JP3961275B2 - Air-fuel ratio control device for internal combustion engine - Google Patents

Description

【００３７】
但し、ｅ(ｔ)は、Ｓ／Ｍ制御部２２１への入力（目標空燃比―実空燃比）、Ｋ_Pは線形項線形ゲイン、Ｋ_Dは線形項微分ゲイン、Ｓ_Pは切換関数線形ゲイン、Ｓ_Dは切換関数微分ゲイン、Ｋ_Iは適応則ゲイン、Ｋ_Nは非線形ゲイン、σ(ｔ)は切換関数で、σ(ｔ) = Ｓ_pｅ(ｔ)＋Ｓ_Dｅ(ｔ)である。
なお、上記各制御ゲインは、後述する制御ゲイン算出部２２４で算出される。
【００３８】
但し、前記オープンループ制御時や燃料カット時は、Ｓ／Ｍ制御部２２１によるフィードバック制御量の算出を禁止するものとし、オープンループ制御時であることや燃料カット時であることは、例えば、燃料噴射弁５の駆動信号やフラグ（燃料カットフラグ）を確認することで行う。
このようにフィードバック制御量の算出を禁止するのは、フィードバック制御を行わない（すなわち、Ｓ／Ｍ制御部２２１で算出したフィードバック制御量を燃料噴射弁５に出力しない）オープンループ制御時や燃料カット時においても、前記フィードバック制御量の算出を継続すると、スライディングモード制御における積分項（エラー量＝目標空燃比−実空燃比に基づき算出される）が増大し、その後、フィードバック制御を再開したときに、適正な燃料噴射制御ができなくなるからである。
【００３９】
そして、オープンループ制御や燃料カットが終了した後は、フィードバック制御（すなわち、前記Ｓ／Ｍ制御部２２１よるフィードバック制御量の算出）が再開されることになるが、本実施形態においては、再開時のスライディングモード制御の積分項に、運転状態に応じてあらかじめ設定された初期値を設定するようにしている。
【００４０】
このように、前記フィードバック制御の再開時に、スライディングモード制御における積分項を、運転状態に応じた初期値によってリセットすることで、フィードバック制御再開後、直ちに適正なフィードバック制御量を燃料噴射弁５に出力できる。
また、フィードバック制御再開後における応答遅れを考慮して、前記初期値を、フィードバック制御再開後の所定期間のあいだ保持するようにしてもよい。
【００４１】
これにより、前記応答遅れの間においても、前記積分項の算出が行われないので、より適正なフィードバック制御量を燃料噴射弁５に出力できる。
なお、オープンループ制御を行うことが、前記フィードバック制御量の算出を行わないこと（すなわち、禁止すること）を意味するものと考えることもできるが、この場合においても、フィードバック制御再開時において、スライディングモード制御の積分項に、運転状態に応じてあらかじめ設定された初期値を設定し、これを所定期間のあいだ保持することで、フィードバック制御再開後の適正な燃料噴射制御を確保できる。
【００４２】
前記むだ時間補償器２２２は、スミス法によるむだ時間補償制御を実行するのものであり、局所フィードバックを行うことにより、プラントに含まれるむだ時間（すなわち、検出した空燃比の位相遅れ）の影響を補償する。
具体的には、図３に示すように、前記むだ時間補償器２２２は、むだ時間を含まないプラントモデル３１と、むだ時間を含むプラントモデル３２と、減算部３３と、を含んで構成されており、前記むだ時間要素を含まないプラントモデル３１で算出される出力（空燃比）予測と、前記むだ時間を含むプラントモデル３２で算出される実出力（実空燃比）予測との偏差ｅ２を算出し、これを前記Ｓ／Ｍ制御部２１の入力側に出力する。
【００４３】
そして、目標空燃比λｔと実空燃比λｒの偏差ｅ１から、前記むだ時間補償器２２の出力ｅ２を減算してｅ３を算出し、該ｅ３を前記Ｓ／Ｍ制御部２２１に入力するようにしている。
なお、前記プラントモデルは、後述するプラントモデル同定部２２３で同定したものであり、前記むだ時間は、後述するむだ時間算出部２２５で算出したものである。
【００４４】
前記プラントモデル同定部２２３は、前記プラントを伝達関数で表したプラントモデルを、燃料噴射量（燃料噴射信号）及び実空燃比（出力）に基づきオンラインで同定する。具体的には、逐次最小二乗法（ＲＬＳ法）を用いてプラントモデルのパラメータの逐次推定を行う。
前記制御ゲイン算出部２２４は、前記Ｓ／Ｍ制御部２２１の制御ゲインを、前記プラントモデル同定部２２３で同定したプラントモデルのパラメータ（推定パラメータ）を用いて算出する。
【００４５】
具体的には、極配置法によるセルフチューニングコントロールを用いて、システム全体（すなわち、プラント（燃料噴射弁５〜空燃比センサ１３間）＋Ｓ／Ｍ制御部２２１＋むだ時間補償器２２２）を閉ループ伝達関数で表し、その極が応答性、行き過ぎ量、整定時間等の点から望ましい極と一致するようＳ／Ｍ制御部２２１の制御ゲインを算出する（詳細は後述する）。
【００４６】
前記むだ時間算出部２２５は、プラントに含まれるむだ時間kを算出する。かかるむだ時間kの算出は、例えば、図４に示すように、吸入空気量Ｑａとむだ時間kと関係をあらかじめテーブル化しておき、検出した吸入空気量Ｑａに基づくテーブル検索により行う。
ここで、前記制御ゲイン算出部２２４で行われる制御ゲインの算出について詳細に説明する。
【００４７】
極配置法によるセルフチューニングコントロールを用いた制御ゲイン算出は、以下のようにして行う。
まず、プラントを伝達関数で表すプラントモデルＧ_P（ｚ^-1）を設定し、その後、Ｓ／Ｍ制御部２２１の伝達関数Ｇ_C（ｚ^-1）及びむだ時間補償器２２の伝達関数Ｇ_L（ｚ^-1）を求める。
【００４８】
そして、これらの伝達関数からシステム全体の閉ループ伝達関数Ｗ（ｚ^-1）を算出し、その極が設定した極となるように制御ゲインを算出する。
（Ａ）プラントモデルの設定について
燃料噴射弁５と空燃比センサ１３との間のプラントを、前記むだ時間算出部２２５で算出したむだ時間ｋ（≧１）を用いて、例えば、次式（２）、（３）のように二次のＡＲＸモデルＡ(ｚ^-1)で表す。
【００４９】
Ａ(ｚ^-1)ｙ(ｔ)＝ｚ^-kｂ₀ｕ(ｔ)＋ε(ｔ) …（２）
Ａ(ｚ^-1)＝１＋ａ₁ｚ^-1＋ａ₂ｚ^-2 …（３）
但し、ｙ(ｔ)は、プラント出力（すなわち、実空燃比）、ｕ(ｔ)は、プラント入力値（すなわち、燃料噴射量）、ε(ｔ)は、不規則雑音である。
すると、プラントモデルの伝達関数Ｇ_P(ｚ^-1)は、次式（４）のように表すことができる。
【００５０】
Ｇ_P(ｚ^-1)＝ｚ^-kｂ₀／Ａ(ｚ^-1) …（４）
なお、推定パラメータベクトルθ(ｔ)及びデータベクトルψ(ｔ-ｋ)は、下記（５）、（６）式のように表すことができる。
θ(ｔ)＝〔ａ₁(ｔ)，ａ₂(ｔ)，ｂ₀(ｔ)〕^T … （５）
ψ(ｔ-ｋ)＝〔-ｙ(ｔ-１)，-ｙ(ｔ-２)、ｕ(ｔ-ｋ)〕^T … （６）
（Ｂ）プラントモデルの同定（パラメータ推定）について
設定したプラントモデルは、前記プラントモデル同定部２２３で同定される。
【００５１】
具体的には、プラントの特性は、運転状態、プラント自体の劣化度合い等のプラント特性により変化するので、式（５）に示すパラメータａ₁(ｔ)、ａ₂(ｔ)、ｂ₀(ｔ)を逐次推定することでプラントモデルを同定する（すなわち、オンライン同定する）。
なお、本実施形態においては、前記パラメータの推定に最小二乗法（ＲＬＳ法）を用いており、実値と推定値の誤差の二乗が最も小さくなるパラメータを逐次算出している。
【００５２】
具体的な演算式は、一般の重みつき逐次最小二乗法（ＲＬＳ法）と同一のものであり、時間更新式：ｔ＝１、２、…、Ｎに対して、次式（７）〜（９）を計算することにより行う。
【００５３】
【数２】

