1. INTRODUCTION

ld that they now with proper performance.

)1 that is a driving factor. A ) which is an old idea, but it ,ns or analog electronics. Now ,ad.

: above will be in focus. The osis functionality are steadily areas that help meeting the

)1 and diagnosis functions in have to be obtained not only of time. Other examples are improved driveability due to e.g. reduce clutch wear. Ltical models will play an im­Mol and diagnosis. They will ntrol, and supervision.

vehicle designs. It will also to ; design leading to:

,re made possible by, and rely

: mechanics and control. The 2 perspectives on automotive ;piring mind teaser:

air cleaner for usual town air. typically somewhat polluted

house heating and industries. t emissions are such that the n be lower than in town air. have been combusted or have

rater and carbon dioxide, the 'uel consumption. heavily on automotive con­

,ir cleaner under all possible This is a mind teaser, but

ep.

2 T hermodynamic Engine Cycles

In this chapter, the thermodynamic characteristics of basic engine cycles are ex­plained. For each concept, the thermal efficiency is derived from thermodynamic equations. An introduction into Thermodynamics can be found in Appendix A.l.

2.1 Ideal Combustion Engines

Commonly used combustion engines in cars are four-stroke engines. They have two intermittent cycles: the gas is compressed, combusted and expanded in the first cycle, and the gas is exchanged in the second cycle. In this section the second (or passive) cycle will not be considered to simplify the mathematical derivations. The processes related to the second cycle will be discussed in Chapter 3.

Two different types of combustion engines have to be distinguished:

l. Spark-ignited Engine: Combustion caused by an electric spark-ignition.

2. Diesel Engine: Combustion caused by self inflammation due to compres­sional heat.

In most sections, p represents the in-cylinder pressure, V the cylinder volume, '13 the in-cylinder temperature, S the entropy, q the thermal energy of the gas, U

it's internal energy and h it's enthalpy.

2.1.1 Spark-ignited (S1) Engine

The first SI engine was presented by Nikolaus Otto in 1862. The combustion process can be modelled as an isochoric process where the gas volume is con­sidered to be constant. The pV-diagram in Figure 2.1 illustrates that the gas

4 2. THERMODYNAMIC ENGINE CYCLES

3 3 q2,3

~ 42,3-.

2 isentropic

\

2

/ /

isentropic 4

1 1 ~ v Q4 , 1 S

Figure 2.1 pV-diagram (left) and 19S-d iagram (right) of the 5I engine process

volume do~s not change between s tep 2 and step 3. The ratio of maximum to minimu lll volume is given by:

(2.1 )

This ratio E is called the compression ratio of the engine. The di fferent steps for a comple te cycle in the pV-diagram and in the 19S-diagram can.be seen in Figure 2.1. Mathematically they can be described as followed:

1 ---> 2 : Isentrop ic compression , dq = 0:

dQ du + dw = 0

QI ,2 o dw -du = - m Cv d19

2

Wl,2 - j mCl) (/19 = - mcl)(192 - 19 d I

The work WI ,2 is used to comp ress the gas and therefore, it is negative.

2 ---> 3 : Isochoric input of thermal energy, dV = 0:

dw p dV = 0 3

j pdV = 0

2

dq du = mCl) dfJ 3

Q2,3 mCl)j dfJ = mcv C8 3 - "I9 2 )

2

T he iucreased thermal energy q2,3 is caused by combustion of the gas.

2. 1. IDEAL COMB[

3 ---> 4 : Isentropic ex

This state chan the output of ki

4 ---> 1 : Isochoric hea

The loss of thel gas is pumped· a cold mixture {II < 194 ) .

The therm al efficienc energies to the inpUl cycle:

The relat ionship for the equation:

This yields:

vIIC ENGINE CYCLES

3

f the 81 engine process

Ie ratio of maximum to

(2.1)

;ine. The different steps diagram can, be seen in lowed:

~re fore, it is negati ve,

- 1'J 2 )

nbustion of the gas.

