Experimental Determination of Transport Delay in aSpark Ignition Engine

Travis Wiens∗, Rich Burton∗, Greg Schoenau∗, Mike Sulatisky†,Sheldon Hill†, Bryan Lung†

Abstract

An important part of the feedback loop of the fuel-air control system in a spark-ignition engine is the delay: the time it takes for the charge mixture to move from theinjection point, through the engine and exhaust system to the oxygen sensor. Manymodern intelligent control schemes are model-based and require a method of automat-ically determining this delay. This paper presents an automatic, empirical method ofdetermining the delay, requiring no specialized equipment. Sample results from anengine running on natural gas are presented. These results show that caution shouldbe exercised when selecting a theoretical model for the engine delay.

1 Introduction

Since the introduction of electronic fuel injec-tion, the performance of traditional feedback-based fuel-air control schemes has been lim-ited by the delay inherent in the system: thefuel takes a finite time to travel from the in-jection point to the oxygen sensor in the ex-haust. This delay generally causes a limitcycle to occur as the fuel-air mixture alter-nates from rich to lean. While this limit cy-cle is necessary for proper catalyst operation,the delay allows large deviations from the op-timum fuel-air ratio (FAR or FA ratio) be-fore the feedback can take effect. In orderto reduce these fuelling errors, a number ofintelligent control schemes have been devel-oped. These control schemes typically gener-

ate an internal model of the engine dynam-ics, which includes the delay. Therefore, amethod of automatically determining the de-lay was developed and experimentally tested,as presented in this paper

2 Fuel-Air System

A typical engine model is shown in Figure1. Generally, the fuel-air controller will mea-sure a number of parameters, such as enginespeed, intake manifold pressure, etc. and at-tempt to estimate the optimum fuelling. Thisoptimum fuelling is typically near the stoi-chiometric point; the fuel-air ratio such thatthere is just enough air to combust the fuel.The fuel is injected into the intake and en-

∗Dept.of Mechanical Engineering,University of Saskatchewan,Saskatoon, Sk†Alternative Energy Products, Saskatchewan Research Council,Saskatoon, Sk

IntakeDynamics

Feedback Controller

FuelMap

Desired λ

λtiN

e

etc

+

+

­

+

Pm

InjectorExhaust

DynamicsEngineOxygen Sensor

Figure 1: Block diagram of a typical engine control unit fuelling section. The controllercomputes an appropriate injection time, ti, given inputs such as engine speed, Ne, intakemanifold pressure, Pm, as well as other parameters. Any errors in the fuel map are correctedby feedback from the oxygen sensor, λ. There is a delay in the feedback loop, due to thetime required for the charge mixture to travel from the injectors to the exhaust gas oxygensensor, via the intake, engine and exhaust system.

ters the engine when the intake valve opens.The charge mixture is then compressed, com-busts and is exhausted, over the course of twoengine revolutions. Finally, the mixture istransported through the exhaust system tothe exhaust gas oxygen (EGO) sensor. Theoxygen sensor signal is then used to correctany steady state fuelling errors.

One common theoretical model for the de-lay time td is given by Kaidantzis et al. [1993]as

td =60 ∗ 2

Ne

+ρiVi

ma

+ρexVex

ma

(1)

where Ne is the engine speed (in RPM), ρi

is the intake air density, ρex is the exhaustdensity, ma is the mass air flow, Vi is the ef-fective volume between the injector and theintake valves and Vex is the effective volumebetween the exhaust valves and the oxygensensor.

As this model includes the exhaust den-sity, a function of its pressure and tem-perature, which are not typically measured,

Kaidantzis makes the “crude approximation”that the exhaust manifold pressure is equalto the intake manifold pressure and that theexhaust temperature is double that of the in-take, resulting in the form:

td =60 ∗ 2

Ne

+ρi

ma

(Vi + 0.5Vex) (2)

which can be simplified to

td =2 ∗ 60

Ne

(1 +

ρi

ρatm

Vi + 0.5Vex

ηvNcylVcyl

)(3)

if one substitutes the definition for volumetricefficiency, ηv,

ηv =ma2 ∗ 60

NeρatmVcylNcyl

(4)

where Vcyl is the cylinder displacement, Ncyl

is the number of cylinders, and ρatm is theatmospheric air density[Heywood, 1988].

