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US5642722A Expired / Lapsed US ⏱️ 0.0 years remaining

Adaptive transient fuel compensation for a spark ignited engine

Assignee: Aumovio Systems Inc
•
Filing: 1995-10-30
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Granted: 1997-07-01
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Expires: 2015-10-30
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Abstract

Abstract A method and system for adaptive transient fuel compensation in a cylinder of a multi-cylinder engine estimates fuel puddle dynamics for the cylinder by determining parameters of a wall-wetting model every engine cycle of the multi-cylinder engine. Fuel delivery to the cylinder is adjusted dependent on the estimated fuel puddle dynamics.

Inventors

  • 👤 Darren A. Schumacher
  • 👤 Kevin J. Bush

Bibliographic Details

Application Number —
Jurisdiction US
Data Source google_patents
Last Synchronized 2026-11-02 16:29
CPC Classifications
F; F02; F02D; F02D41/00; F02D41/02; F02D41/14; F02D41/1401; F02D41/1402; F02D41/04; F02D41/047; F02D2041/141; F02D2041/1413; F02D2041/1415; F02D2041/1417; F02D2041/1418; F02D2041/1433; F02D2041/1434; F02D41/1406

Claims Analysis

Total Claims: 46
Claim 1
Independent Claim 161 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: estimating fuel puddle dynamics for the cylinder of the multi-cylinder engine by determining parameters of a wall-wetting dynamic model every engine cycle of the multi-cylinder engine; and adjusting fuel delivery to the cylinder of the multi-cylinder engine dependent on the estimated fuel puddle dynamics using a lead compensator with adjustable zero tuning and a fixed pole tuning while the estimate of a first wall-wetting parameter is small and a wall-wetting dynamics zero identified dependent on the first and a second wall-wetting parameters is invertible, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while the estimate of the first wall-wetting parameter is large, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while a wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is not invertible.
Claim 2
Independent Claim 161 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: estimating fuel puddle dynamics for the cylinder of the multi-cylinder engine by determining parameters of a wall-wetting dynamic model every engine cycle of the multi-cylinder engine; and adjusting fuel delivery to the cylinder of the multi-cylinder engine dependent on the estimated fuel puddle dynamics using a lead compensator with adjustable zero tuning and a fixed pole tuning while the estimate of a first wall-wetting parameter is small and a wall-wetting dynamics zero identified dependent on the first and a second wall-wetting parameters is invertible, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while the estimate of the first wall-wetting parameter is large, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while a wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is not invertible.
Claim 3
Independent Claim 180 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine in accordance with the following relationship: ##EQU21## estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine in accordance with the following relationship: ##EQU22## where: k is an engine cycle index u is a filtered value of fuel injected y is a filtered value of measured fuel burned v is a weighted covariance of exhaust gas sensor measurements P 1 is an inverse of a weighted covariance of the estimate of c P 2 is an inverse of a weighted covariance of the estimate of b v p(k)=[b.sub.v (k)c(k)]' y(k)=y(k)-y(k-1)+u(k-1)-u(k) h(k)=[(u(k-1)-y(k-1) (u(k-1)-u(k))]; and adjusting fuel delivery to the cylinder of the multi-cylinder engine dependent on the estimated first and second wall-wetting parameters.
Claim 4
Independent Claim 180 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine in accordance with the following relationship: ##EQU21## estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine in accordance with the following relationship: ##EQU22## where: k is an engine cycle index u is a filtered value of fuel injected y is a filtered value of measured fuel burned v is a weighted covariance of exhaust gas sensor measurements P 1 is an inverse of a weighted covariance of the estimate of c P 2 is an inverse of a weighted covariance of the estimate of b v p(k)=[b.sub.v (k)c(k)]' y(k)=y(k)-y(k-1)+u(k-1)-u(k) h(k)=[(u(k-1)-y(k-1) (u(k-1)-u(k))]; and adjusting fuel delivery to the cylinder of the multi-cylinder engine dependent on the estimated first and second wall-wetting parameters.
Claim 5
Dependent Claim 47 words