2.1. IDEAL COMBUSTION ENGINES 5

3 ---. 4 : Isentropic expansion, dq = 0:

Q3,4 = 0

dow -du = -m Cv d1'J

'W3 ,4 -

4Jmcv d1'J = -mCV (1'J 4 - 1'J 3 )

3

This state change describes the power stroke of the engine where 'W3,4 is the output of kinetic energy from the gas, which is positive (1'J 4 < 1'J 3 ).

4 ---. 1 : Isochoric heat loss, d\l := 0:

dow p dV = 0 IJpdV = 0

4

dQ du + dw = m Cv d1'J

mcv JI

d1'J:= mcv (1'J 1 - '8 4 )

<1

The loss of thermal energy Q<1 ,l is due to the gas exchange: The burnt hot gas is pumped into the exhaust and the combustion ch,nnber is fi lled with a cold mixture of unburnt fuel vapour and air (Q4 ,1 is negn l ive because of 1'J 1 < 1'J 4 ).

The thermal efficiency of the engine is equivalent to the rat io of all the ki netic energies to the input of thermal energy Q2,3 at the combustion of a complete cycle:

'W l,2 + W2 ,3 + W3,4 + W4,1 T)th

Q2,3

m cv ( -1'J 2 + 1'J I - 1'J 4 + 1'J 3 )

m cv (1'J 3 - 1'J 2)

1'J 4 -1'J j1 - -,---.,--­

1'J 3 - '8 2

. 1'J I ()4 j{) 1 - 11- - -,----'__-­1'J 2 'lJ 311'J2 - 1

The relationship for isentropic changes 1 ---. 2 and 3 ---. 4 can be used to simplify the equation:

1 (2.2)E",-I

This yields:

1 r1h-1- - ­ (2.3)·,t - c,,- l

6 2. THERMODYNAMIC ENGINE CYCLES

I

\

v

Figure 2.2 pV-diagram for Diesel En:,,;illt:

Please note that the thermal efficiency 'fIth does not depend on the absolute temperature values. It l!l a inly depends on the compression ratio t. Example; For a compression ratio of t = 11 and an adiabatic coefficient of K, = 1.4 the theoretical thermal efficiency 'fIth is:

17th = 0.617

2.1.2 Diesel Engine

Rudolf Diesel developped this engine from 1893 to 1897. In a diesel engine, the combustion takes place in an isobaric state change during the downward movement of the pistoll . At the beginning of this process the combustion is contro lled by the injection of fuel to maintain a constant pressure at the expansion from 2 to 3. The isobaric state change is indicated between steps 2 and 3 in the pV-diagram in Figure 2.2. The more fuel is injected, the longer the distance between steps 2 and 3 and the larger the volume ratio:

(2.4)

This ra tio is called injection ratio or load. The injection ratio p has an impact on the thermodynamic efficiency which is derived after explaining the different parts of the cycle:

1 - ) 2 : Isentropic compression, dq = 0:

dq du + dw = 0

Ql,2 0 dw -du = -m Cv dfJ

Wl,2 -mc'V(192-191)

2.1. IDEAL COMBUSTIOI'

The mechanical work u engine). It is negative.

2 --4 3 : Isobaric gain of ther

In this process, the con duces the kinetic energ

3 --4 4 : Isentropic expansior

Note that W3,4 is posit

4 --4 1 : Isochoric heat loss, ,

dw

dq

q4,l

Note that Q4,1 is negat

With. K = EE. and R = (cp - (Cu

can now be calculated:

Wl,2 + W2,3 T)th

1 19 1 'i1- - - ­

K 19 2 i

This equation can be simplifi (Eq. 2.2) and the relations} the following relationship is

194

19 1

rAMIC ENGINE CYCLES

production

:ng operation

'uel cell engine with with 'drogen methanol

ine concepts [451

lcations at short distances. ~re an internal combustion ectrical motor may be ac­engine and the drivel ine,

t load conditions the com­ory volume and weight are

ldequate energy source. It re of 20 K or a t relati vely periods, H2 leaks through s chemically bound. Since oissions of nitrogen oxyde

N temperatures. Thermal 2 and O2 . The storage of er generated from natural '. The task is to generate n under realtime transient can be modelled, and the

stima ted in realtime, as a a promising a lternative to ~y requirements to move a ystems .