As engine controllers are typically eventbased rather than time based, sampling onceper injection, it is more useful to express the

delay in terms of samples than time. Thesampling period, ps is

ps =2 ∗ 60

NeNcyl

. (5)

The number of samples in the delay is then

kd = Ncyl +ρi

ρatm

Vi + 0.5Vex

ηvVcyl

. (6)

If one notices that volumetric efficiencyis proportional to the ratio of ρi/ρatm, butis only weakly affected by the engine speed[Heywood, 1988]:

ηv ≈ Kρi

ρatm

(7)

equation 6 is no longer dependent on enginespeed or intake manifold pressure and shouldbe only slowly varying with temperatures andfuel properties:

kd = Ncyl +Vi + 0.5Vex

KVcyl

. (8)

When Kaidantzis et al wrote their paper,most vehicles on the road had carburettors orthrottle-body injection, both of which havelarge intake volumes relative to the exhaustvolume. Since the delay was dominated bythe intake, the exhaust volume had little ef-fect, and therefore Kaidantzis’s assumption(of ρex = 0.5ρi) was usually a good one. How-ever, the injectors in most modern vehiclesare mounted in the cylinder head, reducingthe intake volume from the order of litres tomillilitres. This also has the effect of transfer-ring the significant portion of the delay fromthe intake to the exhaust, invalidating the re-sult of a constant delay (with respect to thenumber of injection cycles). The completeform of the equation is then

kd = Ncyl +Vi + ρex

ρiVex

KVcyl

. (9)

Unfortunately, beyond predicting the ex-pected function form, this equation does nothave much practical use for predicting the de-lay, as exhaust density (from pressure andtemperature) is not typically measured inproduction vehicles.

3 Determination of Delay

The test vehicle used for this research wasa 2001 General Motors 2500HD truck witha 2003 6 litre Vortec V-8 engine running onnatural gas, coupled to an automatic trans-mission. In order to experimentally map thedelay as a function of engine speed and intakemanifold pressure, a set of relays were used tomomentarily interupt the signal driving theinjectors as shown in Figure 2. This shut offfuel flow to the engine for a time long enoughfor the oxygen sensor to register ”lean”, butnot so long that the engine speed decreasedsignificantly. Typically this time was approx-imately one engine revolution. While thissetup requires the installation of a relay, inpractical use one would have control of theEngine Control Unit and would simply skip anumber of injector pulses.

If the engine is running rich before theinjector interruption, the oxygen sensor willtransition to lean after the delay time haspassed, as shown in Figure 3. A simple algo-rithm can be used to measure this time differ-ence on-line. In this case, at an engine speedof 2011 RPM and an intake manifold pressureof 50.0 kPa, the delay was 0.112 s or 15.0 in-jections.

This procedure was repeated periodicallywhile driving in order to cover the range of op-erating conditions typically encountered. Thedelay curves in terms of time and injectioncycles are shown in Figures 4 and 5, respec-tively. From Figure 5, notice that the curve is

IntakeDynamics

Feedback Controller

FuelMap

Desired  y

y

ti

Ne

etc

+

+

­

+

Pm

InjectorExhaust

DynamicsEngineOxygen Sensor

Switch/Relay

Figure 2: Block diagram showing the minor changes necessary to measure the delay. Aswitch or relay is used to interupt the injection signal.

Figure 3: When the injection signal is cut off momentarily, the oxygen sensor transitionsfrom rich to lean after the delay time, td has passed. The dashed line shows the relay signal:when the signal is high, the injection signal is interupted. The oxygen sensor signal is shownby the solid line, signals above approximately 0.5 V signify a rich mixture, while those belowsignify the mixture has transitioned to lean. This data was recorded from a GM 6L Vortecengine running on natural gas at 2011 RPM and an intake manifold pressure of 50.0 kPa.

not flat, demonstrating the potential error ofusing the simplified model giving a delay of aconstant number of injections. This data setincludes 698 data points, recorded from ap-proximately 30 minutes of driving. The datain Figure 5 was fit to a linear curve of

kd = (2.33× 10−3 samples/RPM)Ne − . . .

(0.1404 samples/kPa)Pm + . . .

16.96 samples (10)

This curve was converted to time and is alsoshown in Figures 4.

4 Conclusion

This paper has demonstrated that the de-lay between fuel injection and oxygen sen-sor feedback can be determined automaticallyin an on-line manner without the need ofany specialized equipment. Additionally, itwas shown that since the intake volume onmodern sequential injection engines is signif-icantly smaller than with throttle body in-jection or carburetted engines, caution must

exercised when using the standard modelswhich oversimplify the exhaust model.

5 Acknowledgements

The authors would like to acknowledge thesupport of NSERC, in the form of a PGS DScholarship, as well as the Saskatchewan Re-search Council for providing equipment andexpertise. Thanks are also given to Natu-ral Resources Canada and Precarn Inc whofunded initial work in this area.

References

J.B. Heywood. Internal Combustion EngineFundamentals. McGraw Hill, New York,1988.

P. Kaidantzis, P. Rasmussen, M. Jensen,T. Vesterholm, and Elbert Hendricks. Ro-bust, self-calibrating lambda feedback forSI engines. Technical Report 930860, SAE,Warrendale, 1993.

Figure 4: Curves showing the measured delay (in terms of time) over the range of enginespeeds and intake manifold pressures typically experienced. The mesh surface shows a linearcurve fit to the data in Figure 5

Figure 5: Since engine control units typically sample data once per injection, rather than ata constant sampling frequency, the delay data in Figure 4 can be expressed more usefully interms of injections, as shown here. The model presented in Kaidantzis et al. [1993] predictsa constant number of injections while varying engine speed and manifold pressure, which isnot the case here. Note that the axes have been exchanged for clarity.