【００５４】
そして、かかるパラメータ推定式（７）〜（９）を用いてパラメータａ₁(ｔ)、ａ₂(ｔ)、ｂ₀(ｔ)を逐次推定することで、プラントモデルを同定する。
なお、前記忘却係数λ₁、λ₂は、忘却要素なしの場合には前記忘却係数λ₁＝λ₂＝１とし、忘却要素つきの場合にはλ₁＝０.９８、λ₂＝１とした。
また、本実施形態においては、前記パラメータ推定値の初期値θ０を、運転状態の応じてあらかじめ設定した初期値（例えば、ａ₁(０)＝Ａ１、ａ₂(０)＝Ａ２、ｂ₀(０)＝Ｂ１）を設定することで、収束までの時間の短縮化を図っている。
【００５５】
但し、前記オープンループ制御時及び燃料カット時は、前記Ｓ／Ｍ制御部２２１によるフィードバック制御量の算出を禁止するのと同様に、プラントモデルの同定（パラメータ推定）を禁止するようにする。
すなわち、フィードバック制御時においては、前記Ｓ／Ｍ制御部２２１で算出したフィードバック制御量によって燃料噴射制御を行っていたが、オープンループ制御時や燃料カット時は、前記Ｓ／Ｍ制御部２２１で算出したフィードバック制御量とは異なる値が燃料噴射弁５に出力されることになるため、フィードバック制御時とは全く異なるプラントの状態予測（プラントモデルの同定）が行われることになる。これでは、フィードバック制御量を算出するためにプラントの状態予測を行う意味がなく、従って、正しい同定結果が得られない（プラントモデルの同定精度が悪化する）。
【００５６】
かかる同定精度（パラメータ推定精度）の悪化を防止するため、フィードバック制御時以外は、プラントモデルの同定を禁止するのである。
この場合、前記制御ゲイン算出部２２４による制御ゲインの算出も正しく算出されないので、制御ゲインの算出についても禁止するよう構成にしてもよい。
なお、フィードバック制御が再開されたときは、前記プラントモデルの同定も再開されることになるが（制御ゲインの算出を禁止した場合は、制御ゲインの算出も再開される）、同定再開時においては、前記プラントモデルのパラメータとして、前記運転状態に応じてあらかじめ設定した初期値θ０（Ａ１、Ａ２、Ｂ１）を用いるようにする。
【００５７】
このように、同定禁止の直前で用いたパラメータ値を、前記初期値θ０（Ａ１、Ａ２、Ｂ１）でリセットすることで、同定禁止前後のプラント特性の変化を考慮することなく、再開後の同定精度を高く維持できると共に、収束時間の短縮も図れる。
更に、同定再開後の所定期間のあいだ、設定した初期値（パラメータＡ１、Ａ２、Ｂ１）を保持するようにする。
【００５８】
これは、応答遅れにより再開直後のみだけでなく、再開直後の所定期間のあいだは、Ｓ／Ｍ制御部２２１で算出したフィードバック制御量に対応した空燃比を検出できないため、フィードバック制御時以外の場合と同様に、正しい同定結果が得られないからである。
（Ｃ）Ｓ／Ｍ制御部２２１の離散時間伝達関数の算出について
Ｓ／Ｍ制御部２２１を、以下のようにして伝達関数化する。
【００５９】
ｙ(ｔ)をプラント出力値（実空燃比λｒ）、ω(ｔ)を目標値（目標空燃比λｔ）とし、ｅ(ｔ)＝ω(ｔ)−ｙ(ｔ)とすると、１サンプルにおけるプラント入力（すなわち、Ｓ／Ｍ制御部２２１からの出力）ｕ(ｔ)の差分Δｕ(ｔ)は、次式（１０）で与えられる。
【００６０】
【数３】