3 Engine Management Systems

3.1 Basic Engine Operation

3 .1.1 Effective Work

Four-stroke engines are clwntcterised by two alternate cycles: III the first cycle, equ ivalent to the first and second strokes, the gas is compressed, combusted and expanded. In the second cycle , equivalent to the third and fourth strokes, the gas is transferred to the exhaust pip e and the cy linder is fill ed wi th fresh air from the intake manifold. Figure 3.1 shows the two cycles. The crankshaft is turned 360 0

per cycle. 81 and diesel engines are controlled differently: In di esel engines, fuel is directly injected into t,he combustion chamber. T he amount of injected fuel per stroke is then proportional to engine torque. The amount of ai r is almost constant at a given speed. In SI engines, the amount of fu el as we ll as air is controlled. When the fu el is injected into the intake manifo ld , a homogeneous air-fuel mixture is sucked into the cylinders. The mechanical work generated in the combustion cycle can be obtained by an integration in the pV-diagram. The mechanical work can be normal ised by dividing by the displacement volume Vd:

(3.1)

where:

Vd = CYL· (VI CYL

- V2 ) is the displacement volume of a ll cylinders is the number of cy linders is the (normalised) indicated specific work.

26 3. ENGINE lvIANAGEMENT SYSTEMS

p

t compres sion / expansion high pressure cycle

charge exchange Po low pressure cycle

t;I------ Vd --------t>j v TDC BDC

Figure 3.1 pV-diagram of four-stroke com bustion engine

The value of Wi can be determined by measuring the in-cylinder pressure during a cycle. An indicated speci fic work of 1 J/cm 3 is equivalent to a mean pressure of j5 = 10 bar (= lOu F a). Dealing with a four-stroke engine, the measurement has to last for two cycles. The transfer of the combus tion torque to the engine torque available at the crankshaft can be calculated from the following motion equations.

The piston stroke from Top Dead Cent.er (TDC) is

s(exes) = 1(1 - cos(3) + r(l - cosexes)

From Figure 3.2 we get

I sin (3 r sin exes

cos f3 V1- ~: sin2exes (3.2)

which yields lhe piston stroke as

s(exes) = T (1 -cosexes + ~ (1 -V1- ~.: sin2

exes) ) (3.3)

At Top Dead Center , we have exes = 0, s(exes) = 0, and at Bottom Dead Center

3.1. BASIC ENGINE (

TDC '"

FigL

exes = 7r, s(exes) = 2r n

ds

dexes

and

These derivat.ives over C)

time as follows:

ds ds d dt = dexes . ­

d2 s d ( d. dt 2 = dt dex(

d2 s . 2 --2- . exes + . dexes

The indicated specific wo

Wi

Vd

The combustion torque al

fANAGEMENT SYSTEMS

on

charge exchange low pressure cycle

--1----.­V

BDC

nbustion engine

in-cylinder pressure during ,alent to a mean pressure of gine, the measurement has torque to the engine torque following motion equations.

(3.2)

nd at Bottom Dead Center

3.1. BASIC ENGINE OPERATION 27

s piston stroke

----f r crankshaft radiusT DC ­ -- ------------ --- __ J_s etes crankshaft angle I connecting rod length

Figure 3.2 Piston and crankshaft motion

etes = Jr, s{exes) = 2r respectively. The derivatives of the piston stroke are

ds . r sin exe s cos exe s )r smetes + - . ----;:======

detes ( I / r 2 . 2V I - F sm etes

and

2f (cos2 etes - sin o:es) + r; Si1l4 O:es J = r cooexes + J . (3."1) ( (VI - f; sin

2 exes)

