalyst composed of the intermediate block itself Part.
[0016]
According to this, it is possible to set the oxygen storage amount of the portion of the second catalyst composed of one or more blocks located upstream of the block located at the most downstream of the second catalyst to a predetermined amount. Therefore, for example, all (or most) blocks of the second catalyst from the block located at the most upstream position of the second catalyst to the intermediate block located upstream of the block located at the most downstream position are formed by the second catalyst. The predetermined amount is set as the upstream portion of the second catalyst, and the predetermined amount is set to a half amount (CmaxUF / 2) of the maximum oxygen storage amount CmaxUF of the second catalyst as the total capacity Vall of the second catalyst. If the amount (CmaxUF · Vpart) / (2 · Vall) proportionally distributed by the capacity Vpart up to the intermediate block is set, the second catalyst can be maintained in a state of having a purifying action by the oxygen storage function, and thus is empty. Even when exhaust gas whose fuel ratio deviates considerably from the stoichiometric air-fuel ratio flows in, the exhaust gas can be purified. Further, even when exhaust gas cannot be purified up to the intermediate block due to a delay in air-fuel ratio feedback control (that is, when the oxygen storage amount up to the intermediate block has reached “0” or the maximum oxygen storage amount), at least the same intermediate Since the block located downstream of the block can be used as a preliminary catalyst for purifying exhaust gas, the possibility of reducing the emission of harmful exhaust components increases.
[0017]
Further, in such an exhaust gas purification apparatus, the exhaust gas purification related physical quantity estimating means assumes that the output of the first catalyst downstream exhaust gas characteristic detection sensor continues the output at the same time for a predetermined time from the current time. Suitably, it is configured to estimate a physical quantity related to exhaust gas purification.
[0018]
According to this, the state of the second catalyst which is earlier (future) in time than the present time is predicted, and if the predicted state is not preferable, the air-fuel ratio flowing into the second catalyst from the present time can be changed. Thus, the state of the second catalyst can be maintained in a good state regardless of the delay in the feedback control of the air-fuel ratio.
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of a catalyst deterioration determination method according to the present invention will be described with reference to the drawings. FIG. 1 shows a schematic configuration of a system in which an exhaust purification device (air-fuel ratio control device) according to a first embodiment of the present invention is applied to a spark ignition type multi-cylinder (four cylinder) internal combustion engine 10.
[0019]
The internal combustion engine 10 includes a cylinder block 20 including a cylinder block, a cylinder block lower case, and an oil pan, a cylinder head 30 fixed on the cylinder block 20, and a gasoline mixture in the cylinder block 20. And an exhaust system 50 for discharging exhaust gas from the cylinder block 20 to the outside.
[0020]
The cylinder block section 20 includes a cylinder 21, a piston 22, a connecting rod 23, and a crankshaft 24. The piston 22 reciprocates in the cylinder 21, and the reciprocating motion of the piston 22 is transmitted to the crankshaft 24 via the connecting rod 23, whereby the crankshaft 24 rotates. The heads of the cylinder 21 and the piston 22 together with the cylinder head 30 form a combustion chamber 25.
[0021]
The cylinder head section 30 includes an intake port 31 communicating with the combustion chamber 25, an intake valve 32 for opening and closing the intake port 31, and an intake camshaft for driving the intake valve 32, and continuously changes the phase angle of the intake camshaft. Variable intake timing device 33, an actuator 33a of the variable intake timing device 33, an exhaust port 34 communicating with the combustion chamber 25, an exhaust valve 35 for opening and closing the exhaust port 34, an exhaust camshaft 36 for driving the exhaust valve 35, and a spark plug 37 And an igniter 38 including an ignition coil for generating a high voltage applied to the ignition plug 37, and an injector (fuel injection means) 39 for injecting fuel into the intake port 31.
[0022]
The intake system 40 includes an intake pipe 41 including an intake manifold communicating with the intake port 31 and forming an intake passage together with the intake port 31, an air filter 42 provided at an end of the intake pipe 41, and an intake pipe 41. The throttle valve 43 includes a throttle valve 43 that changes the opening cross-sectional area of the intake passage, and a throttle valve actuator 43a that includes a DC motor and constitutes a throttle valve driving unit.
[0023]
The exhaust system 50 includes an exhaust manifold 51 connected to the exhaust port 34, an exhaust pipe (exhaust pipe) 52 connected to the exhaust manifold 51, and an upstream first catalyst (upstream) provided (interposed) in the exhaust pipe 52. 53), and a second catalyst (downstream three-way catalyst or vehicle floor) disposed (interposed) in an exhaust pipe 52 downstream of the first catalyst 53. 54, which is also referred to as an under-floor converter. The exhaust port 34, the exhaust manifold 51, and the exhaust pipe 52 constitute an exhaust passage.
[0024]
On the other hand, this system includes a hot-wire air flow meter 61, a throttle position sensor 62, a cam position sensor 63, a crank position sensor 64, a water temperature sensor 65, and an exhaust passage downstream of the first catalyst 53 and upstream of the second catalyst 54. The disposed air-fuel ratio sensor 66 (this sensor is a value that is disposed in the exhaust passage downstream of the first catalyst 53 and that corresponds to the characteristic of the exhaust gas in the exhaust passage at the disposed portion. A first catalyst downstream exhaust gas characteristic detection sensor that outputs an air-fuel ratio, and is hereinafter referred to as a “first catalyst downstream air-fuel ratio sensor 66”.) The air disposed in the exhaust passage downstream of the second catalyst 54. A fuel ratio sensor 67 (hereinafter, referred to as a “second catalyst downstream air-fuel ratio sensor 67”) and an accelerator opening sensor 68 are provided.
[0025]
The hot wire air flow meter 61 outputs a voltage corresponding to the mass flow rate AFM (= Ga) of the intake air flowing through the intake pipe 41. The throttle position sensor 62 detects the opening of the throttle valve 43 and outputs a signal indicating the throttle valve opening TA. The cam position sensor 63 generates a signal (G2 signal) having one pulse each time the intake camshaft rotates 90 ° (that is, each time the crankshaft 24 rotates 180 °). The crank position sensor 64 outputs a signal having a narrow pulse each time the crankshaft 24 rotates 10 ° and a wide pulse each time the crankshaft 24 rotates 360 °. This signal indicates the engine speed NE. The water temperature sensor 65 detects the temperature of the cooling water of the internal combustion engine 10 and outputs a signal indicating the cooling water temperature THW.
[0026]
As shown in FIG. 2, the first catalyst downstream air-fuel ratio sensor 66 outputs a current corresponding to the air-fuel ratio A / F, and outputs a voltage vabyfs corresponding to the current. As is clear from FIG. 2, the first catalyst downstream air-fuel ratio sensor 66 can accurately detect the air-fuel ratio A / F over a wide range. As shown in FIG. 3, the second catalyst downstream air-fuel ratio sensor 67 outputs a voltage voxs that changes rapidly at the stoichiometric air-fuel ratio. More specifically, when the air-fuel ratio of the exhaust gas flowing out of the second catalyst 54 is leaner than the stoichiometric air-fuel ratio, the second catalyst downstream air-fuel ratio sensor 67 sets the air-fuel ratio of the exhaust gas to approximately 0.1 (V). When the fuel ratio is richer than the stoichiometric air-fuel ratio, a voltage of approximately 0.9 (V) is output, and when the air-fuel ratio of the exhaust gas is the stoichiometric air-fuel ratio, a voltage of approximately 0.5 (V) is output. The accelerator opening sensor 68 detects the operation amount of the accelerator pedal 81 operated by the driver, and outputs a signal indicating the operation amount Accp of the accelerator pedal 81.
[0027]
Further, the system includes an electric control device 70. The electric control device 70 includes a CPU 71 connected to the CPU 71 via a bus, a routine (program) executed by the CPU 71, a table (look-up table, map), a ROM 72 in which constants and the like are stored in advance, and the CPU 71 temporarily stores data as necessary. A microcomputer including a RAM 73 for temporarily storing data, a backup RAM 74 for storing data while the power is turned on and holding the stored data even when the power is turned off, an interface 75 including an AD converter, and the like. . The interface 75 is connected to the sensors 61 to 68, supplies signals from the sensors 61 to 68 to the CPU 71, and in accordance with instructions from the CPU 71, the actuator 33a of the variable intake timing device 33, the igniter 38, the injector 39, and A drive signal is sent to the throttle valve actuator 43a.
[0028]
(Air-fuel ratio control of the first embodiment)
Next, the air-fuel ratio control of the exhaust purification device will be described. FIG. 4 is a time chart in the air-fuel ratio control. FIG. 4A shows the air-fuel ratio of the air-fuel mixture supplied to the engine 10 (therefore, the air-fuel ratio of the exhaust gas upstream of the first catalyst), and FIG. The figure shows the oxygen concentration CgoutUF, O2 <i> flowing out from the i-th block (i-th specific region, hereinafter also referred to as “block i”) of the second catalyst 54 calculated by the corresponding catalyst model.
[0029]
Here, the oxygen concentration CgoutUFO2 <i> flowing out from the block i of the second catalyst 54 will be briefly described. In a catalyst model described later, as shown in FIG. 5, a cylindrical catalyst is virtually divided at equal intervals from the upstream side of the catalyst on a plane orthogonal to the axis of the cylinder to form a plurality of conceptual models. Form a block. Then, the catalyst model performs a predetermined calculation for each block, and obtains the concentration Cgout of a specific component (for example, oxygen, carbon monoxide, hydrocarbon, nitrogen oxide, or the like) flowing out of each block. Each block is defined as a first block, a second block,..., An n-th block in order from the uppermost stream of the catalyst (the side into which exhaust gas flows).
[0030]
The catalyst model of the present embodiment divides the first catalyst 53 into r (r is an integer of 2 or more) blocks and the second catalyst 54 into m (m is an integer of 2 or more) blocks and performs various calculations. I do. In this specification, when the specific component is X and the block of interest is the k-th block (block k), the specific component X (X is , O2 in the case of oxygen, CO in the case of carbon monoxide, HC in the case of hydrocarbons, and NO in the case of nitrogen oxides) in the exhaust gas flowing out of the k-th block of the second catalyst 54, CgoutSC, X <k>. Of the specific component X is expressed as CgoutUF, X <k>.
[0031]
As is clear from the above, the oxygen concentration CgoutUF, O2 <i> represents the oxygen concentration in the exhaust gas flowing out of the block i of the second catalyst 54. The value “i” is set to an integer greater than “1” and smaller than “m” (1 <i <m). Therefore, the oxygen concentration CgoutUF, O2 <i> is determined by the following expression: “a block located at the most downstream position when the second catalyst 54 is virtually divided into a plurality of blocks along the flow direction of the exhaust gas flowing into the second catalyst 54”. The value (oxygen concentration) relating to the amount of the specific component (oxygen) in the exhaust gas flowing out of the intermediate block (block i) located upstream of (block m). When the oxygen concentration CgoutUF, O2 <i> is a positive value, it means that oxygen is excessive and NOx is flowing out of the block i, and when the oxygen concentration is negative, the oxygen is This means that unburned CO and HC are running out of the block i due to shortage.
[0032]
Referring again to FIG. 4, the present exhaust gas purification apparatus obtains the oxygen concentration CgoutUF, O2 <i> from the catalyst model, and maintains the oxygen concentration CgoutUF, O2 <i> in the vicinity of “0” by maintaining the same oxygen concentration CgoutUF, O2 <i>. To control the air-fuel ratio of the air-fuel mixture supplied to the air conditioner. More specifically, when the Cgout, O2 <i> becomes smaller than the negative threshold value Crefmns, the present exhaust gas purification apparatus means that a large amount of unburned components has started to flow out of the block i of the second catalyst 54. Therefore, the air-fuel ratio of the air-fuel mixture supplied to the engine 10 is set leaner by a predetermined value α1 than the stoichiometric air-fuel ratio (see times t1 and t3). On the other hand, when CgoutUF, O2 <i> becomes larger than the positive threshold value Crefpls, it means that a large amount of oxygen (accordingly, NOx) has started to flow out of the block i of the second catalyst 54. The air-fuel ratio of the supplied air-fuel mixture is set to be richer than the stoichiometric air-fuel ratio by a predetermined value α2 (see time t2). The predetermined value α1 and the predetermined value α2 may be different values or may be equal values. Hereinafter, a description will be given assuming that α1 and α2 are equal to each other and have the value α.
[0033]
(Catalyst model)
Next, a catalyst model (estimated model) employed by the present exhaust gas purification apparatus will be described. In constructing the catalyst model, the first catalyst 53 and the second catalyst 54 have the same configuration and function, and therefore, the following description will be made using the second catalyst 54 as an example.
[0034]
As shown in FIG. 6, the second catalyst 54 is a three-way catalyst called a columnar monolith catalytic converter having an elliptical cross section (having a constant cross-sectional area of dA), and has the same shape in a plane perpendicular to the axis. As shown in FIG. 7 which is an enlarged sectional view of the second catalyst 54, the inside is subdivided into an axial space extending in the axial direction by a carrier 54a made of cordierite which is a kind of ceramic. . Each axial space has a substantially square shape when cut along a plane perpendicular to the axis, and is also referred to as a cell. The carrier 54a is coated with a coat layer 54b of alumina, and the coat layer 54b is composed of an active component (catalyst component) made of a noble metal such as platinum (Pt) and ceria (CeO). ₂ ) Is carried.
[0035]
Since the second catalyst 54 carries a noble metal such as platinum, the second catalyst 54 oxidizes unburned components (HC, CO) when the air-fuel ratio of the exhaust gas flowing into the second catalyst 54 is the stoichiometric air-fuel ratio. It has a catalytic function of reducing nitrogen oxides (NOx). Further, the second catalyst 54 has the above-described oxygen storage function of storing (storing, adsorbing) and releasing oxygen molecules in the exhaust gas flowing into the second catalyst 54 by supporting the components such as ceria. Therefore, even if the air-fuel ratio deviates to some extent from the stoichiometric air-fuel ratio, HC, CO, and NOx can be purified by the oxygen storage function.
[0036]
Therefore, if the second catalyst 54 has stored oxygen up to the limit at which it can store oxygen (in other words, if the oxygen storage amount has reached the maximum oxygen storage amount), it flows into the second catalyst 54. When the exhaust air-fuel ratio of the exhaust gas becomes lean, oxygen cannot be stored, so that NOx in the exhaust gas cannot be sufficiently purified. On the other hand, if the second catalyst 54 has completely released oxygen and has not occluded oxygen at all (in other words, if the oxygen storage amount has become “0”), the exhaust gas flowing into the second catalyst 54 Since oxygen cannot be released when the exhaust air-fuel ratio becomes rich, HC and CO in exhaust gas cannot be sufficiently purified.
[0037]
For this reason, in order for the second catalyst 54 to function effectively, the oxygen storage amount OSAUF of the second catalyst 54 is estimated without a time delay, and the oxygen storage amount OSAUF is maintained so as to be maintained at a predetermined value. It is desirable to control the air-fuel ratio of the exhaust gas flowing into the two-catalyst 54.
[0038]
Further, by changing the air-fuel ratio of the exhaust gas flowing into the second catalyst 54, a control delay is unavoidable in the feedback control for controlling the oxygen storage amount of the second catalyst. For this reason, even if the overall oxygen storage amount of the second catalyst 54 is controlled to a predetermined value, the oxygen storage amount of the second catalyst 54 may reach “0” or the maximum oxygen storage amount. On the other hand, the total amount of oxygen storage from the most upstream position of the second catalyst 54 to an arbitrary position (a catalyst composed of the blocks from the most upstream block 1 to the intermediate block i) is estimated, and the estimated value becomes a predetermined value. If the air-fuel ratio control is performed so as to satisfy the value, it is easy to avoid that the oxygen storage amount of the entire second catalyst 54 reaches “0” or the maximum oxygen storage amount, and the emission can be surely reduced. In other words, a block downstream of the intermediate block can be used as a preliminary catalyst (buffer) for exhaust gas purification.
[0039]
Further, if the concentration of a specific exhaust gas component contained in the exhaust gas flowing out of the second catalyst 54 (or the exhaust gas purified by part or all of the second catalyst 54) can be estimated without time delay, the empty space focused on the exhaust gas component can be estimated. By performing the fuel ratio control, the emission of the exhaust gas component can be suppressed with high accuracy. Further, the concentration of the specific exhaust gas component flowing out of the block (intermediate block) located upstream of the most downstream position of the second catalyst 54 is estimated, and the estimated concentration is set to a predetermined value (for example, “0” or “0”). If the air-fuel ratio is controlled so as to maintain the air-fuel ratio within the predetermined range near the "", even if there is an inevitable control delay in the control of the air-fuel ratio, the specific component can be reliably reduced. In other words, also in this case, a block downstream of the intermediate block can be used as a preliminary catalyst (buffer).
[0040]
From the above requirements, the present air-fuel ratio control device estimates the concentration (discharge amount) and the oxygen storage amount of the specific exhaust gas component by using the catalyst model. These estimated values can also be referred to as at least one representative value indicating the state of exhaust gas flowing downstream from all or a specific region of the catalyst, and `` physical quantity related to exhaust gas purification inside the catalyst '' It can also be called.
.
[0041]
Hereinafter, the specific configuration and content of the catalyst model will be described. This catalyst model is applied to both the first catalyst 53 and the second catalyst 54. Hereinafter, for convenience of explanation, a catalyst model for the second catalyst 54 will be described.
[0042]
First, in the catalyst model, as described above, the second catalyst 54 is divided into a plurality of parts by a surface orthogonal to an axis from the inlet (inflow side, most upstream side) Fr of the exhaust gas to the outlet (outflow side, most downstream side) Rr. The area is divided into blocks (see FIG. 5). That is, the second catalyst 54 is virtually divided into a plurality of blocks along the flow direction of the exhaust gas. The length in the axial direction of each divided block is L (a minute length, also referred to as dx). The area of the cross section of the second catalyst 54 cut along a plane perpendicular to the axial direction is defined as dA.
[0043]
Next, paying attention to an arbitrary block (hereinafter, referred to as a “specific region”), consider the balance of a substance of a specific chemical species (specific component) passing through the specific region. The chemical species is a component contained in the exhaust gas. ₂ , Carbon monoxide CO, hydrocarbon HC, and nitrogen oxide NOx. The chemical species is the sum of the components contained in the exhaust gas when the air-fuel ratio of the exhaust gas flowing into the catalyst is rich (rich component), or when the air-fuel ratio of the exhaust gas flowing into the catalyst is lean. The components contained in the exhaust gas may be integrated (lean component). In the catalyst model, various values are defined as shown in Table 1 below.
[0044]
[Table 1]

