Dynamic EGR Estimation for Production Engine Control

SAE TECHNICAL PAPER SERIES

2001-01-0553

Dynamic EGR Estimation for Production Engine Control Martin Müller, Peter M. Olin and Bart Schreurs Delphi Automotive Systems

Reprinted From: Electronic Engine Controls 2001: Modeling, Controls, OBD and Neural Networks (SP–1585)

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2001-01-0553

Dynamic EGR Estimation for Production Engine Control Martin Müller, Peter M. Olin and Bart Schreurs Delphi Automotive Systems

Copyright © 2001 Society of Automotive Engineers, Inc.

ABSTRACT A dynamic EGR State Estimator (ESE) intended for production engine management systems (EMS) implementation is presented. It better describes the development of external exhaust gas recirculation (EGR) concentration at the engine intake ports during EGR transients than traditional models. The dynamics of EGR concentration time and spatial development in the intake manifold are described as a perfect mixing model in the intake manifold plenum volume and non-mixing plug flow in the intake manifold runners. The time scale of EGR transients precludes the use of traditional EGR measurement techniques for model verification. Instead a wide range air fuel (WRAF) sensor is used. Results are shown for a large variation in operating conditions and compared to the performance of a traditional model. The introduction of an exhaust inert ratio model converts the EGR estimate into the inert EGR concentration, the distinction between total and inert EGR concentration being of relevance for lean operating engines.

of EGR. [5] considers the introduction of EGR in the pressure state equation but does not describe the dynamics of the EGR propagation itself. This paper presents an EGR State Estimator based on a model of the fundamental dynamics governing external EGR propagation. MODEL The estimator is based upon a dynamic model describing the propagation of EGR concentration in the intake system for a traditional external EGR hardware configuration where EGR is introduced in the intake manifold plenum. The model consists of an EGR/air perfect mixing model for the intake manifold plenum volume and a transport delay model describing the nonmixing plug flow of the intake manifold runners. Simulation results using 1-dimensional unsteady fluid flow solvers such as WAVE by Ricardo confirm such a description. INTAKE MANIFOLD PLENUM MIXING MODEL

INTRODUCTION It is important to accurately estimate the actual EGR concentration of the gas that enters the combustion chambers in order to properly control the engine parameters that have EGR dependency, especially those affecting combustion stability. This is especially relevant for direct injection gasoline (DI-G) engines which permit large EGR amounts during stratified operation resulting in large changes in EGR levels during combustion mode changes. The execution of the combustion mode change depends on EGR reaching a safe level before entering the new combustion mode. Accurate estimation of the EGR concentration at the engine intake ports, also during transients, is therefore critical. Current practice regarding estimation of EGR concentration for use in production type EMS is the use of the steady-state valid EGR definition. The literature contains extensive reportings on Mean Value Engine Models (MVEM) [1-4] that have a convenient modeling level for control applications. However little attention has been given to the modeling

The EGR/air plenum mixing model describes the dynamics that take place in the intake manifold plenum volume where the incoming flow past the EGR valve m& egr mixes with the diluent (relative to the external EGR & throttle and any additional concentration) throttle air flow m incoming flow, e.g. purge flow m& purge or IAC valve flow m& IAC . The development in time of the plenum EGR concentration EGR IM , plenum is based on the definition of EGR concentration: (1) where

m egr ≡ EGR * m

m is the total mass of any given control volume.

Differentiating (1) with respect to time and applying continuity results in the state equation:

(

d EGR IM, plenum dt

)=

R TIM

EGR

*

MAP VIM , plenum

 1 , total EGR & egr *  −  m EIR , inert EGR     & egr + m & throttle + m & purge + m & IAC + ...  EGR IM , plenum m 

(2) 

(

Throttle AIR mixing

transport delay

EIR (air & inert)

EGR plenum IM

)

EGR port IM

Purge + ...

where R

: gas constant

Figure 1 : Phenomenological model of external EGR propagation.

TIM

: intake manifold temperature

ESTIMATOR STRUCTURE

MAP

: intake manifold absolute pressure

Traditionally, EGR entering the engine is modeled using the steady-state definition of EGR:

VIM , plenum : intake manifold plenum volume EIR

(5)

: Exhaust Inert Ratio

(This is implemented using Euler numerical integration.) The term “+…” designates any additional incoming air flows to the plenum. The ratio term multiplying the parenthesis on the right hand side is the reciprocal of the effective time constant. Therefore, achieving correct mixing dynamics for a specific engine is isolated to calibrating the intake manifold plenum volume, which is a known geometrical property. The choice of products 1 , total EGR represents the choice between  EIR , inert EGR estimating total or inert external EGR concentration, a distinction of relevance for lean operating engines. The exhaust inert ratio (EIR) model is presented below. If estimating inert EGR, a delay model describing the propagation of EIR from the exhaust manifold to EGR valve inlet may likewise, to the intake runner transport delay model, be included. INTAKE RUNNER TRANSPORT DELAY MODEL Bulk motion with very little dispersion dominates the intake runners, and therefore the intake runner dynamics are described as volume displacement or ‘plug’ flow. The engine intake port EGR concentration is therefore modeled as the delayed intake manifold plenum concentration where the amount of delay is in units of engine revolutions. (3)

