Engine Control

y

JA Co ok JW Grizzle and J Sun

January

Intro duction

Automotive engine control systems must satisfy diverse and often conicting requirements

These include regulating exhaust emissions to meet increasingly stringent standards without

sacricing go o d drivability providing increased fuel economy to satisfy customer desires

and to comply with Corp orate Average Fuel Economy CAFE regulations and delivering

these p erformance ob jectives at low cost with the minimum set of sensors and actuators

The dramatic evolution in vehicle electronic control systems over the past two decades is

substantially in resp onse to the rst of these requirements It is the capacity and exibilityof

micropro cessorbased digital control systems intro duced in the s to address the problem

of emission control which have resulted in the improved function and added convenience

safety and p erformance features that distinguish the mo dern automobile

Although the problem of automotive engine control may encompass a number of dier

ent powerplants the one with which this article is concerned is the ubiquitous four stroke

cycle spark ignition internal combustion gasoline engine Mechanicallythispowerplant has

remained essentially the same since Nikolaus Otto built the rst successful example in

In automotive applications it consists most often of four six or eight cylinders wherein re

cipro cating pistons transmit power via a simple connecting ro d and crankshaft mechanism

Ford Motor Company Scientic Research Lab oratory Control Systems Department Maildrop

SRL Dearb orn MI

y

Department of EECS Control Systems Lab oratoryUniversityofMichigan Ann Arb or MI

work supp orted in part by the National Science Foundation under contract NSF ECS

to the wheels Two complete revolutions of the crankshaft comprise the following sequence

of op erations The initial degrees of crankshaft revolution is the intake stroke where the

piston travels from topdeadcenter TDC in the cylinder to b ottomdeadcenter BDC

During this time an intakevalve in the top of the cylinder is op ened and a combustible mix

ture of air and fuel is drawn in from an intake manifold Subsequent degree increments

of crankshaft revolution comprise the compression stroke where the intake valve is closed

and the mixture is compressed as the piston moves back to the top of the cylinder the com

bustion stroke when after the mixture is ignited by a spark plug torque is generated at the

crankshaft by the downward motion of the piston caused by the expanding gas and nally

the exhaust stroke when the piston moves back up in the cylinder exp elling the pro ducts

of combustion through an exhaust valve Three fundamental control tasks aect emissions

p erformance and fuel economy in the spark ignition engine Airfuel ratio control that is

providing the correct ratio of air and fuel for ecient combustion to the prop er cylinder

at the right time ignition control which refers to ring the appropriate spark plug at the

precise instant required and control of exhaust gas recirculation to the combustion pro cess

to reduce the formation of oxide of nitrogen emissions

Ignition Control

The spark plug is red near the end of the compression stroke as the piston approaches

TDC For any engine sp eed the optimal time during the compression stroke for ignition to

o ccur is the point at which the maximum brake torque MBT is generated Spark timing

signicantly in advance of MBT risks damage from the piston moving against the expanding

gas As the ignition event is retarded from MBT less combustion pressure is develop ed and

more energy is lost to the exhaust stream Numerous metho ds exist for energizing the spark

ts were used to develop a plugs For most of automotive historycam activated breaker poin

high voltage in the secondary windings of an induction coil connected between the battery

and a distributor Inside the distributor a rotating switchsynchronized with the crankshaft

connected the coil to the appropriate spark plug In the early days of motoring the ignition

system control function was accomplished by the driver who manipulated a lever lo cated on

the steering wheel to change ignition timing A driver who neglected to retard the spark when

attempting to start a hand cranked Mo del T Ford could suer a broken arm if he exp erienced

kickback Failing to advance the spark prop erly while driving resulted in less than optimal

fuel economy and power Before long elab orate centrifugal and vacuum driven distributor

systems were develop ed to adjust spark timing with resp ect to engine sp eed and torque

The rst digital electronic engine control systems accomplished ignition timing simply by

mimicking the functionality of their mechanical predecessors Mo dern electronic ignition

systems sense crankshaft p osition to provide accurate cycletime information and may use

barometric pressure engine co olant temp erature and throttle p osition along with engine

sp eed and intake manifold pressure to schedule ignition events for the b est fuel economy and

drivability sub ject to emissions and spark kno ck constraints Additionally ignition timing

may be used to mo dulate torque to improve transmission shift quality and in a feedback

lo op as one control variable to regulate engine idle sp eed In mo dern engines the electronic

control mo dule activates the induction coil in resp onse to the sensed timing and op erating

point information and in concert with dedicated ignition electronics routes the high voltage

to the correct spark plug One metho d of providing timing information to the control system

is by using a magnetic proximity pickup and a to othed wheel driven from the crankshaft

to generate a square wave signal indicating TDC for successive cylinders A signature pulse

of unique duration is often used to establish a reference from which absolute timing can be

determined During the past ten years there has b een substantial research and development

interest in using incylinder piezo electric or piezoresistive combustion pressure sensors for

closedlo op feedback control of individual cylinder spark timing to MBT or to the kno ck

limit The advantages of combustion pressure based ignition control are reduced calibration

and increased robustness to variability in manufacturing environment fuel and due to

comp onent aging The cost is in an increased sensor set and additional computing power