【００６１】
ここで、ｅ(ｔ)＝ω(ｔ)−ｙ(ｔ)、ｅ(ｔ)−ｅ(ｔ−１)＝Δｅ(ｔ)であるから、式（１０）より次式（１１）が得られる。
【００６２】
【数４】

【００６３】
但し、Ｋ(ｚ^-1)は次式（１２）で表されるものであり、式（１３）のように展開して各制御ゲインに基づいて算出する。
【００６４】
【数５】

【００６５】
従って、式（１２）よりプラント入力ｕ(ｔ)は、次式（１４）で表される。
【００６６】
【数６】

【００６７】
ここで、非線形項を含めないものとして取り扱うことにすると、Ｓ／Ｍ制御部２２１の離散時間伝達関数Ｇ_C(z^-1)は、次式（１５）のように表すことができる。
Ｇ_C(z^-1) = Ｋ(z^-1)／(1-z^-1) …（１５）
（Ｄ）前記むだ時間補償器２２２の離散時間伝達関数の算出について
上述したように、むだ時間補償器２２２は、むだ時間後の出力予測を行いつつむだ時間要素の影響を補償するスミス法を用いるので、むだ時間補償器２２２の離散時間伝達関数Ｇ_L(ｚ^-1)は、次式（１６）のように算出できる。
【００６８】

なお、ｚ^-1ｂ₀／Ａ(ｚ^-1)は、前記プラントモデルを用いて表したむだ時間がない場合の出力予測であり、ｚ^-kｂ₀／Ａ(ｚ^-1)は、同じく前記プラントモデルを用いて表したむだ時間を含む実出力予測である。
【００６９】
以上のようにして算出した各伝達関数（プラントモデル、Ｓ／Ｍ制御部２１、むだ時間補償器）を用いたブロック図を図５に示す。
次に、システム全体の閉ループ伝達関数化について説明する。
なお、上述したようにＳ／Ｍ制御部２２１の非線形項は含めないものとする。
（Ｅ）システム全体の閉ループ伝達関数Ｗ(ｚ^-1)の算出について
まず、前記Ｓ／Ｍ制御部２２１とむだ時間補償器２２２のフィードバックループを取り出し、目標（目標空燃比λｔ）から出力（フィードバック制御量）への１つの伝達関数を算出する。図５において、Ｓ／Ｍ制御部２２１とむだ時間補償器２２とを含む局所ループの伝達関数Ｇ_CL(ｚ^-1)は、式（１５）、（１６）より次式（１７）のように算出できる。
【００７０】
【数７】

【００７１】
従って、プラント及び式（１７）に示す局所ループを含めたシステム全体の閉ループ伝達関数Ｗ(ｚ^-1)は、次式（１８）のように算出できる。
【００７２】
【数８】

【００７３】
以上の算出結果を示したものが図６のブロック図である。
（Ｆ）極配置法による前記Ｓ／Ｍ制御部２２１の制御ゲインの算出について
前記閉ループ伝達関数Ｗ(ｚ^-1)の特性多項式は、式（１８）より、
(１−ｚ^-1)Ａ(ｚ^-1) +ｚ^-1ｂ₀Ｋ(ｚ^-1)であり、
これを次式（１９）のようにおく。
【００７４】
【数９】

【００７５】
このとき、応答性、行き過ぎ量、整定時間等の点から望ましい極となるようなＴ(ｚ^-1)を設定することで、Ｓ／Ｍ制御部２２１の制御ゲインを以下のようにして算出する。
式（１９）より、次式（２０）が得られる。
【００７６】
【数１０】

【００７７】
ここで、式（１３）より、
Ｋ(ｚ^-1)= (Ｋ_P＋Ｋ_I・Ｓ_P＋Ｋ_I・Ｓ_D＋Ｋ_D)−(Ｋ_P＋Ｋ_I・Ｓ_D＋２Ｋ_D)ｚ^-1＋Ｋ_Dｚ^-2であるので、切換関数線形ゲインＳ_P及び切換関数微分ゲインＳ_Dを１に設定し、線形項線形ゲインＫ_P、適応則ゲインＫ_I、線形項微分ゲインＫ_Dを可変パラメータとすれば、次式（２１）によう表すことができるから、
【００７８】
【数１１】

【００７９】
となり、次式（２２）〜（２４）を得る。
【００８０】
【数１２】

【００８１】
従って、式（２２）〜（２４）をＫ_P、Ｋ_I、Ｋ_Dについて解き、ａ₁、ａ₂、ｂ₀を、それぞれプラントモデル同定部２２３で逐次推定した推定パラメータａ₁(t)、ａ₂(t)、ｂ₀(t)で表すことにより、各ゲインは次式（２５）〜（２７）のように算出できる。
【００８２】
【数１３】