[0045]
Now, considering the balance of chemical species in a specific region in a given period from time t to t + Δt, as shown in FIG. 8, in the exhaust gas phase of the specific region (also simply referred to as “gas phase”). As shown in the following equation (1), the change amount ΔM of the chemical species is calculated from the amount Min of the same chemical species flowing out of the same specific region and the amount Mout of the same chemical species flowing out of the same specific region from the amount Min of the same chemical species flowing into the same specific region. It is equal to the amount obtained by subtracting the amount Mcoat of the same chemical species deprived by the coat layer. As described above, the catalyst model is constructed based on the material balance of the specific component in each specific region.
[0046]
(Equation 1)

[0047]
Hereinafter, each term of the equation (1) will be individually examined. First, the variation ΔM of the chemical species on the left side of the equation (1) can be obtained by the following equation (2). Equation (2) is obtained by multiplying the amount of change in the concentration of the chemical species in the given period (the amount obtained by integrating the amount of change in the concentration Cg of the species over time over the given period) by the minute volume σ · dA · dx. The value is integrated in the axial direction over the entire block (specific area) of interest.
[0048]
(Equation 2)

[0049]
Min in the first term on the right side of the equation (1) is a value corresponding to the volume of the exhaust gas flowing into the specific region per unit time, “the flow velocity vgin of the exhaust gas flowing into the specific region and the sectional area dA of the same specific region. The product vgin · dA (actually, the exhaust gas with the flow velocity vgin flows into the catalyst having the opening area σ with the cross-sectional area dA, so that the flow velocity of the exhaust gas inside the catalyst becomes vgin / σ, and the actual flow velocity vgin / σ and the catalyst Is the product of the concentration Cgin of the chemical species in the exhaust gas flowing into the exhaust gas and the value Cgin · vgin · dA integrated over a given period. Further, Mout of the second term on the right side of the equation (1) is a product vgout · dA of the cross-sectional area dA of the specific area and the flow rate vgout of the exhaust gas flowing out of the specific area (actually, it is substantially equal to the flow rate vgout / σ of the exhaust gas). (Product of the typical cross-sectional area σ · dA) multiplied by the concentration Cgout of the chemical species in the exhaust gas flowing out at the same time, and Cgout · vgout · dA is integrated over a given period. That is, the first and second terms on the right side of the above equation (1) can be described as the following equation (3).
[0050]
[Equation 3]

[0051]
By the way, since there is no significant difference between the flow rate vgin of the exhaust gas flowing into the specific area and the flow rate vgout of the exhaust gas flowing out from the specific area, if vg = vgin = vgout, the equation (3) is expressed by the following equation (4). ).
[0052]
(Equation 4)

[0053]
Next, the amount Mcoat of the chemical species transmitted (moved) to the coat layer in the third term on the right side of the equation (1) will be examined. Since the geometric surface area Sgeo is a surface area that contributes to the reaction of a chemical species per unit volume of the catalyst, the surface area that contributes to the reaction of the chemical species in a specific region is Sgeo · dA · dx, and the unit length of the specific region. The area contributing to the reaction around is Sgeo · dA. Further, the amount of the chemical species transmitted to the coat layer can be considered to be proportional to the difference between the concentration Cg of the chemical species in the exhaust gas phase and the concentration Cw of the chemical species in the coat layer from Fick's law. From these, the following equation (5) is obtained. Note that h _D Is a constant of proportionality, and as shown in Table 1 above, is a value called mass transfer rate.
[0054]
(Equation 5)

[0055]
Therefore, from the above equations (1), (2), (4) and (5), the following equation (6) is obtained.
[0056]
(Equation 6)

[0057]
When a quasi-state approximation is applied to the equation (6), the left side of the equation (6) can be considered to be “0” (∂Cg / ∂t = 0) (that is, the density Cg is (It is considered that the steady value is reached instantaneously), and the following equation (7) is obtained.
[0058]
(Equation 7)

[0059]
Here, the apparent diffusion rate (substantial diffusion rate) R _D Is written as in equation (8), equation (7) is rewritten as equation (9).
[0060]
(Equation 8)

[0061]
(Equation 9)

[0062]
Next, considering the balance of the chemical species (the material balance of the specific component) in the coat layer in the specific region in the same manner as described above, as shown in the following equation (10), the temporal change amount of the chemical species in the coat layer (Amount of change per unit time) ΔMc is calculated from the amount Md of the same chemical species transmitted from the exhaust gas phase to the coat layer per unit time from the amount of the same chemical species consumed by the reaction in the coat layer per unit time. This is an amount obtained by subtracting the amount Mr.
[0063]
(Equation 10)

[0064]
The left side of the equation (10) (the amount of temporal change of the chemical species in the coat layer) ΔMc is, as shown in the following equation (11), the volume change of the chemical species concentration (∂Cw / ∂t) ((1 −σ) · dA · dx), and the first term on the right-hand side (the amount of chemical species Md transferred from the exhaust gas phase to the coat layer per unit time) is the same as the reason explained in the equation (5). For reasons, that is, considering Fick's law, it can be described as the following equation (12).
[0065]
[Equation 11]

[0066]
(Equation 12)

[0067]
The second term on the right side of the equation (10) (the amount Mr of the chemical species consumed by the reaction in the coat layer per unit time) is expressed by the following equation (13) using the consumption rate R of the chemical species in the coat layer. It is obtained by the formula.
[0068]
(Equation 13)

[0069]
Therefore, the following expression (14) is obtained from the expressions (10) to (13).
[0070]
[Equation 14]

[0071]
When the quasi-state approximation is applied to this equation (14) (∂Cw / ∂t = 0), the following equation (15) is obtained.
[0072]
[Equation 15]

[0073]
Here, if the equation (8) is applied to the equation (15), the following equation (16) is obtained.
[0074]
(Equation 16)

[0075]
To summarize the above, equations (9) and (16) are the basic equations of the catalyst model. Equation (9) shows that the “inflow amount into a specific region” of a certain chemical species is balanced with the “diffusion amount from the exhaust gas phase into the coat layer + outflow amount from the specific region”, and expression (16) Indicates that the “diffusion amount from the exhaust gas phase to the coat layer” and “consumption amount in the coat layer” of the same chemical species are balanced.
[0076]
Next, a method for actually calculating the concentration Cgout of the specific chemical species i flowing out of the specific region using the catalyst model will be described. First, when the equation (9) is discretized, the following equation (17) is obtained. In the following, the above dx is represented as L.
[0077]
[Equation 17]

[0078]
Here, as conceptually shown in FIG. 9, the concentration Cgout of the chemical species flowing out of the specific region I is considered to be strongly affected by the concentration Cg (I) of the chemical species in the specific region I. (18). Such a concept is called “windward method”. In other words, the windward method is based on the idea that "chemical species having a concentration Cg (I-1) in the upstream area (I-1) adjacent to the specific area I flow into the specific area I." , (19) below.
[0079]
(Equation 18)

[0080]
[Equation 19]

[0081]
By the way, based on the reaction kinetics, the consumption rate R of a certain chemical species is a function fcw of the average concentration Cw of the coating layer of the chemical species (for example, a function proportional to the nth power of Cw). If fcw is set to be proportional to Cw so as to be the simplest, the consumption speed R can be set as shown in equation (20). In the following, R * in equation (20) is referred to as “consumption rate constant” for convenience.
[0082]
(Equation 20)

[0083]
This equation (20) is converted to the above equation (16) (R = R _D Applying to (Cg-Cw) (16), the following equation (21) is obtained, and by modifying the equation (21), the following equation (22) is obtained.
[0084]
(Equation 21)

[0085]
(Equation 22)

[0086]
Further, according to the above-mentioned upwind method, since Cg = Cgout, the expression (22) can be rewritten into the following expression (23).
[0087]
(Equation 23)

[0088]
Then, the relationship Cg = Cgout is applied to the above equation (17) to eliminate Cg, and when Cw is eliminated from the equation (17) and the above equation (23), the following equation (24) is obtained.
[0089]
[Equation 24]

[0090]
Therefore, if the value SP is set as in the following equation (25), the equation (24) can be rewritten as the equation (26). The value SP is the apparent diffusion rate R _D And the consumption rate constant R * are values that are strongly affected by the smaller value of Cgout. _D ) Or a chemical reaction (R *), and is therefore a value indicating whether the reaction is rate-determining.
[0091]
(Equation 25)