These derivatives over crankshaft angle can be related to t.he derivatives over time as follows:

ds ds dexes ds .- = -- . - - = -- . exes dt detes dt detes

2 detcs ds d2etesd S d (dS detes ) d ( ds ) ._- + -_ . _ ­S dt2 dt 2= dt dexes ' ~ = dt dexes dt dexes

d2s' 2 ds .. -- . exes + -- .etes (3.5)dexbs dexes

The indicated specific work can be written as

I f~ dS j (CI'es)V L...- (pj(exes) - Po) Ap dex detes d j=l es

(3.6):d f Tcomb(etes)detes

The combustion torque a t the crankshaft is thus defined as

(3.7)

3.1. BASIC ENGINE OPl28 3. ENGINE MANAGEMENT SYSTEMS

mI' HI combustion heat Pe is the effective p' We is the effective sl ghl,th theoTetical heat loss, m I is the mass of fu

Wih theoTetical wOTk mI is the fuel flow iJ heat loss caused by HI is the specific en

,r-----.. glll,r incomplete combustwn Vd is the total displ 'W I ,II v (Vd/CY L displa,

The indicated thermodynaJ W"lp low pTessure WOT k

w, indicated wOTk

WIr jTictional wOTk

We ej jective WOTk Some examples of typical Vi

Figure 3.3 The effective work delivered by the engine is much lower than the thermal energy caused by combustion. Table 3.1 Indicated specifi

loss qh.l,r for different engine

Engine TyThe pistol! strokes in different cylinders are shifted by phase.

Wi Sj (Cles) = S (aes - (j -1)· C~L) J = I , ""CYL (3,8)

The average combusLion torque is ghl ,r

TCO'mb 4~ f Tcomb(Cles)daes

Pi (3.9) 3.1.2 Air-Fuel Ratries

where Pi is t ile nlean ind icated power. The total indicated wo rk Wi Vd can now The ratio of air to fuel is nal combustion engines. rbe written a t s tiltiona ry engine operation as amou~t of air ma transfer: throttle butterfly, aerodyni rebounding of already bur other effects. The amount'

and the normali sed work volume Vd under the norrr. density Po = l.29 kg/m3

(3.10) theoretical value is equival

where n = ri es / ('27r) is the engine speed. In reality, the effective work We per volume is much low()l' than the indicated work Wi (see Figuf8 3.3). The effec tive thermodynamic efl iciency 'r7e is at constant fuel flow

Similarly, the ratio of mel equivalent to the relative f

(3.11)

where:

high pTessuTe wOTk

, ,

2

CYL

{AGEMENT SYSTEMS 3,1, BASIC ENGINE OPERATION 29

2t loss

ed bynbustion

Jork

Pe is the effect ive power in W We is the effectiv8 sp8cific work per cycle in Jlm3

m J is the mass of fuel measured per cylinder in kg mJ is the fuel flow in k91s H J is the specific energy of the fuel released in the combustion JI kg Vd is the total displar:emcnt volume in m 3

(VdICY L displacement volume per cylinder)

The indicated thermodynamic efficiency (fr iction not considered) is

1], = Wi Vd

---,-­2mJH J CYL

(3, 12)

Some examples of typical values for the indicated efficiency are given in table 3,1.

Ich lower than the thermal

Table 3.1 Indicated specific work Wi, theoretical heat loss qhl ,lh, and realistic heat loss qhl,r for different engi ne types, related to fuel combustion heat,

,hase,

i = 1, "" CYL (3,8)

Engine Type SI Diesel Big Diesel

W, 33-35 % 40-43 % 45-48 %

{fit I ,Ii? 23-28 % 22-25 % 12-14 %

(fhl, ,' 37-41t % 35-40 % 26-33 %

s

(3,9)

.ted work Wi Vd can now

!Pi

n

(3,10)

e effective work We per ,gure 3.3), The effective

(3.11)

3.1.2 Air-Fuel Ratio

The ratio of air to fuel is very important for the combustion process of inter­nal combustion engines, There are several effects that have an impact on the amount of air ma transferred to the cylinder: Throttling of the air flow by the throttle butterfly, aerodynamic resistance and resonances in the intFtke manifold, rebounding of already burned gases from the cylinder into 1,) e inlet pipes and other effects, The amo unt of air which would theoretically fit in to a displacement volume Vd under the normalised pressure Po = 1.013 bar and the normalised air density Po = 1.29 kglm3 is expressed by ma,t" = Po Vd , The ratio of real to theoretical value is equivalent to the relative air supply:

\ - ~ Aa - (3,13) ma,tlt

Similarly, the ratio of measured fuel mass m f to theoretical fuel mass m J,th is equivalent to the relative fuel supply:

\ _ mJAJ --- (3, 14)

mJ,t1t

36 3. ENGINE MANAGEMENT SYSTEMS 3.1. BASIC ENGINE OPERA

p, [baT]

15 _.

advance <l== 10 ­

5

I I I

I....~ 0 '1--­

/"'011- ---11 0:cs-120° 0:i TDC

Figure 3.9 In-cy linder pressure p over cran kshaft angle acs.

The gas is compressed by the piston in an approximately isentropic process. Wi th ignition at 0:i, the pressure rises only after time lag Td. The maximum pres­sure varies from cycle to cycle. The inflammation lag Td depends on temperature, pressure, air-fuel ratio and self inflammation time as described in the previous section. It also depends on the type of fuel being used. Figure 3.10 shows some inflammation lags for different fuels over temperature. Oil companies adapt their fuel to weather condi tions (summer, winter).

Turbulence cuusted by the upward moving piston has no impact on the time lag Td. For a correct iglJit ion angle , this lag must be conside red . The time lag is convoluted to an :tngle lag , increasing proportional to engine speed. Contrary to that , the engille speed has almo.-i, no impact on the position of energy conversion as turbulences increase the transport velocity with higher engine speeds.

The energy conversio n caused by combustion is shown in Figure 3.11 for different air-fuel ratios A. In these curves, the isentropic pressure curves are suppressed. The differential output of thermal energy per angle dE/d0:cS (its gradient) is normalised to the total thermal energy Eo. The shape of the relative energy convers ion is therefore a lmost cons tant.

If the a ir-fue l ratio is increased e.g. to A = 1.2 as shown in Figure 3.11, the ignition lag Td will rise. At a constant ignition angle 0:i1 the energy conversion is then retarded. Therefore, the ignition angle must be adva nced to 0:i2, to compensate for the increased delay. The energy conversion returns to its previous position. It should be mentioned that a high a ir-fuel ratio A increases the variance of the time lag Td

The ignition angle 0:, depends on A which can be seen in Figure 3.12. The angle is computed by averaging the energy conversion over 0.1 %, 1 %, 10 %, 50 %,

Td, [ms]

103 •

102 ­ ~ 101

600 650

Figure 3.10 InAammat

dE/Eo dacs

Figure 3.11 Normalised energ) ratios A.

NAGEMENT SYSTEMS

-etard

raft angle acs.

.lately isentropic process. ~ Td. The maximum pres­depends on temperature, lescribed in the previous

Figure 3.10 shows some )iJ companies adapt their

,s no impact on the time lsidered . The time lag is 19ine speed. Contrary to tion of energy conversion .er engine speeds. 10wn in Figure 3.11 for Jpic pressure curves are per angle dE/dacs (its

T he shape of the relative

h.own in Figure 3.11, the i1 the energy conversion be advanced to a i2, to

:m returns to its previous ) A increases the variance

een in Figure 3.12. The ~r 0.1 %,1 %,10%,50%,

3.1. BASIC ENGINE OPERATION 37

10-~__~~-+____+1__~__-+~~_____~1

600 650 700 750 800 {), [0 K ]

Figure 3.10 Inflammat ion lag Td over temperature for different fuels .

dE/Eo d r> C 8

energy conversion at A = 1 and ignition angle ail

energy conversion at A = 1.2 and ignition angle at!

energy conversion at A = 1.2 and incresed ignition angle a;.2

Figure 3.11 Normalised energy conversion caused by combustion for different air-fuel

ratios A.

38 3. ENGINE MANAGEMENT SYSTEMS 3.2. FUEL CONTROL

O:cs o:cs

- I I O:E1% ~

I

~~ 0.8 1.0 1.2 A

Figure 3.12 Angle Oe s of energy conversion over air-fuel ratio'\ during ignition (left) and com bust ion (r ight.) process.