A method in accordance with claim 2 wherein the term u is identified by the steps of: determining a value of fuel injected for the cylinder of the multi-cylinder engine; and filtering the value of fuel injected and providing a filtered fuel mass injected variable dependent thereon.
Claim 6
Dependent Claim 23 words
A method in accordance with claim 3 wherein the step of filtering removes high-frequency noise and low frequency bias from the fuel injected.
Claim 7
Dependent Claim 92 words
A method in accordance with claim 2 wherein the term y is determined by: measuring an exhaust fuel/air ratio in an exhaust system of the multi-cylinder engine and providing a fuel/air ratio variable dependent thereon; measuring an air charge for a cylinder of the multi-cylinder engine and providing an air mass factor dependent thereon; solving for a burned fuel mass depending on a product of the provided fuel/air ratio variable and the provided air mass factor; and filtering the burned fuel mass and providing a filmed fuel mass burned variable dependent thereon.
Claim 8
Dependent Claim 24 words
A method in accordance with claim 5 wherein the step of filtering removes high-frequency noise and low frequency bias from the burned fuel mass.
Claim 9
Dependent Claim 43 words
A method in accordance with claim 5 wherein the step of measuring an air charge for a cylinder of the multi-cylinder engine comprises a step of: measuring an output of a mass air flow sensor and providing the air mass variable dependent thereon.
Claim 10
Dependent Claim 53 words
A method in accordance with claim 5 wherein the step of measuring an air charge for a cylinder of the multi-cylinder engine comprises a step of: measuring an intake manifold pressure; determining an engine speed; and providing the air mass factor dependent on the measured intake manifold pressure and the determined engine speed.
Claim 11
Dependent Claim 44 words
A method in accordance with claim 5 wherein the step of measuring an air charge for a cylinder of the multi-cylinder engine comprises a step of measuring an air charge for a cylinder of the multi-cylinder engine once per cylinder bank per engine cycle.
Claim 12
Dependent Claim 38 words
A method in accordance with claim 9 wherein the step of measuring an output of an exhaust gas sensor comprises a step of measuring an output of an exhaust gas sensor once per cylinder bank per engine cycle.
Claim 13
Dependent Claim 51 words
A method in accordance with claim 5 wherein the step of measuring an exhaust fuel/air ratio in an exhaust system comprises a step of: measuring an output of an exhaust gas sensor for an exhaust cycle of one cylinder of the multi-cylinder engine and providing the fuel/air ratio variable dependent thereon.
Claim 14
Dependent Claim 52 words
A method in accordance with claim 11 wherein the step of measuring an exhaust fuel/air ratio in an exhaust system comprises a step of: measuring an output of an exhaust gas sensor for an exhaust cycle of one cylinder of the multi-cylinder engine and providing the exhaust fuel/air ratio variable dependent thereon.
Claim 15
Dependent Claim 31 words
A method in accordance with claim 12 wherein the step of measuring comprises a step of measuring an output of an exhaust gas sensor once per cylinder bank per engine cycle.
Claim 16
Independent Claim 118 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine; and adjusting fuel delivery using a lead compensator with adjustable zero and pole tuning while the estimate of the first wall-wetting parameter is small and a wall-wetting dynamics zero identified dependent on the first and second wall-wetting parameters is invertible.
Claim 17
Independent Claim 118 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine; and adjusting fuel delivery using a lead compensator with adjustable zero and pole tuning while the estimate of the first wall-wetting parameter is small and a wall-wetting dynamics zero identified dependent on the first and second wall-wetting parameters is invertible.
Claim 18
Dependent Claim 71 words
A method in accordance with claim 14 wherein the lead compensator with adjustable zero and pole tuning comprises executing a step of determining a compensated fuel mass to be injected dependent on the following deterministic relationship: ##EQU23## where: b.sub.0 =(1-c(k)) b.sub.1 =(b.sub.v (k)+c(k)-1) a.sub.1 =(1-b.sub.v (k)) k is an engine cycle index m d is a desired fuel mass for combustion m i is a compensated fuel mass to be injected.
Claim 19
Independent Claim 137 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine; and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while the estimate of the first wall-wetting parameter is large, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while a wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is not invertible.