[0092]
(Equation 26)

[0093]
From the above, the consumption rate constant R * and the apparent diffusion rate R _D Is determined, the concentration Cgout of the chemical species flowing out of the specific area can be obtained based on the equations (25) and (26) by giving the chemical species concentration Cgin flowing into the specific area. In addition, since the chemical species concentration Cgin flowing into the next specific region is thereby determined, it is possible to calculate the chemical species concentration Cgout of the same specific region. The above is the basic concept of the catalyst model for calculating the concentration Cgout of the chemical species.
[0094]
Next, the above consumption rate constant R * and apparent diffusion rate R _D The following describes an example of a more specific method for determining the chemical species concentration Cgout flowing out of the specific area while determining the chemical species concentration Cgout. In this example (catalyst model), it is assumed that the three-way reaction, which is an oxidation / reduction reaction in a catalyst, is completed instantaneously and completely, and the resulting oxygen storage / release reaction based on excess / deficiency of oxygen is performed. Let's focus on it. Note that this assumption (catalyst model) is realistic and accurate.
[0095]
In this case, the chemical species i of interest is, for example, oxygen O ₂ Species (storage agents) that produce oxygen (produce oxygen), like nitrogen monoxide NO, which is one of nitrogen oxides, and consume oxygen like carbon monoxide CO and hydrocarbon HC It is a chemical species selected from the chemical species (reduction agent).
[0096]
In the following, the chemical species i of the storage agent (in this case, the chemical species i is O ₂ Or NO), Cgout, stor, i, Cw of the same species i, Cw, stor, i, Cgin of the same species i, Cgin, stor, i, and apparent diffusion rate R of the same species i. _D To R _D , I, the consumption rate of the same species i is represented by Rstor, i, the consumption rate constant of the same species i is represented by R * stor, i, and the reaction-limiting factor SPstor, i of the same species i.
[0097]
Similarly, Cgout of the species i of the reduction agent (in this case, the species i is CO or HC) is Cgout, reduc, i, and Cw of the species i is Cw, reduc, i, and Cgout of the species i. Apparent diffusion rate R of Cgin, Cgin, reduc, i, and the same species i _D To R _D , I, the consumption rate of the same species i is represented by Rreduc, i, the consumption rate constant of the same species i is represented by R * reduc, i, and the reaction-limiting factor SPreduc, i of the same species i. When each value is represented in this way, the following equations (27) to (34) are obtained from the above equations (20), (23), (25), and (26).
[0098]
[Equation 27]

[0099]
[Equation 28]

[0100]
(Equation 29)

[0101]
[Equation 30]

[0102]
(Equation 31)

[0103]
(Equation 32)

[0104]
[Equation 33]

[0105]
[Equation 34]

[0106]
Based on these equations, Cgout, sotr, i (specifically, the concentration Cgout, O2 of oxygen flowing out of the specific region, the concentration Cgout, NO of nitric oxide flowing out of the specific region) and Cgout, reduc, i (Specifically, in order to obtain the concentration Cgout, CO of the carbon monoxide flowing out of the specific region and the concentration Cgout, HC of the hydrocarbon flowing out of the specific region, first, the consumption rate constant R * stor, i and the consumption rate Find a constant R * reduc, i.
[0107]
According to the reaction kinetics, the oxygen consumption rate Rstor, i, which is the rate at which oxygen is occluded (oxygen occlusion rate) by the coat layer in a specific region, is determined by the storage agent (O) of the coat layer. ₂ , NOx, etc.) in proportion to the value of the function f1 (Cw, sto, i) of the concentration Cw, sto, i (for example, Cw, O2, Cw, NO), and the maximum oxygen storage density of the coat layer in the specific region. This is considered to be proportional to the value of a function f2 (Ostmax-Ost) of the difference (Ostmax-Ost) from the actual oxygen storage density. The difference between the maximum oxygen storage density and the oxygen storage density (Ostmax−Ost) indicates the oxygen storage allowance in the particular region of interest.
[0108]
Therefore, if the function f1 (x) = f2 (x) = x for simplicity, the following equation (35) is obtained. In the following equation (35), kstor, i is an oxygen storage rate coefficient (storage side reaction rate coefficient, storage agent consumption rate coefficient), and varies depending on the temperature expressed by the well-known Arrhenius equation. It can be obtained based on the catalyst temperature Temp that is separately detected or estimated and a predetermined function (a map that defines the relationship between the oxygen storage rate coefficient kstor, i and the catalyst temperature Temp may be used). it can. Since the oxygen storage rate coefficient kstor, i changes depending on the degree of deterioration of the catalyst, it may be obtained according to the degree of deterioration of the catalyst.
[0109]
(Equation 35)

[0110]
Therefore, from the equations (27) and (35), the consumption rate constant R * stor, i can be obtained by the following equation (36).
[0111]
[Equation 36]

[0112]
In this catalyst model, which focuses only on the storage (adsorption) and release of oxygen, the reduction agent, which is a reducing agent, is used only for releasing the oxygen stored in the coat layer. The consumption speed Rredcu, i of the agent is equal to the speed (releasing speed of oxygen) Rrel, i at which the oxygen stored in the coat layer is released.
[0113]
Therefore, when examining the oxygen release rate Rrel, i, the release rate Rrel, i is based on the reaction kinetics similarly to the oxygen storage rate Rstor, i, and the chemical species that consumes oxygen in the coat layer (for example, CO, HC) is proportional to the value of the function g1 (Cw, reduc, i) of the concentration Cw, reduc, i (for example, Cw, CO, Cw, HC) and the function g2 (Ost) of the oxygen storage density Ost. It is considered to be proportional to the value.
[0114]
Therefore, if the function g1 (x) = g2 (x) = x for simplicity, the following equation (37) is obtained. In the following equation (37), krel, i is an oxygen release rate coefficient (reaction rate coefficient on the desorption side), and like the oxygen storage rate coefficient kstor, i, varies depending on the temperature expressed by the Arrhenius equation. It is a coefficient and can be obtained based on a predetermined function (a map defining the relationship between the oxygen release rate coefficient krel, i and the catalyst temperature Temp) based on the catalyst temperature Temp separately detected or estimated. it can. Since the oxygen release rate coefficient krel, i changes depending on the degree of catalyst deterioration, it may be obtained according to the degree of catalyst deterioration.
[0115]
(37)

[0116]
As a result, as described above, the consumption rate Rredcu, i of the reduction agent is equal to the oxygen release rate Rrel, i of the coat layer. Therefore, the consumption rate constant R * reduc, i is given by the equations (31) and (37). Can be calculated based on the following equation (38) obtained by comparing
[0117]
[Equation 38]

[0118]
From the above, if the oxygen storage density Ost is obtained (the method for obtaining the oxygen storage density Ost will be described later), the consumption rate constant R * stor, i (for example, R * O2) is calculated from the equation (36). You can ask. On the other hand, the apparent diffusion rate R _D , I (for example, R _D , O2) is Sgeo · h as in equation (8). _D , I, it can be experimentally determined as a function of temperature and flow rate (a function of the temperature of the catalyst and the flow rate of exhaust gas passing through the catalyst). As a result, SPstor, i (for example, SPstor, O2) is determined from Expression (29). When Cgin, stor, i (for example, Cgin, O2) is given as a boundary condition, Cgout is obtained from Expression (30). , Stor, i (for example, Cout, O2). Then, a new Cw, stor, i (for example, Cw, O2) is obtained by equation (28).
[0119]
Similarly, if the oxygen storage density Ost is obtained, the consumption rate constant R * reduc, i (for example, R * reduc, CO) can be obtained from the equation (38). On the other hand, the apparent diffusion rate R _D , I (for example, R _D , CO) is Sgeo · h as in equation (8). _D , I, it can be experimentally determined as a function of temperature and flow rate (a function of the temperature of the catalyst and the flow rate of exhaust gas passing through the catalyst). As a result, SPreduc, i (for example, SPreduc, CO) is determined from Expression (33). When Cgin, reduc, i (for example, Cgin, CO) is given as the boundary condition, Cgout is obtained from Expression (34). , Reduc, i (eg, Cgout, CO). Then, new Cw, reudc, i (for example, Cw, CO) is obtained by the equation (32).
[0120]
Next, a method of obtaining the oxygen storage density Ost required for obtaining Cgout, sto, i, and Cgout, reduc, i will be described.
[0121]
First, focusing on the balance of oxygen as a chemical species in the coat layer, the balance is the difference between the amount of oxygen absorbed and the amount of released oxygen in the coat layer, and is described by the following equation (39). In the equation (39), dAL is the volume dV of the specific area.
[0122]
[Equation 39]

[0123]
By transforming this equation (39), the following equation (40) is obtained.
[0124]
(Equation 40)

[0125]
When the equation (40) is discretized using the equations (35) and (37), the following equation (41) is obtained.
[0126]
(Equation 41)

[0127]
By transforming the equation (41), the following equations (42) to (44) are obtained, from which the oxygen storage density Ost can be obtained (updated).
[0128]
(Equation 42)

[0129]
[Equation 43]

[0130]
[Equation 44]

[0131]
As described above, since the oxygen storage density Ost is obtained from the equations (42) to (44), Cgout, sto, i, Cgout, reduc, i can be obtained as described above. Further, since the oxygen storage density Ost is obtained, the oxygen storage amount OSA of the specific region can be obtained based on the following equation (45).
[Equation 45]