【００８３】
なお、前記特性多項式Ｔ(ｚ^-1)＝１＋ｔ₁ｚ^-1＋ｔ₂ｚ^-2としては、例えば、減衰ζ＝０.７、固有角周波数ω＝３０としたときの二次系の連続時間システム、
Ｇ(ｓ)＝ω² ／ (ｓ²＋２ζω・ｓ＋ω²)
をサンプル時間Ｔ_iで離散化したときの伝達関数の分母を用いることが考えられる。
【００８４】
そして、このように算出した制御ゲインを用いて、前記Ｓ／Ｍ制御部２２１は、プラントへの制御量を算出する（式（１３）参照）。
以上のように、パラメータを逐次推定したプラントモデルを用いてシステム全体を１つの伝達関数で表し、その極が応答性、行き過ぎ量、整定時間等の点から望ましい極と一致するように、プラントへのフィードバック制御量を算出するＳ／Ｍ制御部２２１の制御ゲインを求めるので、プラントの特性変化に対応した良好な制御ゲインが算出でき、ひいては、精度のよい空燃比フィードバック制御が実行できる。
【００８５】
また、上述したように、オープンループ制御時及び燃料カット時においては、前記Ｓ／Ｍ制御部２２１によるフィードバック制御量の算出を禁止すると共に、前記プラントモデル同定部２２３によるパラメータの推定を禁止するので、誤った結果の算出をあらかじめ防止し、フィードバック制御再開時においても適正な燃料噴射制御を実行でき、空燃比を精度よく制御できる。
【００８６】
なお、以上は、スライディングモード制御によりフィードバック制御量を算出するものについて説明したが、これに限定されるものではない。
【図面の簡単な説明】
【図１】本発明の一実施形態を示す内燃機関のシステム図。
【図２】本発明の空燃比制御を示すブロック図。
【図３】本発明で用いるむだ時間補償制御を示すブロック図。
【図４】本発明で用いるむだ時間算出用のテーブルを示す図。
【図５】本発明におけるＳ／Ｍ制御部２２１及びむだ時間補償器２２２を伝達関数で表したブロック図。
【図６】本発明におけるセルフチューニングコントロールを用いたスライディングモード制御による空燃比フィードバック制御全体を示すブロック図。
【符号の説明】
１ エンジン
２ 吸気通路
３ エアフローメータ
４ スロットル弁
５ 燃料噴射弁
６ コントロールユニット（Ｃ／Ｕ）
８ 点火プラグ
１１ 排気通路
１３ Ａ／Ｆセンサ
１４ クランク角センサ
１５ 水温センサ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an air-fuel ratio control apparatus for an internal combustion engine, and more particularly to an air-fuel ratio control apparatus for an internal combustion engine that performs air-fuel ratio feedback control while calculating a control gain by self-tuning.
[0002]
[Prior art]
Conventionally, in an internal combustion engine, feedback control of an air-fuel ratio to a target value is generally performed for the purpose of purifying exhaust gas or improving fuel consumption.
As a technique for performing such air-fuel ratio feedback control with high accuracy, the applicant of the present application disclosed in the previous application (Japanese Patent Application No. 2001-79272) an air-fuel ratio control of an internal combustion engine that calculates a feedback control amount of the fuel injection amount by sliding mode control. In the apparatus, a configuration is proposed in which the control gain of the sliding mode control is calculated by the self-tuning control while performing the dead time compensation control by the Smith method.
[0003]
In such an air-fuel ratio control apparatus, the feedback control amount is calculated as follows.
A plant model in which a plant between the fuel injection unit and the air-fuel ratio detection unit is represented by a transfer function is sequentially identified based on the fuel injection amount and the actual air-fuel ratio.
By using the identified plant model (parameters thereof), the entire system including the plant, the feedback control amount calculation unit (that is, the sliding mode control unit) and the dead time compensation control unit is represented by one transfer function, and its pole is The control gain of the sliding mode control is calculated so as to coincide with a desirable pole in terms of responsiveness, overshoot amount, settling time, and the like.
[0004]
Then, by calculating the feedback control amount of the fuel injection amount by the sliding mode control using the calculated control gain, the air-fuel ratio control corresponding to the plant characteristic change with high accuracy is executed.
[0005]
[Problems to be solved by the invention]
However, the above conventional ones have room for improvement in the following points.
That is, depending on the operation state, there is a case where the open loop control is performed without performing the feedback control as described above or the fuel cut is performed and the feedback control amount calculated by the sliding mode control unit is not output to the fuel injection unit. is there.
[0006]
Even in this case, the air-fuel ratio (that is, the plant output) is detected, and the integral term of the sliding mode control is calculated based on the deviation (error amount) between the target air-fuel ratio and the actual air-fuel ratio. When the fuel injection control with the calculated feedback control amount is resumed after the control or fuel cut is completed, the integral term increases, and the correct feedback control amount is not output to the fuel injection means, and the air-fuel ratio control Accuracy will deteriorate and exhaust emissions will deteriorate.
[0007]
Such a problem is not limited to the calculation of the feedback control amount by the sliding mode control.
The present invention has been made in view of the above problems, and provides an air-fuel ratio control device for an internal combustion engine that can accurately execute air-fuel ratio feedback control by appropriately calculating a feedback control amount of a fuel injection amount. With the goal.
[0008]
[Means for Solving the Problems]
Therefore, the invention according to claim 1
An air-fuel ratio control apparatus for an internal combustion engine comprising air-fuel ratio detection means for detecting an air-fuel ratio, and performing feedback control so that the actual air-fuel ratio becomes a target air-fuel ratio set according to an operating state,
By identifying the plant model, the optimal control gain for calculating the feedback control amount of the fuel injection amount is calculated by using the parameters of the identified plant model while dealing with the characteristic variation of the plant.
[0009]
Then, the feedback control amount is calculated using the calculated control gain, and accurate air-fuel ratio control is performed by fuel injection control based on the feedback control amount. On the other hand, a predetermined operation region (when fuel is cut or open loop control is performed) In other words, the calculation of the feedback control amount is prohibited.
[0011]
Here, when the calculation of the feedback control amount is prohibited and the calculation of the feedback control amount is resumed , the control amount calculation means sets an initial value set in advance according to the operation state as an integral term . . Therefore, when the calculation is resumed after the calculation of the feedback control amount is prohibited, the integral term calculated immediately before the prohibition is not used as it is or is simply cleared (set to 0), but a predetermined initial value. Will be set.
[0012]
The control amount calculation means, after resuming the calculation of the feedback control amount, holds the initial value during, and setting a predetermined time period.
[0013]
The invention according to claim 2 is characterized in that the prohibiting means further includes an identification prohibiting means for prohibiting parameter estimation of the plant model by the identifying means.
[0014]
Here, the identification means after being banned parameters estimated by the identification inhibiting means, when resuming the parameter estimation, sets the preset initial values according to the operating state parameters of the plant model.
As a result, when the calculation of the feedback control amount is resumed, each parameter calculated immediately before the prohibition is not used as it is or is simply cleared (set to 0), but a predetermined initial value is set. Become.
[0015]
Further, the identification means, after resuming the parameter estimation, to hold the initial value during, and setting a predetermined time period.
Thus, uncorrelated, i.e., to avoid identification of plant model in output is optionally such have state that corresponds to the input by a response delay.
[0016]
The invention according to claim 3 is characterized in that the control amount calculation means includes a dead time compensation means for eliminating the influence of the dead time included in the plant using the plant model. Such dead time compensation means includes a Smith method in which local feedback is performed using a plant model.
The invention according to claim 4 is characterized in that the control amount calculation means calculates the feedback control amount by sliding mode control. That is, an air-fuel ratio feedback correction coefficient for converging the exhaust air-fuel ratio to the target air-fuel ratio is obtained by sliding mode control, and a fuel injection amount (that is, a feedback control amount of the fuel injection amount) is obtained using the air-fuel ratio feedback correction coefficient. Will be calculated.
The invention according to claim 5 is characterized in that the identification means estimates the parameters of the plant model using a sequential least square method.
According to a sixth aspect of the present invention, the control gain calculating means represents the entire system including the plant and the controlled variable calculating means by a transfer function, and the controlled variable has a characteristic in which the transfer function of the entire system is set. The control gain of the calculating means is calculated.
[0017]
That is, air-fuel ratio feedback control is performed by control using self-tuning control.
The invention according to claim 7 is characterized in that the predetermined operation state is a fuel cut time or an open loop control time.
[0018]
【The invention's effect】
According to the first aspect of the present invention, at the time of air-fuel ratio feedback control, the air-fuel ratio control is accurately performed using the feedback control amount calculated by the control amount calculation means, and a predetermined operating state (when the fuel is cut or In open loop control, etc. , the calculation of the feedback control amount is prohibited to eliminate the influence of the integral term calculated based on the error amount (target air-fuel ratio-actual air-fuel ratio), and the feedback control is resumed. In this case, it is possible to prevent an erroneous feedback control amount from being calculated (incorrect fuel injection control).
[0019]
Here, when the air-fuel ratio feedback control is resumed, the initial value set in advance according to the operating state is set as the integral term, so that an appropriate feedback control amount can be immediately output to the combustion injection means. In addition, since the set initial value is held for a predetermined period after the restart, the influence of the response delay of the integral term calculated based on the error amount is eliminated after the air-fuel ratio feedback control is restarted. Incorrect feedback control amount calculation can be prevented.
[0021]
According to the second aspect of the present invention, when the feedback control is not performed, the plant model identification is prohibited. Therefore, the plant state prediction completely different from that during the feedback control (that is, calculated by the control amount calculation means) (Prediction of state based on input irrelevant to feedback control amount and output based on it) prevents identification accuracy from deteriorating, and identification accuracy for accurate calculation of control gain and hence feedback control amount Secure.
[0022]
As a result, when the feedback control is resumed, the calculation of the control gain and the calculation of the feedback control amount based on the wrong plant model (plant state) can be reliably prevented.
Here, when the parameter estimation is restarted, the initial value set in advance according to the operation state is set as the parameter of the plant model. Therefore, when the air-fuel ratio feedback control is restarted, it can be converged early and appropriate control can be performed. It is possible to calculate the gain and hence the appropriate feedback control amount at an early stage.
[0023]
In addition, since the set initial value is held for a predetermined period after restarting, after the air-fuel ratio feedback control is restarted, it is possible to prevent plant state prediction that is completely different from the time of the feedback control caused by response delay. Deterioration of identification accuracy can be reliably prevented .
[0024]
According to the third aspect of the invention, it is possible to calculate the feedback control amount with high accuracy while compensating for the influence of the dead time element included in the plant. As a result, it is possible to prevent a slow start of control and an overshoot and to ensure good control.
According to the fourth aspect of the invention, air-fuel ratio feedback control can be performed with high accuracy while suppressing the influence of disturbance.
According to the invention which concerns on Claim 5, the state prediction (identification of a plant model) of a plant can be accurately and easily performed by using the successive least squares method (RLS method).
According to the invention which concerns on Claim 6 , even if it is a case where the optimal control gain used for calculation of a feedback control amount changes with the plant characteristic fluctuation | variation, a suitable control gain can be calculated.
According to the seventh aspect of the present invention, even when the air-fuel ratio feedback control is restarted after the fuel cut or open loop control is performed, the fuel injection control can be performed with an appropriate feedback control amount.
[0025]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is a system diagram of an engine (engine) showing an embodiment of the present invention.
As shown in FIG. 1, the intake passage 2 of the engine 1 is provided with an air flow meter 3 for detecting the intake air amount Qa and a throttle valve 4 for controlling the intake air amount Qa.
[0026]
The fuel injection valve 5 provided in the intake passage 2 is driven to open by an injection signal from a control unit (C / U) 6 having a built-in microcomputer to inject and supply fuel.
Each cylinder is provided with an ignition plug 8 that performs spark ignition in the combustion chamber 7 and ignites the air-fuel mixture sucked through the intake valve 9 by spark ignition.
[0027]
The combustion exhaust is discharged to the exhaust passage 11 through the exhaust valve 10 and is discharged into the atmosphere through the exhaust purification device 12.
In the exhaust passage 11, a wide-range air-fuel ratio sensor 13 that linearly detects the air-fuel ratio according to the oxygen concentration in the exhaust gas is provided on the upstream side of the exhaust purification device 12.
[0028]
Further, a crank angle sensor 14 that outputs a crank angle signal at every predetermined crank angle of the engine 1 and a water temperature sensor 15 that detects a cooling water temperature Tw in the cooling jacket of the engine 1 are provided.
The control unit (C / U) 6 controls the fuel injection valve 5 as follows.
[0029]
First, the basic fuel injection amount Tp = K × Qa × Ne (K is a constant) corresponding to the stoichiometric (λ = 1) is determined from the engine speed Ne detected based on the intake air amount Qa and the signal from the crank angle sensor 14. Calculate.
Next, it is determined whether the air-fuel ratio is feedback-controlled or open-loop controlled according to the operating state, and when the feedback control is performed, the basic fuel injection amount Tp, the target air-fuel ratio λt and the air-fuel ratio sensor 13 are detected. The final fuel injection amount Ti = Tp × (1 / λt) × α is calculated using the air-fuel ratio feedback correction coefficient α calculated based on the signal.
[0030]
In the case of open loop control, the air-fuel ratio feedback correction coefficient α is fixed to 1 (α = 1), and the final fuel injection amount Ti = Tp × (1 / λt) is calculated.
Basically, an injection signal corresponding to the final fuel injection amount Ti is output to the fuel injection valve 5, but when it is determined that the fuel cut is to be performed according to the operating state, The injection signal is not output to the fuel injection valve 5.
[0031]
That is, at the time of open loop control and fuel cut, the control amount (feedback control amount) using the calculated air-fuel ratio feedback control coefficient α is not output to the fuel injection valve 5, and the fuel injection control using the feedback control amount is performed. Will not be executed.
Here, fuel injection control in the present embodiment will be described.
[0032]
As shown in FIG. 2, the fuel injection control unit in the present embodiment includes an output determination unit 21 that determines an output to the fuel injection valve 5, and an air-fuel ratio feedback control unit 22 indicated by a broken line in the drawing. Has been.
The output determination unit 21 determines whether or not to output the feedback control amount calculated by the air-fuel ratio feedback control unit 22 to the fuel injection valve 5 according to the operating state.
[0033]
Specifically, the fuel injection control corresponding to the operation state is determined in the control unit (C / U) 6, and such determination, that is, whether to perform feedback control or open loop control, or to perform fuel cut, Based on the above, it is determined whether or not to output the feedback control amount calculated by the air-fuel ratio feedback control unit 22 to the fuel injection valve 5.
[0034]
At the time of open loop control or fuel cut, the feedback control amount calculated by the air-fuel ratio feedback control unit 22 is not output to the fuel injection valve 5, and the control amount calculated as α = 1 as described above. Output (open loop control) or control amount = 0 (fuel cut).
The air-fuel ratio feedback control unit 22 includes a sliding mode control unit (S / M control unit) 221, a dead time compensator 222, a plant model identification unit 223, a control gain calculation unit 224, and a dead time calculation unit 225. , Including.
[0035]
The S / M control unit 221 calculates the air-fuel ratio feedback correction coefficient α by sliding mode control based on the deviation between the target air-fuel ratio λt and the actual air-fuel ratio λt, and the plant (fuel injection valve 5 to air-fuel ratio sensor). 13), that is, the feedback control amount of the fuel injection valve 5 is calculated as in the following equation (1).
[0036]
[Expression 1]