Exhaust Gas Recirculation

Exhaust gas recirculation EGR systems were intro duced as early as to control emis

sions of oxides of nitrogen NOx The principle of EGR is to reduce NOx formation during

the combustion pro cess by diluting the inducted airfuel charge with inert exhaust gas In

electronically controlled EGR systems this is accomplished using a metering orice in the

exhaust manifold to enable a p ortion of the exhaust gas to ow from the exhaust manifold

through a vacuum actuated EGR control valve and into the intake manifold Feedback based

on the dierence b etween the desired and measured pressure drop across the metering orice

is employed to duty cycle mo dulate a vacuum regulator controlling the EGR valve pintle

p osition Because manifold pressure rate and engine torque are directly inuenced by EGR

the dynamics of the system can have a signicant eect on engine resp onse and ultimately

vehicle drivability Such dynamics are dominated bythevalvechamb er lling resp onse time

to changes in the EGR duty cycle command The system can be represented as a pure

transp ort delay asso ciated with the time required to build up sucient vacuum to overcome

pintle shaft friction cascaded with rst order dynamics incorp orating a time constantwhich

is a function of engine exhaust ow rate Typically the EGR control algorithm is a simple

PI or PID lo op Nonetheless careful control design is required to provide good emission

control without sacricing vehicle p erformance An unconventional metho d to accomplish

NOx control by exhaust recirculation is to directly manipulate the timing of the intake and

exhaust valves Variable cam timing VCT engines have demonstrated NOx control using

mechanical and hydraulic actuators to adjust valve timing and aect the amountofinternal

EGR remaining in the cylinder after the exhaust stroke is completed Early exhaust valve

closing has the additional advantage that unburned hydro carb ons normally emitted to the

exhaust stream are recycled through a second com bustion event reducing HC emissions as

well Although VCT engines eliminate the normal EGR system dynamics the fundamentally

multivariable nature of the resulting system presages a dicult engine control problem

AirFuel Ratio Control

Historically fuel control was accomplished by a carburetor which used a venturi arrangement

and simple oat and valve mechanism to meter the prop er amount of fuel to the engine For

sp ecial op erating conditions such as idle or acceleration additional mechanical and vacuum

circuitry was required to assure satisfactory engine op eration and go o d drivability The

demise of the carburetor was o ccasioned by the advent of threeway catalytic converters

TWC for emission control These devices simultaneously convert oxidizing HC and CO

and reducing NOx sp ecies in the exhaust but as shown in Figure require precise control

of airfuel ratio AF to the stoichiometric value to b e eective Consequently the electronic

100

90

80 GROSS NOx 70 HC 60 CO 50

40

30

20

10 HC, CO, NO CONVERSION EFFICIENCIES (%)

0 14.2 14.4 14.6 14.8

MEAN A/F

Figure Typical TWC Eciency Curves

fuel system of a mo dern spark ignition automobile engine employs individual fuel injectors

lo cated in the inlet manifold runners close to the intake valves to deliver accurately timed

and metered fuel to all cylinders The injectors are regulated by an airfuel ratio control

system which has two primary comp onents a feedback p ortion in which a signal related

to AF from an exhaust gas oxygen EGO sensor is fed back through a digital controller

to regulate the pulse width command sent to the fuel injectors and a feedforward p ortion

in which injector fuel ow is adjusted in resp onse to a signal from an air ow meter The

feedback or closedlo op p ortion of the control system is fully eective only under steady

state conditions and when the EGO sensor has attained the prop er op erating temp erature

The op enlo op or feedforward p ortion of the control system is particularly imp ortantwhen

the engine is cold b efore the closedlo op AF control is op erational and during transient

op eration when the signicant delaybetween the injection of fuel usually during the exhaust

stroke just b efore the intakevalve op ens and the app earance of a signal at the EGO sensor

p ossibly long after the conclusion of the exhaust stroke inhibits go o d control In Section

the op enlo op AF control problem will be examined with emphasis on accounting for

sensor dynamics The closedlo op problem will be addressed in Section from a mo dern

control systems p ersp ective where individual cylinder control of AF is accomplished using

a single EGO sensor

Idle Sp eed Control

In addition to these essential tasks of controlling ignition AF and EGR the typical on