[0132]
Therefore, when the chemical species concentration Cgin, i flowing into the catalyst is given as a boundary condition, the oxygen storage amount OSA of each block is sequentially obtained from the block (specific region) upstream of the catalyst using the equation (45). Accordingly, the distribution of the oxygen storage amount inside the catalyst is accurately estimated. Further, if the oxygen storage amount OSA of each block is integrated for the entire catalyst, the oxygen storage amount of the entire catalyst can be accurately estimated. The above is the catalyst model used by the present exhaust gas purification apparatus, and the exhaust gas purification apparatus uses the concentration of oxygen CgoutUF, O2 <i> flowing out from the block i of the second catalyst 54 estimated by the catalyst model to empty. Perform fuel ratio control.
[0133]
(Actual operation)
Next, the actual operation of the exhaust gas purification apparatus will be described with reference to a flowchart showing a routine executed by the CPU 71. The catalyst model of the present exhaust gas purification apparatus considers oxygen as a storage agent, and considers carbon monoxide and hydrocarbons as reduction agents. On the other hand, nitrogen oxide may be further considered as a storage agent, or a reduction agent may be represented only by carbon monoxide.
[0134]
The CPU 71 repeatedly executes the routine shown in FIG. 10 each time the crank angle of each cylinder reaches a predetermined crank angle (for example, BTDC 90 ° CA) before each intake top dead center. Therefore, when the crank angle of an arbitrary cylinder reaches the predetermined crank angle, the CPU 71 starts processing from step 1000 and proceeds to step 1005, where the CPU 71 determines the intake air amount AFM measured by the air flow meter 61 and the engine rotation speed NE. Based on the map, a basic fuel injection amount Fbase for setting the air-fuel ratio of the air-fuel mixture supplied to the engine to the stoichiometric air-fuel ratio is determined.
[0135]
Next, the CPU 71 proceeds to step 1010, sets a value obtained by adding an air-fuel ratio feedback correction amount DFi described later to the basic fuel injection amount Fbase, and sets the final fuel injection amount Fi in the following step 1015. An instruction to inject fuel is given to the injector 39, and the routine proceeds to step 1095, where the present routine is temporarily ended. As described above, the fuel of the final fuel injection amount Fi subjected to the feedback correction is injected into the cylinders that are in the intake stroke.
[0136]
Next, the calculation of the air-fuel ratio feedback correction amount DFi will be described. The CPU 71 repeatedly executes the routine shown in FIG. 11 every time a predetermined time elapses. Therefore, at a predetermined timing, the CPU 71 starts the process from step 1100 and proceeds to step 1105 to determine whether the air-fuel ratio feedback control condition is satisfied. The air-fuel ratio feedback control condition is, for example, that the cooling water temperature THW of the engine is equal to or higher than a first predetermined temperature, the intake air amount (load) per one revolution of the engine is equal to or lower than a predetermined value, and the first catalyst downstream air-fuel ratio sensor 66 Holds when is normal.
[0137]
Now, an explanation will be given assuming that the air-fuel ratio feedback control condition is satisfied and the oxygen concentration CgoutUF, O2 <i> flowing out of the block i of the second catalyst 54 described later has changed from a state smaller than the positive threshold value Crefpls to a larger state. Continue. In this case, the CPU 71 determines “Yes” in step 1105 and proceeds to step 1110 to determine whether or not CgoutUF, O2 <i> is greater than a positive threshold value Crefpls. According to the above assumption, since CgoutUF, O2 <i> is larger than the positive threshold value Crefpls, the CPU 71 determines “Yes” in step 1110, proceeds to step 1115, and executes this routine last time in step 1115. It is determined whether or not (previous) CgoutUF, O2 <i> at this time is smaller than a threshold value Crefpls. According to the above assumption, since the previous CgoutUF, O2 <i> is smaller than the positive threshold value Crefpls, the CPU 71 determines “Yes” in step 1115, proceeds to step 1120, and performs air-fuel ratio feedback in step 1120. A positive value β is set for the correction amount DFi, and the routine proceeds to step 1195, where the present routine is temporarily ended.
[0138]
As described above, when the oxygen concentration CgoutUF, O2 <i> changes from a state smaller than the positive threshold Crefpls to a state larger than the threshold Crefpls, the exhaust gas purification apparatus sets the air-fuel ratio feedback correction amount DFi to a positive value β, The air-fuel ratio of the air-fuel mixture supplied to the engine (therefore, the air-fuel ratio flowing into the first catalyst 53) is made richer than the stoichiometric air-fuel ratio (theoretical air-fuel ratio-α = theoretical air-fuel ratio-α2). As a result, the exhaust gas having a rich air-fuel ratio flows into the second catalyst 54, and the oxygen concentration CgoutUF, O2 <i> is maintained at substantially “0” as shown at times t2 to t3 in FIG. Will be done.
[0139]
When the current and previous oxygen concentrations CgoutUF, O2 <i> are larger than the positive threshold value Crefpls, the CPU 71 determines “Yes” in step 1110 and “No” in step 1115, and proceeds directly to step 1195. This routine ends once. As a result, the air-fuel ratio feedback correction amount DFi is maintained at a positive value β, and the air-fuel ratio of the air-fuel mixture supplied to the engine is also maintained at an air-fuel ratio richer than the stoichiometric air-fuel ratio (theoretical air-fuel ratio-α).
[0140]
On the other hand, the description is continued assuming that the air-fuel ratio feedback control condition is satisfied and the oxygen concentration CgoutUF, O2 <i> flowing out of the block i of the second catalyst 54 has changed from a state larger than the negative threshold value Crefmns to a smaller state. . In this case, the CPU 71 determines “Yes” in step 1105 and “No” in step 1110, and proceeds to step 1125 to determine whether CgoutUF, O2 <i> is smaller than a negative threshold value Crefmns. According to the above assumption, since CgoutUF, O2 <i> is smaller than the negative threshold value Crefmns, the CPU 71 determines “Yes” in step 1125, proceeds to step 1130, and previously executes this routine in step 1130. It is determined whether or not (previous) CgoutUF, O2 <i> at this time is larger than a threshold value Crefmns. According to the above assumption, since the previous CgoutUF, O2 <i> is larger than the threshold value Crefmns, the CPU 71 determines “Yes” in step 1130 and proceeds to step 1135. In step 1135, the CPU 71 determines the air-fuel ratio feedback correction amount. The value (-β) obtained by setting the sign of the positive value β to minus is set to DFi, and the process proceeds to step 1195 to end this routine once.
[0141]
Thus, when the oxygen concentration CgoutUF, O2 <i> changes from a state larger than the negative threshold value Crefmns to a state smaller than the negative threshold value Crefmns, the exhaust gas purification apparatus sets the air-fuel ratio feedback correction amount DFi to a negative value −β, Accordingly, the air-fuel ratio of the air-fuel mixture supplied to the engine (therefore, the air-fuel ratio flowing into the first catalyst 53) is made leaner than the stoichiometric air-fuel ratio (the stoichiometric air-fuel ratio + α = the stoichiometric air-fuel ratio + α1). As a result, exhaust gas having a lean air-fuel ratio flows into the second catalyst 54, and the oxygen concentration CgoutUF, O2 <i> is substantially reduced as shown at times t1 to t2 and times t3 to t4 in FIG. It will be maintained at "0".
[0142]
When the current and previous oxygen concentrations CgoutUF, O2 <i> are smaller than the negative threshold value Crefmns, the CPU 71 determines “No” in step 1110, “Yes” in step 1125, and “No” in step 1130. Then, the process directly proceeds to step 1195 to end this routine once. As a result, the air-fuel ratio feedback correction amount DFi is maintained at a negative value -β, and the air-fuel ratio of the air-fuel mixture supplied to the engine is also maintained at an air-fuel ratio leaner than the stoichiometric air-fuel ratio (stoichiometric air-fuel ratio + α).
[0143]
If the air-fuel ratio feedback control condition is not satisfied, the CPU 71 determines “No” in step 1105, proceeds to step 1140, and sets “0” to the air-fuel ratio feedback correction amount DFi in step 1140. Then, the routine proceeds to step 1195, where the present routine is temporarily ended. As described above, the air-fuel ratio feedback correction amount DFi is determined such that the oxygen concentration CgoutUF, O2 <i> becomes a predetermined value between the positive threshold value Crefpls and the negative threshold value Crefmns.
[0144]
Next, CgoutUF, O2 <i> of the second catalyst 54 used for determining the air-fuel ratio feedback correction amount DFi is determined, and CgoutSC, O2 <r>, which is the concentration of oxygen flowing out of the first catalyst 53, is determined. For correcting the respective catalyst models for the first catalyst 53 and the second catalyst 54 based on the comparison result between the oxygen concentration CgoutSC, O2 <r> and the output of the first catalyst downstream air-fuel ratio sensor 66. The operation of will be described.
[0145]
The CPU 71 repeatedly executes the routine shown by the flowchart in FIG. 12 every time a predetermined time elapses. Therefore, at a predetermined timing, the CPU 71 starts the process from step 1200, and proceeds to step 1205, where the oxygen storage speed coefficient kstorSC <j>, O2 (k), the coefficient krelSC, CO (k) for the first catalyst 53 are used. <J> and the coefficients krelSC, HC (k) <j> are represented by a temperature TempSC of the first catalyst 53, a deterioration index value REKKASC indicating the degree of deterioration of the first catalyst 53, and a map (lookup) as shown in FIG. Up table). Note that, for example, as in ktorSC, O2 (k) <j>, a value to which SC is assigned means a value for the first catalyst, and a value to which <j> is assigned is a value in block j. (The j-th block) (the same applies hereinafter).
[0146]
The catalyst temperature TempSC and a catalyst temperature TempUF of the second catalyst 54 described later are estimated according to the operating state of the engine 10 (for example, the intake air amount Ga and the engine speed NE). The deterioration index value REKKASC of the first catalyst 53 and the deterioration index value REKKAUF of the second catalyst catalyst 54 are obtained according to the maximum oxygen storage amount CmaxSC of the first catalyst 53 and the maximum oxygen storage amount CmaxUF of the second catalyst 54, respectively. . For example, the deterioration index value REKKASC is obtained as a value that increases as the maximum oxygen storage amount CmaxSC decreases, and the deterioration index value REKKAUF is obtained as a value that increases as the maximum oxygen storage amount CmaxUF decreases.
[0147]
Further, the maximum oxygen storage amounts CmaxSC and CmaxUF are obtained as follows. That is, if the first catalyst downstream air-fuel ratio sensor 66 and the second catalyst downstream air-fuel ratio sensor 67 detect an air-fuel ratio leaner than the stoichiometric air-fuel ratio when the engine 10 is in a predetermined steady-state operating state, The air-fuel ratio of the exhaust gas flowing into the catalyst 53 (the air-fuel ratio of the air-fuel mixture supplied to the engine) is maintained at a predetermined rich air-fuel ratio, whereby the oxygen stored in each of the first catalyst 53 and the second catalyst 54 is maintained. Consume all. As a result, first, the first catalyst downstream air-fuel ratio sensor 66 outputs a value corresponding to an air-fuel ratio richer than the stoichiometric air-fuel ratio from a value corresponding to an air-fuel ratio leaner than the stoichiometric air-fuel ratio. The fuel ratio sensor 67 outputs a value corresponding to an air-fuel ratio richer than the stoichiometric air-fuel ratio from a value corresponding to an air-fuel ratio leaner than the stoichiometric air-fuel ratio. This time is referred to as time T10.
[0148]
Next, from time T10, the air-fuel ratio of the exhaust gas flowing into the first catalyst 53 is set to a predetermined lean air-fuel ratio. As a result, oxygen starts to be stored in the first catalyst 53, and eventually reaches the maximum oxygen storage amount CmaxSC. At this time, the first catalyst downstream air-fuel ratio sensor 66 outputs a value corresponding to an air-fuel ratio leaner than the stoichiometric air-fuel ratio from a value corresponding to an air-fuel ratio richer than the stoichiometric air-fuel ratio. This time is defined as time T20.
[0149]
The CPU 71 obtains the amount of oxygen contained in the exhaust gas flowing into the first catalyst 53 from the time point T10 to the time point T20 based on the following equations (46) and (47). The air-fuel ratio AF of the exhaust gas in the equation (46) is obtained by calculating the intake air mass Ga per unit time measured by the air flow meter 61 from the supplied fuel mass per unit time obtained based on the final fuel injection amount Fi and the engine speed NE. It is obtained by dividing by Gf. The integrated value O2storage obtained by the following equation (47) is the maximum oxygen storage amount CmaxSC.
[0150]
[Equation 46]

[0151]
[Equation 47]

[0152]
Next, after time T20, the air-fuel ratio of the exhaust gas flowing into the first catalyst 53 is maintained at the predetermined lean air-fuel ratio. As a result, exhaust gas having a lean air-fuel ratio flows out of the first catalyst 53, so that oxygen starts to be stored in the second catalyst 54 at the same time T20, and after a predetermined time elapses, the oxygen storage amount of the second catalyst 54 becomes the maximum oxygen storage amount. CmaxUF is reached. As a result, the second catalyst downstream air-fuel ratio sensor 67 outputs a value corresponding to an air-fuel ratio leaner than the stoichiometric air-fuel ratio from a value corresponding to an air-fuel ratio richer than the stoichiometric air-fuel ratio. This time is referred to as time T30.
[0153]
The CPU 71 obtains the amount of oxygen contained in the exhaust gas flowing into the first catalyst 53 from the time T20 to the time T30 based on the above equations (46) and (47). In this case, the integration interval of the above equation (47) is from T20 to time T30. The integrated value O2storage obtained by the equation (47) is the maximum oxygen storage amount CmaxUF.
[0154]
Referring again to FIG. 12, the CPU 71 proceeds to step 1210 to execute a subroutine for calculating CgoutSC of each specific component of the first catalyst 53. This subroutine is shown by the flowcharts of FIGS. 13 to 15, and the CPU 71 executes these routines to execute the routine, whereby the oxygen concentration CgoutSC, O2 <r> flowing out of the first catalyst 53 and the carbon monoxide concentration CgoutSC, CO <r> and the hydrocarbon concentration CgoutSC, HC <r> are calculated. As described above, in the catalyst model, the specific components are obtained by dividing the first catalyst 53 into r blocks.
[0155]
Here, the specific processing in step 1210 will be described. When the CPU 71 proceeds to step 1210, the CPU 71 starts the processing from step 1300 in FIG. 13 and proceeds to step 1305 to set the value of the variable j to “0”. . This variable j is a variable that determines the order of the block to be operated in the following. Next, the CPU 71 increases the value of the variable j by “1” in step 1310 and determines whether or not the value of the variable j has become equal to r + 1 in step 1315, that is, for each specific component for all the blocks. It is determined whether or not the calculation of has been completed.
[0156]
Since the value of the variable j at this stage is “1”, the CPU 71 determines “No” in step 1315 and proceeds to step 1320, where it is calculated in step 1355 described later in the previous calculation of this routine. The oxygen concentration CwSC, O2 (k + 1) <j> of the coat layer of the j-th block (block j) is set to the oxygen concentration CwSC, O2 (k) <j> of the current coat layer, and in the subsequent step 1325 The oxygen storage density OstSC (k + 1) <j> calculated in step 1615 of FIG. 16 described later in the previous calculation of this routine is set to the value of the current oxygen storage density OstSC (k) <j>. When the current calculation is performed for the first time after the start of the engine 10, an appropriate initial value is given to each of the above values.
[0157]
Next, at step 1330, the CPU 71 obtains the oxygen consumption rate constant R * storSC, O2 (k) <j> according to the equation described in the step 1330 (see equation (36)). The maximum oxygen storage density OstSCmax <j> used in step 1330 may be a fixed value, but is preferably determined according to the catalyst deterioration index value REKKASC (or the maximum oxygen storage amount CmaxSC) (hereinafter the same). .). Thereafter, the CPU 71 determines in step 1335 the apparent diffusion speed R _D SC, O2 (k) <j> are mapped to catalyst temperature TempSC and map MapR. _D Determined from SCO2.
[0158]
Subsequently, the CPU 71 obtains the oxygen reaction rate-limiting factor SPstorSC, O2 <j> in step 1340 by using the equation described in step 1340 (see the above equation (29)). The oxygen concentration CgoutSC, O2 (k) <j-1> flowing out from the previous (ie, upstream) block j-1 is taken in as the oxygen concentration CginSC, O2 (k) <j> flowing into the block j.
[0159]
At this stage, since the value of j is "1", the block j is the most upstream block of the first catalyst 53, and there is no preceding (upstream) block j-1. Therefore, CgoutSC, O2 (k) <j-1> of the previous block in step 1345 is the oxygen concentration CginSC, O2 of the exhaust gas flowing into the first catalyst 53. The oxygen concentration CginSC, O2 (= Cgin, O2) of the exhaust gas flowing into the first catalyst 53 is obtained by a function fO2 based on the air-fuel ratio of the exhaust gas flowing into the first catalyst 53 and the flow rate of the exhaust gas. The right side of the following equation (48) is a specific example of the function fO2. The air-fuel ratio AF of the exhaust gas used in the equation (48) is obtained by calculating the intake air mass Ga per unit time measured by the air flow meter 61 based on the final fuel injection amount Fi and the engine rotation speed NE. It is obtained by dividing by the fuel mass Gf.
[0160]
[Equation 48]