90 % points. The angles for 0:£1% and higher are almost independent of the air­fuel ratio A. In-cy linder pressure measurements can be used to control the ignition angle in a closed loop to maintain a constant position of energy conversion as shown in Figure 3 13. The angle of maximum pressure gradient max(dp/do:cs) may be used as a control variable. The controller time constant must be relatively large because of the high delay time variances between consecutive cycles. Thus closed loop ignition control may be too slow for the dynamic response of the engine.

The ignition angle is determined to find a compromise between fuel consump­tion , emissions or knocki ng. An equiva lent procedure can be found for the fuel injection angle a t Diesel engines.

3.2 Fuel C ontrol

3.2.1 Emissions of Internal Combustion Engines

Mixture formation can be achieved by manifold or by in-cylinder inject ion. With sufficient time the mixture is distributed homogeneously in the cylinder with an air-fuel ratio in the range of 0.9 < A < 1.3. For very lean mixtures A > l.3, a rich stratified charge must be concentrated in a portion of the combustion chamber.

The combustion process is started by an electric spark at SI engines and by self-inflammation at Diesel engines. The inflammation is delayed as described in the previous section.

• Homogeneous mixture, stochiometric air-fuel ratio: The flame has a char­acteristic blue color . Almost no soot (carbon particulates) is produced.

• Strati fied cllLLrge , lean air-fuel ratio: The flame has a characteristic yellow co lor. Soot is prod uced.

p, [bar]

15

10 ­(dp/do:cs

5

0 +----- 1-­-120°

o:cs((dp/d

Figure 3.13 Closed-loop cont of energy conversion.

• Inflammation starts cor

The inflammation process del and activation energy E of tl according to the concentratio

This ratio is temperature dep The pollutant emissions I.

ratio which is shown in Figur

A < 1: Increased emission of

A = 1: Stochiometric combm converter.

A ~ l.1: Highest nitrogen oxi temperatures.

A> 1.1: Decreasing nitrogen temperatures. Increasir

A > 1.5: Lean operation. For verter is required.

The concentration of oxygen air-fuel ratio A for A :2: 1 usin

1ANAGEMENT SYSTEMS

O:E90% -....,.-----­

I O:E1% ~

I

~ ~~

l.0 l.2 A

ol ratio A during ignition (left)

lOst independent of the air­) used to control the ignition Ion of energy conversion as LIe gradient max(dp/do:cs ) constant must be relatively

on consecutive cycles. Thus e dynamic response of the

nise between fuel consump­e can be found for the fuel

III Engines

in-cylinder injection. With lsly in the cylinder with an ,an mixtures A > 1.3, a rich f the combustion chamber. 3park at 81 engines and by 1 is delayed as described in

. tio: The flame has a char­~rticulates) is produced.

has a characteristic yellow

3.2. FUEL CONTROL 39

p, [barl

15

10

5

II

~1-l2--I

/ ;II

'DC~----1-C2--'"o:CS00----~i 00

o:cs((dp/clo:cs)max) O:CS(Pmax)

Figure 3.13 Closed-loop control of ignition angle (Xi to maintain a constant position of energy conversion.

• Inflammation starts combustion from one location.

The inflammation process depends on pressure p, temperat.urPI9 , air-fuel ratio A and activation energy E of the fuel. For A < 1 the exha ll ~ t. gases are generated according to the concentration ratio

k = nco' nH2 0 (3.20)nC0 2 • nH2

This ratio is temperature dependant. A typical value for {) = 1850 0 f{ is k = 3.6. The pollutant emissions like CO, HC, NO x depend strongly on the air-fuel

ratio which is shown in Figure 3.14

A < 1: Increased emission of hydrocarbon HC and carbon monoxide CO.

A = 1: 8tochiometric combustion. Very low emissions after three way catalytic converter.

A ~ l.1: Highest nitrogen oxide NO x emissions due to highest combustion peak temperatures.