Claim 20
Independent Claim 137 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine; and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while the estimate of the first wall-wetting parameter is large, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while a wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is not invertible.
Claim 21
Dependent Claim 71 words
A method in accordance with claim 16 wherein the lead compensator with adjustable zero tuning and a fixed pole comprises executing a step of determining a compensated fuel mass to be injected dependent on the following deterministic relationship: ##EQU24## where: b.sub.1 =b.sub.v (k) a.sub.1 =1-bb.sub.v (k) k is an engine cycle index m d is a desired fuel mass for combustion m i is a compensated fuel mass to be injected.
Claim 22
Independent Claim 169 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: measuring an air charge ingested by the cylinder of the multi-cylinder engine and providing an air mass variable dependent thereon; determining and filtering a value of fuel injected for the cylinder of the multi-cylinder engine and providing a fuel mass injected variable dependent thereon; measuring an exhaust fuel/air ratio in an exhaust system and providing an exhaust fuel/air ratio variable dependent thereon; combining the air mass variable and the exhaust fuel/air ratio variable and providing a measure of fuel burned; filtering the measure of fuel burned and providing a filtered fuel mass burned variable dependent thereon; estimating fuel puddle dynamics for the cylinder of the multi-cylinder engine by determining parameters of a wall-wetting dynamic model on an engine cycle-by-cycle basis dependent on the fuel mass injected variable, and the filtered fuel mass burned variable; and adjusting fuel delivery for the cylinder of the multi-cylinder engine dependent-on the estimated fuel puddle dynamics.
Claim 23
Independent Claim 169 words
A method of adaptive transient fuel compensation for a cylinder in a multi-cylinder engine comprising the steps of: measuring an air charge ingested by the cylinder of the multi-cylinder engine and providing an air mass variable dependent thereon; determining and filtering a value of fuel injected for the cylinder of the multi-cylinder engine and providing a fuel mass injected variable dependent thereon; measuring an exhaust fuel/air ratio in an exhaust system and providing an exhaust fuel/air ratio variable dependent thereon; combining the air mass variable and the exhaust fuel/air ratio variable and providing a measure of fuel burned; filtering the measure of fuel burned and providing a filtered fuel mass burned variable dependent thereon; estimating fuel puddle dynamics for the cylinder of the multi-cylinder engine by determining parameters of a wall-wetting dynamic model on an engine cycle-by-cycle basis dependent on the fuel mass injected variable, and the filtered fuel mass burned variable; and adjusting fuel delivery for the cylinder of the multi-cylinder engine dependent-on the estimated fuel puddle dynamics.
Claim 24
Dependent Claim 168 words
A method in accordance with claim 18 wherein the step of estimating and determining parameters of a wall-wetting dynamic model comprises the steps of: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine in accordance with the following relationship: ##EQU25## estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine in accordance with the following relationship: ##EQU26## where: k is an engine cycle index u is a filtered value of fuel injected y is a filtered value of measured fuel burned v is a weighted covariance of exhaust gas sensor measurements P 1 is an inverse of a weighted covariance of the estimate of c P 2 is an inverse of a weighted covariance of the estimate of b v pP(k)=[b.sub.v (k)c(k)] y(k)=y(k)-y(k-1)+u(k-1)-u(k); and h(k)=[(u(k-1)-y(k-1)) (u(k-1)-u(k))]. 20.
Claim 25
Dependent Claim 116 words
A method in accordance with claim 18 wherein the step of adjusting fuel delivery comprises: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine; and adjusting fuel delivery using a lead compensator with adjustable zero and pole tuning while the estimate of the first wall-wetting fraction parameter is small and a wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is invertible.
Claim 26
Dependent Claim 71 words