[0161]
The air-fuel ratio AF of the exhaust gas flowing into the first catalyst 53 is Ga / Gf, and the air mass required to obtain the stoichiometric air-fuel ratio with respect to Gf is defined as Gastoich. Then, the stoichiometric air-fuel ratio AFstoich becomes Gastoich / Gf. On the other hand, when the air-fuel ratio becomes AF when the supplied fuel mass is Gf, the excess air mass with respect to the air mass necessary to obtain the stoichiometric air-fuel ratio AFstoich is Ga-Gastoich. In other words, the following equation (49) is obtained, and the above equation (48) is obtained from the equation (49).
[0162]
[Equation 49]

[0163]
Next, the CPU 71 proceeds to step 1350, and obtains CgoutSC, O2 (k + 1) <j> in accordance with the equation (see equation (30)) described in step 1350. The value of vg is the intake air flow rate AFM (= Ga) detected by the air flow meter 13. As described above, in step 1350, the oxygen concentration CgoutSC, O2 flowing out of the target block j is newly calculated. Next, the CPU 71 proceeds to step 1355, and obtains CwSC, O2 (k + 1) <j> in accordance with the equation described in step 1355 (see equation (28)). That is, the CPU 71 newly calculates the oxygen concentration CwSC, O2 of the coat layer of the target block j in step 1355, and proceeds to step 1400 shown in FIG. As described above, the routine shown in FIG. 13 constitutes the exhaust gas phase oxygen concentration estimating means and the coat layer oxygen concentration estimating means in the block j (specific region j) of the first catalyst 53.
[0164]
Next, the CPU 71 proceeds from step 1400 to step 1405, and applies the carbon monoxide CwSC, CO (k + 1) <j> of the coat layer calculated in step 1435 described later in the previous calculation of this routine to the current coat. The layer is set to the concentration of carbon monoxide CwSC, CO <j> (k). When the current calculation is performed for the first time after the start of the engine 10, an appropriate initial value is given to CwSC, CO <j> (k).
[0165]
Next, the CPU 71 calculates the consumption rate constant R * reducSC, CO (k) <j> in step 1410 according to the equation described in the step 1410 (see the above equation (38)). Apparent diffusion rate R at _D SC, CO (k) <j> are mapped to catalyst temperature TempSC and map MapR. _D Determined from SCCO.
[0166]
Subsequently, in step 1420, the CPU 71 obtains the reaction rate-limiting factor SPreducSC, CO <j> of carbon monoxide by the equation described in the step 1420 (see the above equation (33)). The carbon monoxide concentration CgoutSC, CO (k) <j-1> flowing out of the block j-1 before (i.e., upstream) is replaced with the carbon monoxide concentration CginSC, CO (k) flowing into the block j. Import as <j>.
[0167]
At this stage, since the value of j is "1", the target block j is the most upstream block of the first catalyst 53, and there is no block j-1 upstream therefrom. Therefore, CgoutSC, CO (k) <j-1> of the previous block in step 1425 is the concentration of carbon monoxide CginSC, CO of the exhaust gas flowing into the first catalyst 53. In this case, the relationship between the air-fuel ratio A / F of the exhaust gas flowing into the first catalyst 53 (calculated as “Ga / Gf”) and the carbon monoxide concentrations CginSC, CO is shown in the graph of FIG. Therefore, this relationship is obtained in advance by experiments and stored as a map, and the carbon monoxide concentrations CginSC and CO are obtained from the actual air-fuel ratio A / F of the exhaust gas obtained by calculation and the map.
[0168]
Next, the CPU 71 proceeds to step 1430, and obtains CgoutSC, CO (k + 1) <j> according to the equation described in step 1430 (see equation (34)). That is, the concentration of carbon monoxide CgoutSC, CO flowing out of the block j is newly calculated. Next, the CPU 71 proceeds to step 1435, and obtains CwSC, CO (k + 1) <j> in accordance with the equation described in step 1435 (see equation (32)). That is, the CPU 71 newly calculates the carbon monoxide concentration CwSC, CO of the coat layer of the target block j in step 1435, and proceeds to step 1500 shown in FIG. Thus, the routine shown in FIG. 14 constitutes the exhaust gas phase carbon monoxide concentration estimating means and the coat layer carbon monoxide concentration estimating means in the block j of the first catalyst 53.
[0169]
The routine shown in FIG. 15 is a routine for performing an operation on hydrocarbon HC, and is a routine similar to the above-described routine of FIG. 14 for performing an operation on carbon monoxide CO.
[0170]
In brief, the CPU 71 proceeds from step 1500 to step 1505, in which the carbon monoxide CwSC, HC (k + 1) <j> of the coat layer calculated in step 1535, which will be described later, in the previous calculation of this routine, is CwSC, HC (k) <j>, which are the values of the carbon monoxide concentration Cw, HC of the coat layer of FIG. When the current calculation is performed for the first time after the start of the engine 10, an appropriate initial value is given to each of the above values.
[0171]
Next, the CPU 71 calculates the consumption rate constant R * reducSC, HC (k) <j> in step 1510 according to the equation described in the step 1510 (see the equation (38)). Apparent diffusion rate R at _D SC, HC (k) <j> are converted to catalyst temperature TempSC and map MapR. _D Determined from SCHC.
[0172]
Subsequently, in step 1520, the CPU 71 obtains the reaction rate-limiting factor SPreducSC, HC <j> of the hydrocarbon by the equation described in the step 1520 (see the above equation (33)). The hydrocarbon concentration CgoutSC, HC (k) <j-1> flowing out of the block j-1 before (that is, upstream) is defined as the hydrocarbon concentration Cgin, HC (k) <j> flowing in the block j. take in.
[0173]
At this stage, since the value of j is "1", the block j is the most upstream block of the first catalyst 53, and there is no block j-1 upstream therefrom. Therefore, Cgout, HC (k) <j-1> in step 1525 is the hydrocarbon concentration Cgin, HC of the exhaust gas flowing into the first catalyst 53. In this case, the relationship between the air-fuel ratio A / F of the exhaust gas flowing into the first catalyst 53 (calculated as “Ga / Gf”) and the hydrocarbon concentrations Cgin, HC is as shown in the graph of FIG. Therefore, this relationship is obtained in advance by experiments and stored as a map, and the hydrocarbon concentrations Cgin and HC are obtained from the actual air-fuel ratio A / F of the exhaust gas obtained by calculation and the map.
[0174]
Next, the CPU 71 proceeds to step 1530, and obtains CgoutSC, HC (k + 1) <j> according to the equation described in step 1530 (see equation (34)). That is, the hydrocarbon concentration CgoutSC, HC flowing out of the block j is newly calculated. Next, the CPU 71 proceeds to step 1535, and obtains CwSC, HC (k + 1) <j> in accordance with the equation described in step 1535 (see equation (32)). That is, the CPU 71 newly calculates the hydrocarbon concentration Cw, HC of the coat layer of the block j in step 1535, and proceeds to step 1600 shown in FIG. Thus, the routine shown in FIG. 15 constitutes the exhaust gas phase hydrocarbon concentration estimating means and the coat layer hydrocarbon concentration estimating means in block j (specific region j).
[0175]
Next, the CPU 71 proceeds from step 1600 to step 1605, obtains the coefficient P <j> by the equation described in the step 1605 based on the equation (43), and in the subsequent step 1610, calculates the coefficient P <j>. A coefficient Q <j> is obtained by the equation described in the same step 1610 based on the coefficient. Next, in step 1615, the CPU 71 obtains the oxygen storage density OstSC (k + 1) <j> by the expression described in the step 1615 based on the expression (42), and in the next step 1620 the oxygen storage density OstSC (k + 1) <j> based on the expression (45). By adding the oxygen storage amount OstSC (k + 1) <j> · dA · L of the block j to the oxygen storage amount OSASC (j−1) of the block 1 to the block j−1 by the equation described in step 1620, The oxygen storage amount OSASC (j) from the first block to the block j is obtained, and the process returns to the step 1310 in FIG. The value of the oxygen storage amount OSASC (0) is set to “0”. As described above, the routine shown in FIG. 16 constitutes the oxygen storage density calculating means of the block j of the first catalyst 53 and the oxygen storage amount calculating means of the blocks 1 to j.
[0176]
Returning to step 1310, the CPU 71 increases the value of the variable j by "1", so that various values of the next downstream block are sequentially calculated in the same manner as described above. Then, when various values up to the block r are calculated, the value of the variable j is made equal to r + 1 in step 1310. Therefore, the CPU 71 determines “Yes” in step 1315, and proceeds to step 1395. The process proceeds to Step 1215 of FIG.
[0177]
In step 1215, the CPU 71 determines the actual air-fuel ratio (detected air-fuel ratio) AFSCdwn of the exhaust gas flowing through the exhaust passage downstream of the first catalyst 53 from the output vabyfs of the first catalyst downstream air-fuel ratio sensor 66 and the map MapAF shown in FIG. , Act, and in the following step 1220, the exhaust gas downstream of the first catalyst 53 is determined based on the oxygen concentration CgoutSC, O2 <r> flowing out of the first catalyst 53 previously determined by the catalyst model and the following equation (50). An estimated air-fuel ratio AFSCdwn, est of the exhaust gas flowing through the passage is obtained. This equation (50) is derived from the above equation (46).
[0178]
[Equation 50]