[0037]
Where e (t) is an input to the S / M control unit 221 (target air-fuel ratio-actual air-fuel ratio), K _P is a linear term linear gain, K _D is a linear term differential gain, and S _P is a switching function linear gain. , S _D is a switching function derivative gain, K _I is an adaptive law gain, K _N is the nonlinear gain, sigma (t) is a switching function, is _{σ (t) = S p e} (t) + S D e (t) .
Each control gain is calculated by a control gain calculation unit 224 described later.
[0038]
However, the calculation of the feedback control amount by the S / M control unit 221 is prohibited at the time of the open loop control or the fuel cut. This is done by checking the drive signal and flag (fuel cut flag) of the injection valve 5.
In this way, the calculation of the feedback control amount is prohibited because the feedback control is not performed (that is, the feedback control amount calculated by the S / M control unit 221 is not output to the fuel injection valve 5) or during the fuel cut. Even when the calculation of the feedback control amount continues, the integral term (error amount = calculated based on the target air / fuel ratio−the actual air / fuel ratio) in the sliding mode control increases, and then when the feedback control is resumed. This is because proper fuel injection control cannot be performed.
[0039]
Then, after the open loop control and the fuel cut are completed, the feedback control (that is, the calculation of the feedback control amount by the S / M control unit 221) is resumed. An initial value set in advance according to the operating state is set in the integral term of the sliding mode control.
[0040]
As described above, when the feedback control is resumed, the integral term in the sliding mode control is reset to the initial value corresponding to the operation state, so that an appropriate feedback control amount is output to the fuel injection valve 5 immediately after the feedback control is resumed. it can.
The initial value may be held for a predetermined period after the feedback control is resumed in consideration of a response delay after the feedback control is resumed.
[0041]
Thus, since the integral term is not calculated even during the response delay, a more appropriate feedback control amount can be output to the fuel injection valve 5.
Note that performing open loop control may mean that the feedback control amount is not calculated (that is, prohibited), but even in this case, when feedback control is resumed, sliding is performed. By setting an initial value set in advance in accordance with the operating state in the integral term of the mode control and holding it for a predetermined period, it is possible to ensure proper fuel injection control after the feedback control is resumed.
[0042]
The dead time compensator 222 executes dead time compensation control by the Smith method. By performing local feedback, the dead time included in the plant (that is, the phase delay of the detected air-fuel ratio) is affected. To compensate.
Specifically, as shown in FIG. 3, the dead time compensator 222 includes a plant model 31 that does not include a dead time, a plant model 32 that includes a dead time, and a subtracting unit 33. The deviation e2 between the output (air / fuel ratio) prediction calculated by the plant model 31 not including the dead time element and the actual output (actual air / fuel ratio) prediction calculated by the plant model 32 including the dead time is calculated. This is output to the input side of the S / M control unit 21.
[0043]
Then, e3 is calculated by subtracting the output e2 of the dead time compensator 22 from the deviation e1 between the target air-fuel ratio λt and the actual air-fuel ratio λr, and this e3 is input to the S / M control unit 221. Yes.
The plant model is identified by a plant model identification unit 223 described later, and the dead time is calculated by a dead time calculation unit 225 described later.
[0044]
The plant model identification unit 223 identifies a plant model representing the plant by a transfer function online based on the fuel injection amount (fuel injection signal) and the actual air-fuel ratio (output). Specifically, the plant model parameters are sequentially estimated using a sequential least squares method (RLS method).
The control gain calculation unit 224 calculates the control gain of the S / M control unit 221 using the plant model parameter (estimated parameter) identified by the plant model identification unit 223.
[0045]
Specifically, by using self-tuning control based on the pole placement method, the entire system (that is, the plant (between the fuel injection valve 5 and the air-fuel ratio sensor 13) + S / M control unit 221 + dead time compensator 222) is closed-loop transfer function. The control gain of the S / M control unit 221 is calculated so that the pole matches the desired pole in terms of responsiveness, overshoot amount, settling time, and the like (details will be described later).
[0046]
The dead time calculation unit 225 calculates a dead time k included in the plant. For example, as shown in FIG. 4, the dead time k is calculated by making a table of the relationship between the intake air amount Qa and the dead time k in advance and performing a table search based on the detected intake air amount Qa.
Here, the calculation of the control gain performed by the control gain calculation unit 224 will be described in detail.
[0047]
Calculation of control gain using self-tuning control by the pole placement method is performed as follows.
First, a plant model G _P (z ⁻¹ ) representing the plant by a transfer function is set, and then the transfer function G _C (z ⁻¹ ) of the S / M control unit 221 and the transfer function G _L of the dead time compensator 22 are set. Find (z ^-1 ).
[0048]
Then, the closed loop transfer function W (z ⁻¹ ) of the entire system is calculated from these transfer functions, and the control gain is calculated so that the pole becomes the set pole.
(A) Setting of plant model For the plant between the fuel injection valve 5 and the air-fuel ratio sensor 13, using the dead time k (≧ 1) calculated by the dead time calculating unit 225, for example, the following equation (2 ) And (3) are expressed by a secondary ARX model A (z ⁻¹ ).
[0049]
A (z ⁻¹ ) y (t) = z ^−k b ₀ u (t) + ε (t) (2)
A (z ⁻¹ ) = 1 + a ₁ z ⁻¹ + a ₂ z ⁻² (3)
However, y (t) is a plant output (ie, actual air-fuel ratio), u (t) is a plant input value (ie, fuel injection amount), and ε (t) is irregular noise.
Then, the transfer function G _P (z ⁻¹ ) of the plant model can be expressed as the following equation (4).
[0050]
G _P (z ⁻¹ ) = z ^−k b ₀ / A (z ⁻¹ ) (4)
The estimated parameter vector θ (t) and the data vector ψ (tk) can be expressed as the following equations (5) and (6).
θ (t) = [a ₁ (t), a ₂ (t), b ₀ (t)] ^T (5)
ψ (t−k) = [− y (t−1), −y (t−2), u (t−k)] ^T (6)
(B) The plant model set for plant model identification (parameter estimation) is identified by the plant model identification unit 223.
[0051]
Specifically, since the characteristics of the plant change depending on the plant characteristics such as the operating state and the degree of deterioration of the plant itself, parameters a ₁ (t), a ₂ (t), b ₀ (t ) Is sequentially estimated to identify the plant model (ie, online identification).
In the present embodiment, the least square method (RLS method) is used for the estimation of the parameter, and the parameter that minimizes the square of the error between the actual value and the estimated value is sequentially calculated.
[0052]
A specific arithmetic expression is the same as that of a general weighted sequential least squares method (RLS method). For the time update equations: t = 1, 2,... This is done by calculating 9).
[0053]
[Expression 2]