A method in accordance with claim 20 wherein the lead compensator with adjustable zero and pole tuning comprises executing a step of determining a compensated fuel mass to be injected dependent on the following deterministic relationship: ##EQU27## where: b.sub.0 =(1-c(k)) b.sub.1 =(b.sub.v (k)+c(k)-1) a.sub.1 =(1-bb.sub.v (k)) k is an engine cycle index m d is a desired fuel mass for combustion m i is a compensated fuel mass to be injected.
Claim 27
Dependent Claim 71 words
A method in accordance with claim 20 wherein the lead compensator with adjustable zero tuning and a fixed pole comprises executing a step of determining a compensated fuel mass to be injected dependent on the following deterministic relationship: ##EQU28## where: b.sub.1 =b.sub.v (k) a.sub.1 =1=b.sub.v (k) k is an engine cycle index m d is a desired fuel mass for combustion m i is a compensated fuel mass to be injected.
Claim 28
Dependent Claim 136 words
A method in accordance with claim 18 wherein the step of adjusting fuel delivery comprises: estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine; and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while the estimate of the first wall-wetting fraction parameter is small, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while the identified wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is not invertible.
Claim 29
Dependent Claim 47 words
A method in accordance with claim 18 wherein the term u is identified by the steps of: determining a value of fuel injected for the cylinder of the multi-cylinder engine; and filtering the value of the fuel injected and providing a fuel mass injected variable dependent thereon.
Claim 30
Dependent Claim 23 words
A method in accordance with claim 24 wherein the step of filtering removes high-frequency noise and low frequency bias from the fuel injected.
Claim 31
Dependent Claim 93 words
A method in accordance with claim 18 wherein the term y is determined by: measuring an exhaust fuel/air ratio in an exhaust system of the multi-cylinder engine and providing a fuel/air ratio variable dependent thereon; measuring an air charge for a cylinder of the multi-cylinder engine and providing an air mass variable dependent thereon; solving for a burned fuel mass depending on a product of the provided exhaust fuel/air ratio variable and the provided air mass variable; and filtering the burned fuel mass and providing a filtered fuel mass burned variable dependent thereon.
Claim 32
Dependent Claim 24 words
A method in accordance with claim 26 wherein the step of filtering removes high-frequency noise and low frequency bias from the burned fuel mass.
Claim 33
Dependent Claim 43 words
A method in accordance with claim 26 wherein the step of measuring an air charge for a cylinder of the multi-cylinder engine comprises a step of measuring an output of a mass air flow sensor and providing the air mass variable dependent thereon.
Claim 34
Dependent Claim 53 words
A method in accordance with claim 26 wherein the step of measuring an air charge for a cylinder of the multi-cylinder engine comprises a step of: measuring an intake manifold pressure; determining an engine speed; and providing the air mass factor dependent on the measured intake manifold pressure and the determined engine speed.
Claim 35
Dependent Claim 40 words
A method in accordance with claim 29 wherein the step of measuring an air charge for a cylinder of the multi-cylinder engine comprises a step of measuring an air charge for a cylinder once per cylinder bank per engine cycle.
Claim 36
Dependent Claim 171 words
An adaptive transient fuel compensation apparatus for controlling an amount of fuel injected into a cylinder of a multi-cylinder engine comprising: a control system for estimating fuel puddle dynamics for the cylinder of the multi-cylinder engine by determining parameters of a wall-wetting dynamic model every engine cycle of the multi-cylinder engine; and a compensator for adjusting fuel delivery to the cylinder of the multi-cylinder engine dependent on the estimated fuel puddle dynamics using a lead compensator with adjustable zero tuning and a fixed pole tuning while the estimate of a first wall-wetting parameter is small and a wall-wetting dynamics zero identified dependent on the first and a second wall-wetting parameters is invertible, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while the estimate of the first wall-wetting parameter is large, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while a wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is not invertible.
Claim 37
Dependent Claim 171 words