(

EGR IM ,port = delay EGR IM ,plenum

)

The delay amount is proportional to the ratio of intake manifold runner volume to cylinder displacement volume, both known geometrical properties. (4) delay ≅ 2

volume of intake runners [engine revolutions] engine displaceme nt volume

EGR SS IM =

& egr m

1 , total EGR * & m engine EIR , inert EGR

where & engine m

: engine total flow

which is typically filtered to somewhat account for the EGR dynamics. This steady-state valid EGR model may be substantially erroneous during EGR transients as shown in the results section. The steady-state solution to the dynamic model is:

(6)

@ SS = EGR dynamic IM

& egr m

1 , total EGR & egr *  m EIR , inert EGR & throttle + m & purge + m & IAC + ... +m

Since mass conservation equates & engine = m & egr + m & throttle + m & purge + m & IAC + ... m

to the

dynamic model and steady-state model estimates during steady-state are identical in principal. In practice, however, errors are associated with the individual flow dynamic @ SS

estimates causing EGR IM ≠ EGR SS IM . This will mainly be due to inaccurate estimates of the two largest flows, namely throttle flow and engine port flow estimates. Of the two estimates the speed-density based engine port flow estimate is considered the most globally accurate. In contrast the throttle flow estimate is sensitive to pressure estimation errors at high manifold absolute pressure (MAP) operation due to the strong non-linearity versus throttle pressure ratio, an operating region especially relevant for DI-G engines. The ideal estimation algorithm would therefore use the dynamic EGR model during transients and the steady-state EGR model during steady-state operation. This is in practice obtained by implementing the dynamic EGR model in an estimator structure where the estimator feedback signal is the steady-state EGR model estimate (as opposed to a traditional estimator implementation

which includes a measurement feedback). Integral correction is applied, to eliminate bias errors between the estimates.

(

ˆR d EG IM, plenum dt

(7)

) = d(EGˆR

IM , plenum

)

2gear, 1300 RPM Tip-In

e=

where

∫

+ K P e + K I e dt ,

dt mod el

EGR SS IM

of change of EGR is clearly opposite for the two EGR models during the first part of the transient.

80 70

ˆR − EG IM , plenum

(

ˆR d EG IM , plenum dt

Combustion Mode Change

Stratified

Homogeneous

EGR Valve Pos

60 50

)

[%]

is given by (2).

Throttle Valve Pos 40 SS EGR

30

mod el

20

EXHAUST INERT CONCENTRATION

SS EGR Filtered

10

Inert EGR estimation requires a model of the exhaust inert ratio (EIR). It is derived by interrelating the composition of air and inert mass in the combustion chamber at the three distinct engine cycle conditions; 1) end of combustion, 2) end of induction and 3) end of exhaust. The simplified case of no residuals (internal EGR) results in: (8)

 1  EIR = EGR inert IM, engine 1 − λ IM, engine 

Dyn EGR

0 1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

Time [s]

Figure 2 : Comparison of dynamic and steady-state EGR estimates during tip-in causing stratified to homogeneous mode change where EGR is purged before entering homogeneous operation.

 1 +  λ IM,engine 

2gear, 1500 RPM Tip-out 60

where λ IM,engine =

A FIM ,engine

is the relative air fuel

50

ratio at the engine intake port. The EIR model equals one during stoichiometric operation as expected. The model was validated against EIR calculated from emissions data with good agreement.

40

A Fstoichiome tric

EGR Valve Pos

[%]

30

Throttle Valve Pos

20 Dyn EGR

RESULTS

SS EGR Filtered

10 SS EGR

The following results show the substantial errors of the traditional steady-state valid EGR model and in contrast the more accurate performance of the dynamic EGR state estimator. The results are from vehicle data with a DI-G engine. The transient of Figure 2 was caused by a tip-in maneuver resulting in a combustion mode change from stratified to homogeneous operation on a DI-G engine. During the initial part of the tip-in, while still in stratified combustion, both the throttle valve and EGR valve open simultaneously in order to maintain similar air fuel ratio and EGR level during increasing engine torque. This results in a simultaneous increase in both throttle (=air) and EGR valve flows. The net effect as described by the dynamic model is that EGR concentration does not change much due to the canceling effects of simultanious increases of throttle and EGR flows. In contrast, the steady-state model does not comprehend the increase of the throttle air flow which acts as a diluent of the increasing EGR flow. The net effect is that SSEGR falsely increases rapidly, filtering somewhat reducing the error. Figure 3 shows similar model difference during a stratified tip-out maneuver. The sign

0 2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

3.1

3.2

Time [s]