[0054]
Then, the plant model is identified by sequentially estimating the parameters a ₁ (t), a ₂ (t), and b ₀ (t) using the parameter estimation equations (7) to (9).
The forgetting factors λ ₁ and λ ₂ are set to λ ₁ = λ ₂ = 1 when there is no forgetting factor, and λ ₁ = 0.98 and λ ₂ = 1 when the forgetting factor is provided. .
In this embodiment, the initial value θ0 of the parameter estimation value is set in advance according to the operating state (for example, a ₁ (0) = A1, a ₂ (0) = A2, b ₀ ( By setting 0) = B1), the time until convergence is shortened.
[0055]
However, at the time of the open loop control and fuel cut, plant model identification (parameter estimation) is prohibited in the same manner as the calculation of the feedback control amount by the S / M control unit 221 is prohibited.
That is, during the feedback control, the fuel injection control is performed using the feedback control amount calculated by the S / M control unit 221. However, during the open loop control or the fuel cut, the fuel injection control is performed by the S / M control unit 221. Since a value different from the feedback control amount is output to the fuel injection valve 5, plant state prediction (plant model identification) completely different from that during feedback control is performed. In this case, it is meaningless to predict the state of the plant in order to calculate the feedback control amount, and therefore a correct identification result cannot be obtained (the identification accuracy of the plant model deteriorates).
[0056]
In order to prevent such deterioration of identification accuracy (parameter estimation accuracy), plant model identification is prohibited except during feedback control.
In this case, since the control gain calculation by the control gain calculation unit 224 is not correctly calculated, the control gain calculation may be prohibited.
When feedback control is resumed, the identification of the plant model is resumed (when the calculation of the control gain is prohibited, the computation of the control gain is also resumed). The initial value θ0 (A1, A2, B1) preset according to the operating state is used as the parameter of the plant model.
[0057]
Thus, by resetting the parameter value used immediately before the prohibition of identification with the initial value θ0 (A1, A2, B1), the identification after the restart is performed without considering the change in the plant characteristics before and after the prohibition of identification. The accuracy can be kept high and the convergence time can be shortened.
Further, the set initial values (parameters A1, A2, B1) are held for a predetermined period after the identification is resumed.
[0058]
This is because the air / fuel ratio corresponding to the feedback control amount calculated by the S / M control unit 221 cannot be detected not only immediately after the restart due to a response delay but also during a predetermined period immediately after the restart. This is because a correct identification result cannot be obtained in the same manner as in FIG.
(C) Calculation of discrete time transfer function of the S / M control unit 221 The S / M control unit 221 is converted into a transfer function as follows.
[0059]
When y (t) is a plant output value (actual air-fuel ratio λr), ω (t) is a target value (target air-fuel ratio λt), and e (t) = ω (t) −y (t), The difference Δu (t) of the plant input (that is, the output from the S / M control unit 221) u (t) is given by the following equation (10).
[0060]
[Equation 3]