A > l.1: Decreasing nitrogen oxide NO x concentration and lower combustion temperatures. Increasing hydrocarbon HC emissions at eventual misfires .

A > l.5: Lean operation. For very low emissions, a NO x reducing catalytic con­verter is required.

The concentration of oxygen O2 in the exhaust gas can be used to determine the air-fuel ratio A for A :::: 1 using a lambda-sensor.

40 3. ENGINE MANAGEMENT SYSTEMS

Figure 3.14 Raw e lflis~ion s of CO, HC, NO x and O2 over air- fuel rati o A for 81 engines.

3.2.2 Fuel Measurement

The air-fuel rat io A is an important variable for fuel control which is based on different control concepts:

rich mixture A < 1: Maximum power per displacement volume because of in­creased relat ive fuel supply Af. It was used at high engine loads until 1970. Nowadays it is only used for cold engines during the warm-up phase. High emission ra tes.

stochiometric mixture A = 1: Acceptable power output. This ratio is required for proper upenll ion of three-way catalytic converters. At high engine loads, a good compromise between power output and exhaust emissions is achieved .

moderately lean mixture 1 < A < 1.5: Good efficiency because of increased air supply Aa , but high emissions of NO x . This method was used at part loads untl' 1. 980.

lean mixture A> 1.5: High efficiency because of high Aa· NOx emissions are still high, so dw,t catalytic converters for NO x reduction are required. This method is used in lean-burn engines at part loads and in Diesel engines. Maxiruurll e ligi ne power cannot be reached.

The reference torque desired by the driver controls either the relative air supply Aa via the throttle angle at at SI engines or the relative fuel supply Af at Diesel engines. The amount of fuel being mixed with the air is regulated by the fuel control system to obtain a predefined air-fuel ratio A. There are two different injection systems:

3.2. FUEL CONTROL

1. Manifold injection: T front of the inlet ports. Problems may occur at i( a low air flow velocity ir air flow into the different is less accurate at idling controlled: Errors due t( on the amount of fuel j

of manifold injection is in the cylinder at A =

restrictions for the desi§ optimised without majo the inlet valves. The inle at low engine speed . '] effective work We withol the evaporating fuel. T allows higher compressic is phase-shifted for each before the inlet valve is ( can be controlled indivi for each cylinder: limita at coasting or cylinder s

2. In-cylinder injection: The aim is to assemble a limited portion of th~ the spark plug at the ti pressure (thus fuel atom of injection) and the inj( point. The swirl is cont

The aim is to burn very I injection. By an early . ing throughout the cor to the swirl. The folio' which is burning fast \0

reduced amount of the I

also reduced. The earl afterwards. Since the IT

ing maximum allowable charge, soot was genera' this can be effectively r,

The total amount of injected

• aspirated air flow per ti

• intake manifold pressur

• throttle angle at and it

ANAGEMENT SYSTEMS

the inlet pipe and fuel flow

(3.64)

a proportional part (1 - c) tant T. For wall wetting . the allocated fuel mass:

(3.65)

l~C and a time constant the operation point of the

amic transients by varying imized. Fig 3.20 shows test d effectively leading to less

lilt of possi ble disruptions However, the consequences wetting model is completed time constant.

les

les do not require a spark ation due to compressional ces the ignition angle.

tting range is very impor­i well as on emission rates. wo phases:

,e considerably within this :pends on the temperature, Ivoluted into an equivalent eed.

I phase is almost constant 1 by the piston movement, as the combustion process.

.ion angles, the emission of tudes at advanced ignition

3.3. IGNITION CONTROL IN SI ENGINES 53

<D

§.,., §."".,., (,j <D .....,

·S

'" '" Cl ~ ~

."" '+...,

';) ;l

'+...,

.l compensated not compensated

~ t

.l

~ t

Figure 3 .20 Compensation of fuel film dynamics at a tes t engine

angles increase the emission of NO x ' NO x can be reduced by delaying the ignition at the expense of a higher fuel consumption 2 The following parameters are used to control the ignition angle:

• Intake manifold pressure Pm

• Mass air flow rha

• Engine speed n

• Throttle angle Ctt

• Air-fuel ratio ,A

20ver all, the determination of the right ignition angle is Ii compromise between different objectives.