[0179]
Next, the CPU 71 proceeds to step 1225 to determine whether or not the absolute value of the difference between the detected air-fuel ratio AFSCdwn, act and the estimated air-fuel ratio AFSCdwn, est is smaller than a threshold value AFth. That is, it is determined whether the catalyst model error of the first catalyst 53 is small. When the catalyst model error is large, the CPU 71 determines “No” in step 1225 and proceeds to step 1230. In step 1230, the CPU 71 corrects the oxygen storage speed coefficient ktorSC, ktorSC, to correct the catalyst model for the first catalyst 53. O2 (k) <j>, coefficients krelSC, CO (k) <j>, and coefficients krelSC, HC (k) <j> are modified by, for example, changing (increase or decrease) by a predetermined amount, and then Returning to step 1210, CgoutSC of each specific component of the first catalyst 53 is calculated again.
[0180]
When such a process is repeatedly performed, the catalyst model error of the first catalyst 53 becomes smaller, so that the absolute value of the difference between the detected air-fuel ratio AFSCdwn, act and the estimated air-fuel ratio AFSCdwn, est becomes smaller than the threshold value AFth. As a result, the CPU 71 determines “Yes” in step 1225, and proceeds to step 1235. In step 1235, the CPU 71 calculates the average value of the coefficients kstorSC, O2 (k) <j> obtained for each block by kstorSC, O2ave. , KrelSC, CO (k) <j> are determined as krelSC, COave, and the average values of coefficients krelSC, HC (k) <j> are determined as krelSC, HCave. ,
[0181]
Next, the CPU proceeds to step 1240, and in step 1240, calculates a correction coefficient of the catalyst model of the second catalyst 54 for each block of the second catalyst 54. As described above, in the catalyst model, the specific components are obtained by dividing the second catalyst 54 into m blocks. The processing in step 1240 will be specifically described. The CPU 71 corrects for the block j of the second catalyst 54 based on the predetermined conversion map MapsktorO2 <j> determined for each block j and the average values kstorSC and O2ave. The coefficients coef, kstorUF, O2 <j> are obtained, and similarly, the correction coefficients coef, kstorUF for the block j are obtained from the predetermined conversion map MapkrelCO <j> determined for each block j and the average values krelSC, COave. , CO <j>, and the correction coefficients coef, krelUF, HC for the block j of the second catalyst 54 from the predetermined conversion map MapkrelHC <j> determined for each block j and the average values krelSC, HCave. <J> is obtained.
[0182]
Next, the CPU 71 proceeds to step 1245, in which the oxygen storage rate coefficient basic value ktorUFong, O2 (k) <j>, the basic coefficient krelUFong, CO (k) <j>, and the basic coefficient krelUFong, HC ( k) <j> is determined from the temperature TempUF of the second catalyst 54, a deterioration index value REKKAUF indicating the degree of deterioration of the second catalyst 54, and a map similar to the map shown in FIG. It should be noted that, for example, a value to which UF is assigned, such as kstoUForg, O2 (k) <j>, is a value for the second catalyst (hereinafter the same).
[0183]
Next, the CPU 71 proceeds to step 1250, in which the oxygen storage speed coefficient ktorUF, O2 (k) <j> for each block j for the second catalyst 54 is converted into the oxygen storage speed coefficient basic value ktorUForg, O2 (k) <j. > Is multiplied by the above-mentioned correction coefficients coef, ktorUF, O2 <j>, and similarly, the coefficients krelUF, CO (k) <j> are similarly obtained by adding the above-mentioned correction coefficients coef, CO (k) <j> krelUF, CO <j> are multiplied, and the coefficients krelUF, HC (k) <j> are obtained by adding the correction coefficients coef, krelUF, HC <j> to the basic coefficient coefficients krelUFForg, HC (k) <j>. Find by multiplying.
[0184]
Then, the CPU 71 proceeds to step 1255 to execute a subroutine for calculating CgoutUF of each specific component of the second catalyst 54. This subroutine is shown by the flowcharts of FIGS. 20 to 23 which are respectively similar to the routines shown by the flowcharts of FIGS. 13 to 16, and the CPU 71 executes these routines to execute each block j of the second catalyst 54. , Oxygen concentration CgoutUF, O2 <j>, carbon monoxide concentration CgoutUF, CO <j>, and hydrocarbon concentration CgoutUF, HC <j>.
[0185]
In brief, the CPU 71 sets the value of the variable j to “0” in a step 2005 following the step 2000, increases the value of the variable j by “1” in a step 2010, and increases the value of the variable j by “1” in a step 2015. It is determined whether or not the value of the variable j has become equal to m + 1, that is, whether or not the calculation of each specific component has been completed for all blocks.
[0186]
Since the value of the variable j at this stage is “1”, the CPU 71 determines “No” in step 2015 and proceeds to step 2020, where the coat layer of the block j calculated in the previous calculation of this routine is determined. The oxygen concentration CwUF, O2 (k + 1) <j> of the current coat layer is set to the oxygen concentration CwUF, O2 (k) <j> of the current coat layer, and the oxygen calculated in the previous calculation of the present routine in the subsequent step 2025 is set. The storage density OstUF (k + 1) <j> is set to the value OstUF (k) <j> of the current oxygen storage density Ost. When the current calculation is performed for the first time after the start of the engine 10, an appropriate initial value is given to each of the above values.
[0187]
Next, the CPU 71 calculates an oxygen consumption rate constant R * storUF, O2 (k) <j> in step 2030, and in the subsequent step 2035, the apparent diffusion rate R _D UF, O2 (k) <j> are mapped to the catalyst temperature TempUF and the map MapR. _D Determined from UFO2. Subsequently, the CPU 71 obtains the oxygen reaction rate-limiting factor SPstorUF, O2 <j> in step 2040, and in step 2045, the oxygen concentration CgoutUF, O2 (k) <j flowing out of the block j-1 upstream of the block j. -1> is taken as the oxygen concentration CginUF, O2 (k) <j> flowing into the block j.
[0188]
At this stage, since the value of j is "1", block j is the most upstream block of the second catalyst 54, and there is no block j-1 upstream therefrom. Accordingly, CgoutUF, O2 (k) <j-1> of the previous block in step 2045 is the oxygen concentration CginUF, O2 of the exhaust gas flowing into the second catalyst 54. The oxygen concentration CginUF, O2 of the exhaust gas flowing into the second catalyst 54 is obtained based on the above equation (48). At this time, the CPU 71 obtains the air-fuel ratio AF of the exhaust gas used in equation (48) from the output vabyfs of the first catalyst downstream air-fuel ratio sensor 66 and the map shown in FIG. That is, in this case, the oxygen concentration CginUF, O2 (= CginUF, O2 (k) <1>) of the exhaust gas flowing into the second catalyst 54 is based on the output (detected air-fuel ratio) of the first catalyst downstream air-fuel ratio sensor 66. Determined and obtained.
[0189]
Next, the CPU 71 proceeds to step 2050 to obtain the oxygen concentration CgoutUF, O2 (k + 1) <j> flowing out of the block j, and in a subsequent step 2055, the oxygen concentration CwUF, O2 (k + 1) <j of the coat layer of the block j. > Then, the CPU 71 proceeds to step 2100 shown in FIG. 21 via step 2060. As described above, the routine shown in FIG. 20 constitutes an exhaust gas phase oxygen concentration estimating unit and a coat layer oxygen concentration estimating unit in the block j (specific region j) of the second catalyst 54.
[0190]
Next, the CPU 71 proceeds to step 2105, in which the carbon monoxide CwUF, CO (k + 1) <j> calculated at the time of the previous calculation of the present routine is used as the carbon monoxide concentration CwUF, CO of the present coat layer. <J> Set to (k). If the current calculation is performed for the first time after the start of the engine 10, an appropriate initial value is given to CwUF, CO <j> (k).
[0191]
Next, in steps 2110 to 2120, the CPU 71 calculates a consumption rate constant R * reducUF, CO (k) <j>, and obtains an apparent diffusion rate R _D UF, CO (k) <j> are converted to catalyst temperature TempUF and map MapR. _D From UFCO, the reaction rate-limiting factor SPreducUF, CO <j> of carbon monoxide is determined. Then, in step 2125, the carbon monoxide concentration CgoutUF, CO (k) <j-1> flowing out of the block j-1 before (that is, upstream of) the block j is converted to the monoxide flowing into the block j. Imported as carbon concentration CginUF, CO (k) <j>.
[0192]
At this stage, since the value of j is "1", the target block j is the most upstream block of the second catalyst 54, and there is no block j-1 upstream therefrom. Therefore, CgoutUF, CO (k) <j-1> of the previous block in step 2125 is the concentration of carbon monoxide CginUF, CO of the exhaust gas flowing into the second catalyst 54. In this case, the relationship between the air-fuel ratio A / F of the exhaust gas flowing into the second catalyst 54 and the carbon monoxide concentrations CginUF, CO is as shown in the graph of FIG. The actual air-fuel ratio A / F (detected air-fuel ratio) of the exhaust gas obtained from the output vabyfs of the first catalyst downstream air-fuel ratio sensor 66 and the map shown in FIG. The carbon oxide concentration CginUF, CO (= CginUF, CO (k) <1>) is determined.
[0193]
Next, the CPU 71 proceeds to step 2130 to obtain the carbon monoxide concentration CgoutUF, CO (k + 1) <j> flowing out of the block j, and in step 2135, the carbon monoxide concentration CwUF, CO (k + 1) of the coat layer of the block j. <J> is obtained, and then the process proceeds to the step 2200 shown in FIG. In this manner, the routine shown in FIG. 21 constitutes the exhaust gas phase carbon monoxide concentration estimating means and the coat layer carbon monoxide concentration estimating means in the block j of the second catalyst 54.
[0194]
The routine shown in FIG. 22 is a routine for performing an operation on hydrocarbon HC, and is a routine similar to the routine of FIG. 21 described above for performing an operation on carbon monoxide CO.
[0195]
In brief, the CPU 71 proceeds from step 2200 to step 2205, in which the carbon monoxide CwUF, HC (k + 1) <j> of the coat layer calculated in the previous calculation of the present routine is replaced with the current coat layer monoxide. The carbon concentration is set to CwUF, HC (k) <j>. When the current calculation is performed for the first time after the start of the engine 10, an appropriate initial value is given to each of the above values.
[0196]
Next, the CPU 71 calculates the consumption rate constant R * reducUF, HC (k) <j> in step 2210, and then in step 2215 the apparent diffusion rate R _D UF, HC (k) <j> are converted to catalyst temperature TempUF and map MapR. _D UFHC, and then, in step 2220, the reaction rate-limiting factor SPreducUF, HC <j> of the hydrocarbon is determined. Then, in step 2225, the hydrocarbon concentration CgoutUF, HC (k) <j-1> flowing out of the block j-1 before (ie, upstream of) the block j is converted into the hydrocarbon concentration Cgin flowing into the block j. , HC (k) <j>.
[0197]
At this stage, since the value of j is "1", block j is the most upstream block of the second catalyst 54, and there is no block j-1 upstream therefrom. Therefore, CgoutUF, HC (k) <j-1> in step 2225 is the hydrocarbon concentration CginUF, HC of the exhaust gas flowing into the second catalyst 54. In this case, the relationship between the air-fuel ratio A / F of the exhaust gas flowing into the second catalyst 54 and the hydrocarbon concentrations Cgin, HC is as shown in the graph of FIG. From the output vabyfs of the first catalyst downstream air-fuel ratio sensor 66 and the actual exhaust gas air-fuel ratio A / F (detected air-fuel ratio) obtained from the map shown in FIG. The concentration CginUF, HC (= CginUF, HC (k) <1>) is determined.
[0198]
Next, the CPU 71 proceeds to step 2230 to obtain the carbon monoxide concentration CgoutUF, HC (k + 1) <j> flowing out of the block j, and in step 2235, the carbon monoxide concentration CwUF, HC (k + 1) of the coat layer of the block j. <J> is obtained, and the flow advances to step 2300 shown in FIG. 23 via step 2295. Thus, the routine shown in FIG. 22 constitutes the hydrocarbon concentration estimating means of the exhaust gas phase and the hydrocarbon concentration estimating means of the coat layer in the block j (specific region j) of the second catalyst 54.
[0199]
Next, the CPU 71 proceeds from step 2300 to step 2305 to calculate a coefficient P <j>, and in a subsequent step 2310, calculates a coefficient Q <j>. Next, in step 2315, the CPU 71 obtains the oxygen storage density OstUF (k + 1) <j> by the expression described in the step 2315 based on the expression (42), and in the next step 2320 based on the expression (45). By adding the obtained oxygen storage amount of block j (= OstUF (k + 1) <j> .dAL) to the oxygen storage amount OSAUF (j-1) of block 1 to block j-1, block 1 to block j are obtained. The oxygen storage amount OSAUF <j> up to is obtained, and the process returns to step 2010 of FIG. Note that the value of the oxygen storage amount OSAUF (0) is set to “0”. In this way, the routine shown in FIG. 23 constitutes the oxygen storage density calculation means of the block j of the second catalyst 54 and the oxygen storage amount calculation means of the blocks 1 to j. Note that all the oxygen storage amounts OSAUF <j> are stored in the RAM 73. Therefore, the oxygen storage amounts OSAUF <i> of blocks 1 to i are also stored in the RAM.
[0200]
Since the CPU 71 returns to step 2010, the value of the variable j is increased by “1”, so that various values of the next downstream block are sequentially calculated in the same manner as described above. Therefore, when the value of the variable j becomes the value i, the oxygen concentration CgoutUF, O2 <i> (= CgoutUF, O2 (k + 1) <i>) used for determining the air-fuel ratio feedback correction amount is obtained. Can be Then, when various values up to the block m are calculated, the value of the variable j is made equal to m + 1 in step 2010. Therefore, the CPU 71 determines “Yes” in step 2015 and proceeds to step 2095 through FIG. The process proceeds to Step 1295 of FIG.
[0201]
As described above, the CPU 71 uses the catalyst model, and indicates the state relating to the exhaust gas purification of the second catalyst 54 “the oxygen concentration CgoutUF, O2 <i, which is a value relating to the amount of the specific component flowing out from the block i of the second catalyst 54”. >> is estimated and obtained by calculation using the output of the first catalyst downstream air-fuel ratio sensor 66, and the oxygen concentration CgoutUF, O2 <i> is equal to a predetermined value (Crefmns smaller than “0” and larger than “0”). The air-fuel ratio of the air-fuel mixture supplied to the engine (therefore, the air-fuel ratio of the exhaust gas flowing into the second catalyst 54) is controlled so that the air-fuel ratio becomes a value between Crefpls).
[0202]
Accordingly, the present exhaust gas purification apparatus acquires a state (in this case, CgougUF, O2 <i>) related to exhaust gas purification of the second catalyst 54 at a time earlier than the output change of the O2 sensor provided downstream of the second catalyst 54. By controlling the air-fuel ratio of the air-fuel mixture supplied to the engine 10 based on the obtained state, the air-fuel ratio of the exhaust gas flowing into the second catalyst 54 can be appropriately controlled. As a result, the present exhaust gas purification apparatus can further reduce the emission of harmful components.
[0203]
Further, the present exhaust gas purification apparatus uses a value relating to the amount of the specific component flowing out of the intermediate block (block i) for air-fuel ratio control, and controls the specific component to be substantially “0” up to the intermediate block of the second catalyst 54. Therefore, even if the specified component flows out of the intermediate block due to an unavoidable delay in the air-fuel ratio control error and the air-fuel ratio feedback control, it must be purified by a block downstream of the intermediate block. Can be. In other words, at least a block located downstream of the intermediate block of the second catalyst 54 can be provided as a preliminary catalyst (buffer-like catalyst) for purifying exhaust gas. Can be further reduced.
[0204]
Furthermore, in this embodiment, the output of the first catalyst downstream air-fuel ratio sensor 66 that is disposed upstream of the second catalyst 54 and that can directly detect the air-fuel ratio of the exhaust gas flowing into the second catalyst 54 is used for calculation. A value CgoutUF, X (CgoutUF, O2 <i>) relating to the amount of the specific component of the second catalyst 54 is obtained. Therefore, for example, as compared with the case where the value CgoutUF, X relating to the amount of the specific component of the second catalyst 54 is obtained based on the output of the air-fuel ratio sensor provided upstream of the first catalyst 53, the second catalyst 54 is more accurately obtained. A value CgoutUF, X for the amount of the 54 particular components can be determined.
[0205]
<Modification of First Embodiment>
The exhaust gas purifying apparatus according to the modification of the first embodiment determines the concentration CgoutUF, O2 <m> flowing out of the block m (the outlet of the second catalyst 54) at the most downstream of the second catalyst 54 as the threshold Crefmns and the threshold Crefmns. Crefpls) to control the air-fuel ratio of the air-fuel mixture supplied to the engine 10. Specifically, the CPU 71 according to the modification executes a routine in which the oxygen concentrations CgoutUF, O2 <i> in steps 1110, 1115, 1125, and 1130 in FIG. 11 are replaced with oxygen concentrations CgoutUF, O2 <m>.
[0206]
As described above, in the modification of the first embodiment, the concentration CgoutUF, O2 <m> flowing out from the most downstream block (the outlet of the second catalyst 54) is used for the feedback control of the air-fuel ratio. Similarly to the exhaust gas purification device of the embodiment, the value CgoutUF, O2, <m> relating to the amount of the specific component of the second catalyst 54 is obtained by using the output of the first catalyst downstream air-fuel ratio sensor 66 for calculation. It is possible to perform quicker control than the air-fuel ratio feedback control based on the output of the air-fuel ratio sensor downstream of the second catalyst 54, and based on the output of the air-fuel ratio sensor provided upstream of the first catalyst 53. The value CgoutUF, O2 <m> relating to the amount of the specific component of the second catalyst 54 is more accurately determined as compared with the case where the value CgoutUF, O2, <m> relating to the amount of the specific component is determined. It is possible.
[0207]
<Second embodiment>
Next, a second embodiment of the exhaust gas purifying apparatus according to the present invention will be described. This exhaust gas purifying apparatus uses the second catalyst 54 instead of the concentration CgoutUF, O2 <i> of oxygen flowing out from the block i of the second catalyst 54. Oxygen storage amount OSAUF <i> from block 1 to block i (i.e., from the block located at the most upstream position when the second catalyst 54 is divided into a plurality of blocks along the flow direction of exhaust gas, Mixing supplied to the engine 10 so that the oxygen storage amount of a portion constituted by blocks up to the intermediate block located upstream of the located block has a predetermined value (in this case, a value of OSAreflow to OSArefhigh). Only the point of controlling the air-fuel ratio of the air is different from the exhaust gas purification apparatus of the first embodiment. Therefore, the following description focuses on such differences.
[0208]
(Air-fuel ratio control of the second embodiment)
First, the air-fuel ratio control of the exhaust emission control device according to the second embodiment will be described. FIG. 24 is a time chart in the air-fuel ratio control. FIG. 24A shows the air-fuel ratio of the air-fuel mixture supplied to the engine 10 (therefore, the air-fuel ratio of the exhaust gas upstream of the first catalyst), and FIG. FIG. 9 shows the oxygen storage amount OSAUF <i> stored in the portion from the first block to the i-th block (block 1 to block i) of the second catalyst 54 calculated by the catalyst model described above.
[0209]
The present exhaust gas purification apparatus obtains the oxygen storage amount OSAUF <i> from the catalyst model, and sets the engine so that the oxygen storage amount OSAUF <i> becomes approximately half the maximum oxygen storage amount CmaxUF of the second catalyst 54. The air-fuel ratio of the air-fuel mixture supplied to 10 is controlled. More specifically, when the oxygen storage amount OSAUF <i> becomes smaller than the low-side threshold OSArefflow, the present exhaust gas purification apparatus is considered to have a possibility that the oxygen storage amount of the second catalyst 54 may become too small. Then, the air-fuel ratio of the air-fuel mixture supplied to the engine 10 is set leaner by a predetermined value α1 than the stoichiometric air-fuel ratio (see times t11 and t13).
[0210]
On the other hand, when the oxygen storage amount OSAUF <i> becomes larger than the high-side threshold OSArefhigh, it is considered that the oxygen storage amount of the second catalyst 54 may become excessively large. Is set to be richer than the stoichiometric air-fuel ratio by a predetermined value α2 (see time t12). The predetermined value α1 and the predetermined value α2 may be different values or may be equal values. Hereinafter, a description will be given assuming that α1 and α2 are equal to each other and have the value α.
[0211]
The low side threshold value OSAreflow and the high side threshold value OSArefhigh are set such that the half amount (CmaxUF / 2) of the maximum oxygen storage amount CmaxUF of the second catalyst is equal to the total capacity Vall of the second catalyst and the capacity (block) up to the intermediate block. It is set so as to sandwich the quantity Cmid = (CmaxUF · Vpart) / (2 · Vall) proportionally distributed by Vpart. That is, OSAreflow <Cmid <OSArefhigh.
[0212]
(Actual operation)
Next, the actual operation of the exhaust gas purification apparatus will be described with reference to a flowchart showing a routine executed by the CPU 71. The CPU 71 of the present exhaust gas purification device executes the same routine as the CPU 71 of the exhaust gas purification device according to the first embodiment, except that the CPU 71 of the exhaust gas purification device according to the first embodiment executes the routine shown in the flowchart of FIG. 25 instead of FIG. Therefore, the following description focuses on the operation based on the routine shown in FIG. In FIG. 25, the same steps as those in FIG. 11 are denoted by the same reference numerals, and detailed description thereof will be omitted.