[0061]
Here, since e (t) = ω (t) −y (t) and e (t) −e (t−1) = Δe (t), the following equation (11) is obtained from the equation (10). It is done.
[0062]
[Expression 4]

[0063]
However, K (z ⁻¹ ) is expressed by the following equation (12), and is calculated as shown in equation (13) based on each control gain.
[0064]
[Equation 5]

[0065]
Therefore, the plant input u (t) is expressed by the following equation (14) from the equation (12).
[0066]
[Formula 6]

[0067]
Here, if it is handled as not including a nonlinear term, the discrete time transfer function G _C (z ⁻¹ ) of the S / M control unit 221 can be expressed as the following equation (15).
G _C (z ^-1 ) = K (z ^-1 ) / (1-z ^-1 ) (15)
(D) As described above with respect to the calculation of the discrete time transfer function of the dead time compensator 222, the dead time compensator 222 uses the Smith method that compensates for the influence of the dead time element while performing output prediction after the dead time. Therefore, the discrete time transfer function G _L (z ⁻¹ ) of the dead time compensator 222 can be calculated as the following equation (16).
[0068]

Note that z ⁻¹ b ₀ / A (z ⁻¹ ) is an output prediction when there is no dead time expressed using the plant model, and z ^−k b ₀ / A (z ⁻¹ ) This is an actual output prediction including a dead time expressed using the plant model.
[0069]
FIG. 5 is a block diagram using the transfer functions (plant model, S / M control unit 21, dead time compensator) calculated as described above.
Next, the closed-loop transfer function conversion of the entire system will be described.
As described above, the nonlinear term of the S / M control unit 221 is not included.
(E) Calculation of the closed loop transfer function W (z ⁻¹ ) of the entire system First, the feedback loop of the S / M control unit 221 and the dead time compensator 222 is taken out and output (feedback) from the target (target air-fuel ratio λt). One transfer function to the control amount is calculated. In FIG. 5, the transfer function G _CL (z ⁻¹ ) of the local loop including the S / M control unit 221 and the dead time compensator 22 is expressed by the following equation (17) from equations (15) and (16). It can be calculated.
[0070]
[Expression 7]

[0071]
Therefore, the closed loop transfer function W (z ⁻¹ ) of the entire system including the plant and the local loop shown in the equation (17) can be calculated as the following equation (18).
[0072]
[Equation 8]