An adaptive transient fuel compensation apparatus for controlling an amount of fuel injected into a cylinder of a multi-cylinder engine comprising: a control system for estimating fuel puddle dynamics for the cylinder of the multi-cylinder engine by determining parameters of a wall-wetting dynamic model every engine cycle of the multi-cylinder engine; and a compensator for adjusting fuel delivery to the cylinder of the multi-cylinder engine dependent on the estimated fuel puddle dynamics using a lead compensator with adjustable zero tuning and a fixed pole tuning while the estimate of a first wall-wetting parameter is small and a wall-wetting dynamics zero identified dependent on the first and a second wall-wetting parameters is invertible, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while the estimate of the first wall-wetting parameter is large, and adjusting fuel delivery using a lead compensator with adjustable zero tuning and a fixed pole while a wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is not invertible.
Claim 38
Dependent Claim 77 words
An apparatus in accordance with claim 31 wherein the control system comprises: means for estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; and means for estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine.
Claim 39
Dependent Claim 152 words
An apparatus in accordance with claim 32 further comprising: an exhaust gas sensor for measuring an exhaust fuel/air ratio in an exhaust system of the multi-cylinder engine and providing a fuel/air ratio variable dependent thereon; an intake air charge sensor for measuring an air charge for a cylinder of the multi-cylinder engine and providing an air mass factor dependent thereon; a means for determining a burned fuel mass depending on a product of the provided fuel/air ratio variable and the provided air mass factor; a filter for filtering a value of the burned fuel mass and providing a filtered fuel mass burned variable dependent thereon; and wherein the first means for estimating a first wall-wetting parameter estimates the first wall-wetting parameter dependent on the filtered fuel mass burned variable, and the second means for estimating a second wall-wetting parameter estimates the second wall-wetting parameter dependent on the filtered fuel mass burned variable.
Claim 40
Dependent Claim 22 words
An apparatus in accordance with claim 33 wherein the filter removes high-frequency noise and low frequency bias from the burned fuel mass.
Claim 41
Dependent Claim 19 words
An apparatus in accordance with claim 33 wherein the intake air charge sensor comprises a mass air flow sensor.
Claim 42
Dependent Claim 17 words
An apparatus in accordance with claim 33 wherein the exhaust gas sensor comprises an oxygen gas sensor.
Claim 43
Dependent Claim 18 words
An apparatus in accordance with claim 33 wherein the exhaust gas sensor comprises a linear oxygen gas sensor.
Claim 44
Dependent Claim 54 words
An apparatus in accordance with claim 33 wherein the intake air charge sensor measures an intake manifold pressure, the apparatus further comprises: an engine speed sensor for determining engine speed; and wherein the intake air charge sensor provides the air mass factor dependent on the measured intake manifold pressure and the determined engine speed.
Claim 45
Dependent Claim 124 words
An apparatus in accordance with claim 31 wherein the control system for adjusting fuel delivery comprises: means for estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; means for estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine; and wherein the compensator comprises a lead compensator with adjustable zero and pole tuning that adjusts fuel delivery while the estimate of the first wall-wetting parameter is small and a wall-wetting dynamics zero identified dependent on the first and second wall-wetting parameters is invertible.
Claim 46
Dependent Claim 128 words
An apparatus in accordance with claim 31 wherein the control system for adjusting fuel delivery comprises: means for estimating a first wall-wetting parameter indicative of a fraction of an amount of fuel injected that is retained on surfaces of an intake system for the cylinder of the multi-cylinder engine; means for estimating a second wall-wetting parameter indicative of a fraction of an amount of fuel vaporized from the surfaces in the intake system for the cylinder of the multi-cylinder engine; and wherein the compensator comprises a lead compensator with adjustable zero tuning and a fixed pole that adjusts fuel delivery while the estimate of the first wall-wetting parameter is large, and while a wall-wetting dynamics zero, identified dependent on the first and second wall-wetting parameters, is not invertible.

References Cited (Backward Citations)

US4357923A Cited
US4388906A Cited
US4481928A Cited
JPS593136A Cited
EP0152019A2 Cited
US4939658A Cited
US5448978A Cited

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