[0213]
The CPU 71 executes the routine shown in FIG. 25 every time a predetermined time elapses. Therefore, at a predetermined timing, the CPU 71 starts the process from step 2500 and proceeds to step 1105 to determine whether the air-fuel ratio feedback control condition is satisfied.
[0214]
Now, the description will be continued assuming that the air-fuel ratio feedback control condition is satisfied. If the oxygen storage amount OSAUF <i> up to the block i of the second catalyst 54 changes from a state smaller than the high-side threshold OSArefhigh to a larger state, The CPU 71 determines “Yes” in step 2510 to determine whether or not the oxygen storage amount OSAUF <i> is larger than the high-side threshold OSArefhigh, and determines whether the oxygen storage amount OSAUF <i> is higher than the high-side threshold OSArefhigh. In step 2515 of determining whether the amount OSAUF <i> is smaller than the high-side threshold value OSArefhigh, “Yes” is determined, and the process proceeds to step 1120. In step 1120, the air-fuel ratio feedback correction amount DFi has a positive value β. Is set, and then the routine proceeds to step 2595, where this routine is temporarily terminated. That. As a result, the air-fuel ratio of the air-fuel mixture supplied to the engine (therefore, the air-fuel ratio flowing into the first catalyst 53) becomes richer than the stoichiometric air-fuel ratio (theoretical air-fuel ratio-α = theoretical air-fuel ratio-α2). Exhaust gas with a rich air-fuel ratio flows into the second catalyst 54, and the oxygen storage amount OSAUF <i> decreases as shown from time t12 to t13 in FIG.
[0215]
On the other hand, when the current and previous oxygen storage amounts OSAUF <i> are larger than the high-side threshold OSArefhigh, the CPU 71 determines “Yes” in step 2510 and “No” in step 2515, and proceeds directly to step 2595. To end this routine once. As a result, the air-fuel ratio feedback correction amount DFi is maintained at a positive value β, and the air-fuel ratio of the air-fuel mixture supplied to the engine is also maintained at an air-fuel ratio richer than the stoichiometric air-fuel ratio (theoretical air-fuel ratio-α).
[0216]
On the other hand, when the oxygen storage amount OSAUF <i> up to the block i of the second catalyst 54 changes from a state larger than the low threshold OSAreflow to a smaller state when the air-fuel ratio feedback control condition is satisfied, the CPU 71 sets the oxygen In step 2525 of determining whether or not the storage amount OSAUF <i> is smaller than the low-side threshold OSArefflow, “Yes” is determined, and whether or not the previous oxygen storage amount OSAUF <i> is greater than the low-side threshold OSArefflow Is determined as "Yes" in step 2530, and the process proceeds to step 1135. In step 1135, the air-fuel ratio feedback correction amount DFi is set to a negative value -β, and then the process proceeds to step 2595 to execute this routine. Stop once. As a result, the air-fuel ratio of the air-fuel mixture supplied to the engine becomes leaner than the stoichiometric air-fuel ratio (theoretical air-fuel ratio + α = theoretical air-fuel ratio + α1), so that the exhaust gas having a lean air-fuel ratio also flows into the second catalyst 54. As a result, as shown at times t11 to t12 in FIG. 4, the oxygen storage amount OSAUF <i> increases.
[0217]
When the current and previous oxygen concentrations CgoutUF, O2 <i> are smaller than the low threshold OSAreflow, the CPU 71 determines “No” in step 2510, “Yes” in step 2525, and “No” in step 2530. The determination is made, and the process proceeds to step 2595 to end the present routine once. As a result, the air-fuel ratio feedback correction amount DFi is maintained at a negative value -β, and the air-fuel ratio of the air-fuel mixture supplied to the engine is also maintained at an air-fuel ratio leaner than the stoichiometric air-fuel ratio (stoichiometric air-fuel ratio + α).
[0218]
If the air-fuel ratio feedback control condition is not satisfied, the CPU 71 determines “No” in step 1105 and proceeds to step 1140, in which the CPU 71 sets the air-fuel ratio feedback correction amount DFi to “0”. Then, the routine proceeds to step 2595, where the present routine is temporarily ended.
[0219]
As described above, the exhaust gas purification apparatus according to the second embodiment includes the physical quantity indicating the state related to the exhaust gas purification of the second catalyst 54, “the portion of the second catalyst 54 composed of the blocks 1 to i of the second catalyst 54 ( The oxygen storage amount OSAUF <i> of the upstream portion) is estimated and obtained by calculation using the output of the first catalyst downstream air-fuel ratio sensor 66, and the oxygen storage amount OSAUF <i> is set to a predetermined value (low side threshold OSArefflow). The air-fuel ratio of the exhaust gas flowing into the second catalyst 54 is controlled by controlling the air-fuel ratio of the air-fuel mixture supplied to the engine so that the air-fuel ratio becomes a value between the air-fuel ratio and the high-side threshold OSArefhigh).
[0220]
Therefore, the present exhaust gas purification apparatus can acquire a state relating to exhaust gas purification of the second catalyst 54 at a time earlier than the output change of the O2 sensor provided downstream of the second catalyst 54, and based on the acquired state. Thus, the air-fuel ratio of the air-fuel mixture supplied to the engine 10 is controlled, so that the state of the second catalyst 54 can be maintained in a good state regardless of the control delay of the feedback control. As a result, the present exhaust gas purification apparatus can further reduce the emission of harmful components.
[0221]
Further, the present exhaust gas purification apparatus includes the second catalyst 54 from the most upstream block (block 1) to the intermediate block (block i) located upstream of the most downstream block (block m). The oxygen storage amount OSAUF <i> of the portion of the catalyst (upstream portion) is set to a half (CmaxUF / 2) of the maximum oxygen storage amount CmaxUF of the second catalyst to the total capacity Vall of the second catalyst and the intermediate block. The control is performed so as to be in a range (OSArefflow to OSArefhigh) sandwiching the amount Cmid = (CmaxUF · Vpart) / (2 · Vall) proportionally distributed by the capacity Vpart, so that the second catalyst 54 performs the purifying action by the oxygen storage function. It is highly likely that it will be maintained.
[0222]
Further, even when exhaust gas cannot be purified up to the intermediate block due to a delay in air-fuel ratio feedback control (that is, when the oxygen storage amount up to the intermediate block has reached “0” or the maximum oxygen storage amount), at least the same intermediate Since blocks (blocks i + 1 to m) located downstream of the blocks can be used as preliminary catalysts for purifying exhaust gas, there is a high possibility that the emission of harmful exhaust components can be reduced.
[0223]
Further, also in the present embodiment, by using the output of the first catalyst downstream air-fuel ratio sensor 66 disposed upstream of the second catalyst 54 and capable of directly detecting the air-fuel ratio of the exhaust gas flowing into the second catalyst 54, the calculation is performed. The oxygen storage amount OSAUF <i> of the second catalyst 54 is determined. Therefore, for example, it is more accurate to obtain the oxygen storage amount OSAUF <i> than when obtaining the oxygen storage amount OSAUF <i> based on the output of the air-fuel ratio sensor provided upstream of the first catalyst 53. it can.
[0224]
<Modification of Second Embodiment>
In the modification of the second embodiment, the oxygen storage amount OSAUF <m> of the entire second catalyst 54 becomes a predetermined value (OSArefflow to OSArefhigh) instead of the oxygen storage amount OSAUF <i> up to the intermediate block i. In addition, the air-fuel ratio of the air-fuel mixture supplied to the engine 10 is controlled. More specifically, the CPU 71 of the modification executes a routine in which the oxygen storage amount OSAUF <i> in steps 2510, 2515, 2525, and 2530 in FIG. 25 is replaced with the oxygen storage amount OSAUF <m>.
[0225]
As described above, in the modified example of the second embodiment, the entire oxygen storage amount OSAUF <m> of the second catalyst 54 is used for the feedback control of the air-fuel ratio. Since the oxygen storage amount OSAUF <m> is obtained by using the output of the first catalyst downstream air-fuel ratio sensor 66 for the calculation, it is quicker than the air-fuel ratio feedback control based on the air-fuel ratio sensor output downstream of the second catalyst 54. Control is possible, and the oxygen storage amount OSAUF <m> is more accurately compared to the case where the oxygen storage amount OSAUF <m> is obtained based on the output of the air-fuel ratio sensor provided upstream of the first catalyst 53. m> can be obtained.
[0226]
<Third embodiment>
Next, a third embodiment of the exhaust gas purifying apparatus according to the present invention will be described. This exhaust gas purifying apparatus assumes that the output of the first catalyst downstream air-fuel ratio sensor 66 continues the output at the current time for a predetermined time from the current time. The oxygen concentration CgoutUF, O2 <i> flowing out of the block i after the predetermined time is predicted and estimated, and supplied to the engine 10 so that the estimated value becomes a predetermined value (in this case, a value of Crefmns to Crefpls). Only in that the air-fuel ratio of the air-fuel mixture to be controlled is controlled, it is different from the exhaust gas purification apparatus of the first embodiment. Therefore, the following description focuses on such differences.
[0227]
The difference is that the CPU 71 of the exhaust gas control apparatus according to the third embodiment adds the routine shown by the flowchart in FIG. 26 to the routine executed by the CPU 71 of the exhaust gas control apparatus according to the first embodiment, and every time a predetermined time elapses. This is caused by executing
[0228]
More specifically, the CPU 71 starts the process from step 2600 at a predetermined timing, proceeds to step 2605, sets the value of the variable n to “0”, and sets the value of the variable n to “0” in step 2610. In step 2615, it is determined whether or not the value of the variable n is smaller than a predetermined value nmax that is larger than “1”. In this case, since the value of n is “1”, the CPU 71 determines “Yes” in step 2615 and proceeds to step 2620, where CgoutUF, X (k) <0> (CgoutUF, O2 (k) <0> , CgoutUF, CO (k) <0>, CgoutUF, HC (k) <0>) are determined based on the current output of the first catalyst downstream air-fuel ratio sensor 66, and the determined values are held. That is, each concentration CginUF, O2 (k) <1>, CginUF, CO (k) <1>, CginUF, HC (k) <1> flowing into the second catalyst 54 is supplied to the first catalyst downstream air-fuel ratio sensor 66. And the stored map described above, and the value is held.
[0229]
Then, the CPU 71 proceeds to step 2625, and executes steps 2000 to 2095 in step 2625 to execute CgoutUF, X (k) <j> (CgoutUF, O2 (k) <j>, CgoutUF, CO (k) <J>, CgoutUF, HC (k) <j>) (j = 1 to m) are obtained, and the process returns to step 2610 again. At this time, the values held above are used for CginUF, O2 (k) <1>, CginUF, CO (k) <1>, CginUF, HC (k) <1>. In this way, the CPU 71 assumes that the output of the first catalyst downstream air-fuel ratio sensor 66 is maintained at the current output (does not change) until the value of the variable n reaches the predetermined value nmax, and CgoutUF, X ( k) <j> is repeatedly calculated.
[0230]
When executing the routine shown in FIG. 11, the CPU 71 sets CgoutUF, O2 <i> in step 1110 and step 1125 when the value of the variable n in the routine shown in FIG. 26 is (nmax−1). The CgoutUF, O2 <m> obtained in step 1115 and step 1130 are used as the CgoutUF, O2 <i> obtained when the value of the variable n in the routine shown in FIG. 26 is (nmax-2). The obtained CgoutUF, O2 <m> is adopted.
[0231]
As described above, the calculation is performed on the assumption that the output of the first catalyst downstream air-fuel ratio sensor 66 is maintained at the current output (does not change) until the value of the variable n becomes nmax-1, that is, for a predetermined time from the current time. The air-fuel ratio control based on the oxygen concentration CgoutUF, O2 (k) <m> flowing out of the block m located at the most downstream side of the second catalyst 54 is performed.
[0232]
According to the third embodiment, the state of the second catalyst 54 that is earlier (future) in time is predicted, and the air-fuel mixture supplied to the engine based on the predicted value CgoutUF, O2 (k) <m>. The air-fuel ratio is feedback-controlled, so that the exhaust gas can be more effectively purified regardless of the unavoidable control delay inherent in the feedback control.
[0233]
<Fourth embodiment>
Next, a fourth embodiment of the exhaust gas purifying apparatus according to the present invention will be described. This exhaust gas purifying apparatus assumes that the output of the first catalyst downstream air-fuel ratio sensor 66 continues the output at the current time for a predetermined time from the current time. The oxygen storage amount OSAUF <m> of the entire second catalyst 54 after the predetermined time is predicted and estimated, and the oxygen storage amount is supplied to the engine 10 so that the estimated value becomes a predetermined value (in this case, a value of OSAreflow to OSArefhigh). Only in the point that the air-fuel ratio of the air-fuel mixture to be controlled is controlled, it is different from the exhaust gas purification apparatus of the second embodiment. Therefore, the following description focuses on such differences.
[0234]
The difference is that the CPU 71 of the exhaust gas purification apparatus of the fourth embodiment additionally executes the routine shown by the flowchart in FIG. 26 in addition to the routines executed by the CPU 71 of the exhaust gas purification apparatus of the second embodiment. Caused by That is, by executing the routine of FIG. 26, the CPU 71 assumes that the output of the first catalyst downstream air-fuel ratio sensor 66 is maintained at the current output (does not change) for a predetermined time from the current time. Is obtained as the total oxygen storage amount OSAUF <m>.
[0235]
When executing the routine shown in FIG. 25, the CPU 71 determines the OSAUF <i> in steps 2510 and 2525 when the value of the variable n in the routine shown in FIG. 26 is (nmax−1). The OSAUF <m> obtained when the value of the variable n in the routine shown in FIG. 26 is (nmax−2) as the OSAUF <i> in steps 2515 and 2530 by using the obtained OSAUF <m>. Is adopted.
[0236]
As described above, the calculation is performed on the assumption that the output of the first catalyst downstream air-fuel ratio sensor 66 is maintained at the current output (does not change) until the value of the variable n becomes nmax-1, that is, for a predetermined time from the current time. The air-fuel ratio control based on the oxygen storage amount OSAUF <m> of the entire second catalyst 54 is performed.
[0237]
According to the fourth embodiment, the oxygen storage amount, which is the state of the second catalyst 54 that is earlier (future) in time, is predicted, and the air-fuel mixture supplied to the engine based on the predicted value OSAUF <m>. The air-fuel ratio is feedback-controlled, so that the exhaust gas can be more effectively purified regardless of the unavoidable control delay inherent in the feedback control.
[0238]
As described above, according to each embodiment of the present invention, the physical quantity related to the exhaust purification of the second catalyst 54 (the physical quantity of the second catalyst 54) is determined by the output of the first catalyst downstream air-fuel ratio sensor 66 and the catalyst model. The oxygen concentration flowing out of the predetermined block, the oxygen storage amount of the entire second catalyst 54 or the oxygen storage amount of the upstream portion of the second catalyst 54, etc. are estimated without time delay, and the physical amount becomes the desired amount. Since the air-fuel ratio of the exhaust gas flowing into the second catalyst 54 is controlled, it is possible to maintain the second catalyst 54 in a state where the exhaust gas can be satisfactorily purified. As a result, each exhaust gas purification device can more effectively reduce the emission amount of harmful components. Further, the model error of the catalyst model for the first catalyst 53 is reduced based on the output of the first catalyst downstream air-fuel ratio sensor 66, and the result is reflected in the correction of the catalyst model of the second catalyst 54. . Therefore, the physical quantity related to the exhaust gas purification of the second catalyst 54 can be further accurately estimated.
[0239]
Note that the present invention is not limited to the above embodiment, and various modifications can be adopted within the scope of the present invention. For example, the amplitudes (represented by α1, α2, α) from the stoichiometric air-fuel ratio in the air-fuel ratio control are, as shown in FIG. 27, the temperature TempUF of the second catalyst 54, the intake air amount Ga, and the It may be variable according to at least one of the deterioration index value REKKAUF of the two-catalyst 54 and the like. According to this, it is possible to appropriately eliminate the primary poisoning of the second catalyst 54 due to oxygen, and to maintain the state of the second catalyst 54 more favorably. Further, the first catalyst downstream air-fuel ratio sensor 66 may be replaced with an exhaust gas characteristic detection sensor capable of detecting at least one (preferably, all) of the CO concentration, the HC concentration, and the NOx concentration.
[0240]
Further, in the first and third embodiments, the oxygen concentration CgoutUF, O2 <i> is used as an index value for air-fuel ratio control, but the carbon monoxide concentration CgoutUF, CO <i>, which is another specific component. , Hydrocarbon concentration CgoutUF, HC <i>, etc. may be used as control index values.
[Brief description of the drawings]
FIG. 1 is a schematic diagram of an internal combustion engine equipped with an exhaust gas purification device according to a first embodiment of the present invention.
FIG. 2 is a graph showing a relationship between an output of a first catalyst downstream air-fuel ratio sensor shown in FIG. 1 and an air-fuel ratio.
FIG. 3 is a graph showing a relationship between an output of a second catalyst downstream air-fuel ratio sensor shown in FIG. 1 and an air-fuel ratio.
FIG. 4 is a time chart for explaining air-fuel ratio control by the exhaust gas purification device shown in FIG. 1;
FIG. 5 is a schematic diagram of a catalyst for explaining a catalyst model.
FIG. 6 is an external view of the catalyst shown in FIG.
FIG. 7 is a partial sectional view of the catalyst shown in FIG. 6;
FIG. 8 is a schematic diagram for explaining a catalyst model.
FIG. 9 is a schematic diagram for explaining an upwind method used in a catalyst model.
FIG. 10 is a flowchart showing a routine for calculating a fuel injection amount executed by a CPU shown in FIG. 1;
FIG. 11 is a flowchart showing a routine for calculating an air-fuel ratio feedback correction amount executed by the CPU shown in FIG. 1;
FIG. 12 is a flowchart showing a routine executed by a CPU shown in FIG. 1 to calculate a specific gas component concentration in a catalyst and to correct a catalyst model.
FIG. 13 is a flowchart showing a routine for obtaining an oxygen concentration in a first catalyst according to a catalyst model.
FIG. 14 is a flowchart showing a routine for obtaining the concentration of carbon monoxide inside the first catalyst according to a catalyst model.
FIG. 15 is a flowchart showing a routine for obtaining a hydrocarbon concentration in a first catalyst according to a catalyst model.
FIG. 16 is a flowchart showing a routine for obtaining an oxygen storage density and an oxygen storage amount of a first catalyst according to a catalyst model.
FIG. 17 is a map for obtaining respective coefficients (multipliers) used in a catalyst model from a catalyst deterioration degree and a catalyst temperature.
FIG. 18 is a map that defines the relationship between the air-fuel ratio of exhaust gas used to determine the concentration of carbon monoxide flowing into the catalyst and the same carbon oxide concentration.
FIG. 19 is a map that defines the relationship between the air-fuel ratio of exhaust gas used to determine the concentration of hydrocarbons flowing into the catalyst and the concentration of the hydrocarbons.
FIG. 20 is a flowchart showing a routine for obtaining the oxygen concentration inside the second catalyst according to the catalyst model.
FIG. 21 is a flowchart showing a routine for obtaining the concentration of carbon monoxide inside the second catalyst according to the catalyst model.
FIG. 22 is a flowchart showing a routine for obtaining a hydrocarbon concentration in a second catalyst according to a catalyst model.
FIG. 23 is a flowchart showing a routine for obtaining an oxygen storage density and an oxygen storage amount of a second catalyst according to a catalyst model.
FIG. 24 is a time chart for explaining air-fuel ratio control by an exhaust gas purification device according to a second embodiment of the present invention.
FIG. 25 is a flowchart illustrating a routine for calculating an air-fuel ratio feedback correction amount executed by a CPU of the exhaust gas purification apparatus according to the second embodiment.
FIG. 26 is a flowchart illustrating a routine executed by the CPU of the exhaust gas purification apparatus according to the third embodiment to calculate a predicted value (future value) of the oxygen concentration.
FIG. 27 is a graph showing the control width of the air-fuel ratio in the air-fuel ratio control of each embodiment.
[Explanation of symbols]
Reference Signs List 10: internal combustion engine, 53: first catalyst, 54: second catalyst, 66: first catalyst downstream air-fuel ratio sensor (first catalyst downstream exhaust gas characteristic detection sensor), 70: electric control device, 71: CPU.