[0073]
FIG. 6 is a block diagram showing the above calculation results.
(F) Regarding the calculation of the control gain of the S / M control unit 221 by the pole placement method, the characteristic polynomial of the closed-loop transfer function W (z ⁻¹ ) is obtained from the equation (18):
(1-z ⁻¹ ) A (z ⁻¹ ) + z ⁻¹ b ₀ K (z ⁻¹ ),
This is set as the following equation (19).
[0074]
[Equation 9]

[0075]
At this time, the control gain of the S / M control unit 221 is calculated as follows by setting T (z ⁻¹ ) that is a desirable pole in terms of responsiveness, overshoot amount, settling time, and the like. .
From the equation (19), the following equation (20) is obtained.
[0076]
[Expression 10]

[0077]
Here, from equation (13),
Since K (z ⁻¹ ) = (K _P + K _I · S _P + K _I · S _D + K _D ) − (K _P + K _I · S _D + 2K _D ) z ⁻¹ + K _D z ⁻² , the switching function is linear. If the gain S _P and the switching function differential gain S _D are set to 1 and the linear term linear gain K _P , the adaptive law gain K _I , and the linear term differential gain K _D are variable parameters, the following expression (21) is obtained. Because you can
[0078]
[Expression 11]

[0079]
Thus, the following equations (22) to (24) are obtained.
[0080]
[Expression 12]

[0081]
Therefore, equations (22) to (24) are solved for K _P , K _I , and K _D , and a ₁ , a ₂ , and b ₀ are estimated parameters a ₁ (t) sequentially estimated by the plant model identification unit 223, respectively. Representing by a ₂ (t) and b ₀ (t), each gain can be calculated as in the following equations (25) to (27).
[0082]
[Formula 13]

[0083]
The characteristic polynomial T (z ⁻¹ ) = 1 + t ₁ z ⁻¹ + t ₂ z ⁻² is, for example, a continuous time of the secondary system when the attenuation ζ = 0.7 and the natural angular frequency ω = 30. system,
G (s) = ω ² / (s ² + 2ζω · s + ω ² )
The contemplated for use the denominator of the transfer function when the discretized sample time T _i.
[0084]
And using the control gain calculated in this way, the S / M control unit 221 calculates a control amount to the plant (see Expression (13)).
As described above, the entire system is represented by a single transfer function using the plant model with the parameters estimated sequentially, and the poles match the desired poles in terms of responsiveness, overshoot, settling time, etc. Since the control gain of the S / M control unit 221 for calculating the feedback control amount is obtained, a good control gain corresponding to the change in the plant characteristics can be calculated, and hence the air-fuel ratio feedback control with high accuracy can be executed.
[0085]
Further, as described above, during open loop control and fuel cut, calculation of the feedback control amount by the S / M control unit 221 is prohibited and parameter estimation by the plant model identification unit 223 is prohibited. Thus, calculation of an erroneous result can be prevented in advance, and proper fuel injection control can be executed even when feedback control is resumed, and the air-fuel ratio can be controlled with high accuracy.
[0086]
In the above description, the feedback control amount is calculated by the sliding mode control. However, the present invention is not limited to this.
[Brief description of the drawings]
FIG. 1 is a system diagram of an internal combustion engine showing an embodiment of the present invention.
FIG. 2 is a block diagram showing air-fuel ratio control of the present invention.
FIG. 3 is a block diagram showing dead time compensation control used in the present invention.
FIG. 4 is a view showing a dead time calculation table used in the present invention.
FIG. 5 is a block diagram showing the S / M control unit 221 and the dead time compensator 222 according to the present invention in terms of transfer functions.
FIG. 6 is a block diagram showing the entire air-fuel ratio feedback control by sliding mode control using self-tuning control according to the present invention.
[Explanation of symbols]
1 Engine 2 Intake passage 3 Air flow meter 4 Throttle valve 5 Fuel injection valve 6 Control unit (C / U)
8 Spark plug 11 Exhaust passage 13 A / F sensor 14 Crank angle sensor 15 Water temperature sensor

Claims (7)

An air-fuel ratio control apparatus for an internal combustion engine comprising air-fuel ratio detection means for detecting an air-fuel ratio and performing feedback control so that the detected actual air-fuel ratio becomes a target air-fuel ratio set according to an operating state,
Identifying means for estimating a plant model parameter representing a plant between the fuel injection means and the air-fuel ratio detection means as a transfer function based on the fuel injection amount and the detected actual air-fuel ratio;
Control gain calculating means for calculating a control gain for calculating the feedback control amount of the fuel injection amount using the estimated parameters of the plant model;
A control amount calculating means for calculating the feedback control amount using the calculated control gain;
Prohibiting means for prohibiting calculation of the feedback control amount by the control amount calculating means in a predetermined operation state;
Equipped with a,
When the calculation of the feedback control amount is prohibited and the calculation of the feedback control amount is resumed, the control amount calculation means sets an initial value set in advance according to the operation state as an integral term, and after the restart An air-fuel ratio control apparatus for an internal combustion engine, which retains a set initial value for a predetermined period . The prohibition means further comprises an identification prohibition means for prohibiting parameter estimation of the plant model by the identification means,
After the parameter estimation is prohibited by the identification prohibition unit, the identification unit sets an initial value set in advance according to an operation state as the parameter of the plant model when the parameter estimation is restarted, 2. The air-fuel ratio control apparatus for an internal combustion engine according to claim 1 , wherein the set initial value is maintained during the period . The air-fuel ratio control of an internal combustion engine according to claim 1 or 2, wherein the control amount calculation means includes a dead time compensation means for eliminating the influence of the dead time included in the plant using the plant model. apparatus. The air-fuel ratio control apparatus for an internal combustion engine according to any one of claims 1 to 3 , wherein the control amount calculation means calculates the feedback control amount by sliding mode control. The air-fuel ratio control apparatus for an internal combustion engine according to any one of claims 1 to 4 , wherein the identification unit estimates the parameters of the plant model using a sequential least square method. The control gain calculating means represents the entire system including the plant and the controlled variable calculating means as a transfer function, and calculates the control gain of the controlled variable calculating means so that the transfer function of the entire system has a set characteristic. The air-fuel ratio control apparatus for an internal combustion engine according to any one of claims 1 to 5 , wherein The air-fuel ratio control apparatus for an internal combustion engine according to any one of claims 1 to 6 , wherein the predetermined operation state is a fuel cut time or an open loop control time.

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