VAGEMENT SYSTEMS

ence cylinder

'01. The ignition angle O:i

pproximated by injection of engine speed n. This ,-up table also covers the ,ad and speed. Retarded romise for reduced emis­;ermined for each engine

on delay 'd.

rature {)a to avoid knock­loY be used.

<\ retarded ignition angle where the exhaust valves

,alytic converter are then

ignition angles at lower

gles in conjunction with

der to avoid knocking.

tion energy.

engine speed and load.

lportant parameters that of pollutants. This has

re is a conflict between s shown in Figure 3.22. umption, the engine raw n the other hand, if the

3.3. IGNITION CONTROL IN SI ENGINES

Figure 3.21 Ignition angle map

ignition angle is selected to mmlmlse emiSSions, the fuel consumption will be higher. A compromise must consider fuel consumption and emission levels at all engine operating points. Emission levels can be very high at some particular operating points. There, the optimisation must focus on the emissions. Other operating points show acceptable emission rates. At these points the optimisation must focus on fuel consumption.

Fuel consumption and emission levels are mCiL'iured in special road driving cycles like the ECE-test or FTP-test. These tests specify the vehicle velocity over time. Translating vehicle to engine speeds, a test cycle is equivalent to a sequence of different engine operating points over time. Every operating point is defined by several control parameters including engine speed and load.

The fuel consumption can be described by the volume V of combusted fuel over time. The minimisation criterium is the integral over the test cycle.

T

V = .I V(t) dt --; min (3.66)

o

The total fuel consumption V for a test cycle time T can also be obtained by a discrete summation over the engine operating points.

N

V = L Iii (O:i , Ad ti --; min (3.67) i=l

An analysis of the test cycle shows that most operating points are visited several times. The individual time periods where the engine stays in the same operating point i can be summarised into a total time period ti. The fuel consumption over time Iii can then be minimised independently for each operating point. The resulting values of 0:, and Ai are stored into look-up tables O:i(tmj, n) and Ai(tinj , n) for every operating point.

I

55

56 3. ENGINE NIANAGEMENT SYSTEMS

n = 2400 rpm T = 45Nm ,A = 1.13

500 30 7.5

450 20 5

400 10 2.5

350 0 0

Figure 3.22 Fuel consumption and emission levels over ignition angle ai.

When optimising fuel consumption, the maximum allowable emission levels are treated as optimisation constraints. The maximum emission rates are fixed by laws which specify the maximum integral masses of the different pollutants generated during a test cycle.

N

HC LHC(O'",A,) t ; ~ lic (3.68) i= !

N

CO L C'O(O'" ,A , ) ti ~CO (3.69) i=1 N

NO", L NOx(O'i, ,A i ) ti ~ NO", (3.70) i=1

The emission levels per time HC, c'o, NO can be influenced by the values of O'i and ,Ai at each operating point i. The emission limits are only given for the integral mass over the whole test cycle. It is therefore not obvious which 0';

and ,Ai values must be adopted at each operating point i. Such an optimisation problem with constraints can be solved by using the Lagrange multiplication method 14]. The differences between actually achieved and acceptable emission levels are weighted by Lagrange factors L. Equation 3.67 and equations 3.68 to

3.3. IGNITION CONTROL

3.70 are combined into a sin!

Now the cost function W ml were at the acceptable limit consumption would disappea can be divided into two part operating points i and a vari

N

W = L V;(O'i, ,Ai)t;-t

i=1

i=l

-LHelic - Le N

W L Z(O'i, ,Ai)ti ­

i=1

where:

and:

Z(O'i, .

The value of W can be mini] operating point:

Figure 3.23 shows V(O'i, ,Ai) a on ignition angle O'i and air-fl test bed run. The pair O'i,,Ai

It can be seen that fuel slightly higher than the absoh NO",(O'i, ,Ai)' The value W is for the Lagrange factors LHe iterations with modified Lagri which also meets the legal err low fuel consumption V is att