Figure 3 : Comparison of dynamic and steady-state EGR estimates during stratified tip-out. The two previous examples used qualitative arguments for the validity of the dynamic EGR estimator. Traditional EGR measurements based on intake and exhaust manifold CO 2 measurements are not fast enough to also quantitatively validate transient EGR estimates. Instead, correct description of EGR dynamics is validated during stoichiometric operation by disabling closed-loop fueling and obtaining no deviation of the measured air fuel ratio (AF) during EGR transients, using a wide range air fuel (WRAF) sensor. It is assumed that the accuracy of the intake port total flow estimate (speed-density) is unchanged during the EGR transient and therefore that any deviation in measured AF during the EGR transient due to incorrect intake port air flow estimation is caused by incorrect intake port EGR estimation. These errors represent the impact of EGR estimation error on port air flow estimation. The apparent magnitude of errors are somewhat smaller than actual due to WRAF sensor

dynamics. Figures 4 compare the measured AF errors using the dynamic and steady-state models for 10% EGR steps over an engine speed range of 1000-4000 RPM. The engine displacement was 1.8liter with a manifold plenum volume of 2.5liter and intake runner total volume of 1.8liter resulting in a runner delay of 2 engine revolutions. The plots include the estimated EGR signals as step input reference (out of scale). Filtering of the traditional steady-state model was optimized for the 1900RPM condition and the filter coefficient was reused at the other engine speeds. For this case the two estimates are comparable, although the steady-state model is still slightly inferior due to the missing runner delay model. However, reusing the filter calibration of 1900RPM at the other engine speeds shows the steadystate model as clearly inferior to the dynamic model with port airflow estimation errors exceeding 6%. An alternative approach might therefore seem to be the combination of the runner delay model and the steadystate EGR model using filter coefficient scheduling. However, the steady state model using filter coefficient scheduling would not be an alternative to the dynamic model for transients such as those shown in Figures 2,3.

REFERENCES 1.

Hendricks, E., Sorenson, S. C., “Mean Value Modelling of Spark Ignition Engines”, SAE Technical Paper, no. 900616, 1990.

2.

Hendricks, E., Jensen, M., Chevalier, A., Sorenson, S.C., Trumphy, D., Asik, J., “Modelling of the Intake Manifold Filling Dynamics:, SAE Technical Paper, no. 960037, 1996.

3.

Maloney, P. J., Olin, P. M., “Pneumatic and Thermal State Estimators for Production Engine Control and Diagnostics”, SAE Technical Paper, no. 980517, 1998.

4.

Chevalier, A., Müller, M., Hendricks, E., “On the Validity of Mean Value Engine Models during Transient Operation”, SAE Technical Paper 2000-01-1261.

5.

Føns M., Vigild, C., Chevalier, A., Hendricks, E., Sorenson, S.C., Müller, M., “Mean Value Engine Modelling of an SI Engine with EGR”, SAE Technical Paper 199901-0909.

DEFINITIONS CONCLUSION A model describing the dynamics of external EGR propagation has been developed and validated. Its performance during EGR transients is shown to be superior to a traditional steady state model. The model detail level is equivalent to existing Mean Value Engine Models (MVEM) and therefore suitable for production engine management systems (EMS). Implementation and testing in a production intent EMS software package has been performed.

Air and inert Exhaust composition is considered the combination of air and inert, where inert is all matter that is not air, and air is defined as having the molar relationship O 2 + 3.76 N 2 . Tip In / Tip Out Tip In and Tip Out maneuvers in the DI-G case refers to accelerator pedal movement and not throttle position movement. Diluent The following meaning of diluent is used in this paper: Air is considered the diluent in regards to the EGR concentration in the intake manifold. This should not be confused with EGR acting as a diluent of the combustion mixture.

1100RPM, IMEP:310kPa, EGR:0-10%, EGR Valve Pos:0-10%, MAP:38-41kPa

6

SS EGR model Dyn EGR model 4

AF error [%]

AF error : SS EGR model AF error : Dyn EGR model

2

0

-2

SS EGR filtered Dyn EGR

-4

EGR est's not to scale. Actual=[0-10]%

-6 5

6

7

8

9

10

11

12

13

14

Time [s] 1900RPM, IMEP:410kPa, EGR:0-10%, EGR Valve Pos:0-30%, MAP:42-47kPa

4

SS EGR model Dyn EGR model

3

AF error [%]

2

SS EGR

1

0 -1

SS EGR -2

Dyn EGR -3

Dyn EGR

-4 9

10

11

12

13

14

15

16

17

18

Time [s] 2900RPM, IMEP:410kPa, EGR:0-10%, EGR Valve Pos:0-41%, MAP:42-48kPa

5

SS EGR model Dyn EGR model

4

AF error [%]

3 2 1 0 -1

SS EGR

-2 -3

Dyn EGR -4 13

14

15

16

17

18

19

20

21

22

Time [s] 3800RPM, IMEP:350kPa, EGR:0-10%, EGR Valve Pos:0-41%, MAP:33-38kPa SS EGR model Dyn EGR model

AF error [%]

6

4

2

0 -2

SS EGR

-4

Dyn EGR -6 4

5

6

7

8

Time [s]

Figure 4

9

10

11

12

13