Claims (5)

A first catalyst disposed in an exhaust passage of the internal combustion engine;
A first catalyst downstream exhaust gas characteristic detection sensor that is disposed in the exhaust passage downstream of the first catalyst and outputs a value corresponding to characteristics of exhaust gas in the exhaust passage at the disposition portion;
A second catalyst disposed in the exhaust passage downstream of the first catalyst downstream exhaust gas characteristic detection sensor;
An exhaust gas purification apparatus for an internal combustion engine, comprising:
Exhaust gas purification-related physical quantity estimating means for estimating a physical quantity related to exhaust gas purification inside the second catalyst by at least calculation using an output of the first catalyst downstream exhaust gas characteristic detection sensor;
Air-fuel ratio control means for controlling an air-fuel ratio of exhaust gas flowing into the second catalyst so that a physical quantity related to the estimated exhaust gas purification becomes a predetermined value;
An exhaust gas purification device for an internal combustion engine, comprising: The exhaust gas purification device for an internal combustion engine according to claim 1,
The exhaust gas purification related physical quantity estimating means estimates at least one of a value related to an amount of a specific component in the exhaust gas passing through the second catalyst and a value related to the oxygen storage amount of the second catalyst as a physical quantity related to the exhaust gas purification. An exhaust gas purification device for an internal combustion engine configured to perform the following. The exhaust gas purification device for an internal combustion engine according to claim 1,
The exhaust gas purification-related physical quantity estimating means flows out of an intermediate block located upstream of a block located at the most downstream position when the second catalyst is virtually divided into a plurality of blocks along the flow direction of the exhaust gas. An exhaust gas purification device for an internal combustion engine configured to estimate a value relating to an amount of a specific component in the exhaust gas as a physical quantity related to the exhaust gas purification. The exhaust gas purification device for an internal combustion engine according to claim 1,
The exhaust gas purification related physical quantity estimating means includes a single or plural blocks located upstream from a block located at the most downstream position when the second catalyst is virtually divided into plural blocks along the flow direction of the exhaust gas. An exhaust gas purification device for an internal combustion engine configured to estimate an oxygen storage amount of the second catalyst portion as a physical quantity related to the exhaust gas purification. The exhaust gas purification device for an internal combustion engine according to any one of claims 1 to 4,
The exhaust gas purification related physical quantity estimating means is configured to assume that the output of the first catalyst downstream exhaust gas characteristic detection sensor continues the output at the same time from the present time for a predetermined time, and the physical quantity related to the exhaust gas purification after a predetermined time from the current time. An exhaust gas purifying apparatus for an internal combustion engine configured to estimate the exhaust gas.

Images