b oard micropro cessor p erforms many other diagnostic and control functions These include

electric fan control purge control of the evap orative emissions canister turb o charged engine

wastegate control oversp eed control electronic transmission shift scheduling and control

cruise control and idle sp eed control ISC The ISC requirement is to maintain constant

engine RPM at closed throttle while rejecting disturbances such as automatic transmission

neutraltodrive transition air conditioner compressor engagement and p ower steering lo ck

up The idle sp eed problem is a dicult one esp ecially for small engines at low sp eeds

where marginal torque reserve is available for disturbance rejection The problem is made

more challenging by the fact that signicant parameter variation can be exp ected over the

substantial range of environmental conditions in which the engine must op erate Finallythe

idle sp eed control design is sub ject not only to quantitative p erformance requirements such

as oversho ot and settling time but also to more sub jective measures of p erformance such as

idle quality and the degree of noise and vibration communicated to the driver through the

body structure The idle sp eed control problem will be addressed in Section

Air Fuel Ratio Control System Design

Due to the precipitous fall o of TWC eciency away from stoichiometry the primary

ob jective of the AF control system is to maintain the fuel metering in a stoichiometric

prop ortion to the incoming air ow the only exception to this o ccurs in heavy load situations

where a rich mixture is required to avoid premature detonation or kno ck and keep the TWC

from overheating V ariation in air ow commanded by the driver is treated as a disturbance

to the system A blo ck diagram of the control structure is illustrated in Figure and the

two ma jor sub comp onents treated here are highlighted in b old Subsection describ es

CAC Cylinder Air Charge Speed Stoichiometric Estimator MAF A/F Air Tailpipe Base Fuel + Fuel ENGINE Exhaust Emissions TWC + Feedforward

Feedback EGO

- A/F Controller + Stoichiometric

A/F

Figure Basic AF Control Lo op Showing Ma jor Feedforward and Feedback Elements

the development and implementation of a cylinder air charge estimator for predicting the

air charge entering the cylinders downstream of the intake manifold plenum on the basis

of available measurements of air mass ow rate upstream of the throttle The air charge

estimate is used to form the base fuel calculation which is often then mo died to account

for any fuel puddling dynamics and the delay asso ciated with closedvalve fuel injection

timing Finally a classical timeinvariant singleinput singleoutput SISO PI controller

is normally used to correct for any p ersistent errors in the op en lo op fuel calculation by

adjusting the average AF to p erceived stoichiometry

Even if the average AF is controlled to stoichiometry individual cylinders may be op

erating consistently rich or lean of the desired value This cylindertocylinder AF mald

istribution is due in part to injector variability Consequently fuel injectors are machined

to close tolerances to avoid individual cylinder ow discrepancies resulting in high cost per

injector Ho wever even if the injectors are p erfectly matched maldistribution can arise from

individual cylinders having dierent breathing characteristics due to a combination of factors

such as intake manifold conguration and valve characteristics It is known that such AF

maldistribution can result in increased emissions due to shifts in the closedlo op AF set

point relative to the TWC Subsection describ es the development of a nonclassical

p erio dically timevarying controller for tuning the AF in each cylinder to eliminate this

maldistribution

Hardware Assumptions The mo deling and control metho ds presented here are applicable

to just ab out any fuel injected engine For illustration purp oses only it is assumed that the

engine is a p ort fuel injected V with indep endent fuel control for each bank of cylinders

The cylinders are numb ered one through four starting from the front of the right bank and

ve through starting from the front of the left bank The ring order of the engine is

which is not symmetric from bank to bank Fuel injection is timed to o ccur

on a closed valve prior to the intake stroke induction event For the purp ose of closedlo op

control the engine is equipp ed with a switchingtyp e EGO sensor lo cated at the conuence

of the individual exhaust runners and just upstream of the catalytic converter Such sensors

typically incorp orate a ZrO ceramic thimble employing a platinum catalyst on the exterior

surface to equilibrate the exhaust gas mixture The interior surface of the sensor is exp osed

to the ratio of O partial to the atmosphere The output voltage is exp onentially related

pressures across the ceramic and thus the sensor is essentially a switching device indicating

by its state whether the exhaust gas is rich or lean of stoichiometry

Cylinder Air Charge Computation

This subsection describ es the development and implementation of an air charge estimator

for an eight cylinder engine A very real practical problem is posed by the fact that the

hotwire anemometers currently used to measure mass air ow rate have relatively slow

dynamics Indeed the time constant of this sensor is often on the order of an induction

event for an engine sp eed of revolutions p er minute and is only ab out four to ve times

faster than the dynamics of the intake manifold Taking these dynamics into accountinthe

air charge estimation algorithm can signicantly improve the accuracy of the algorithm and

ha ve substantial b enets for reducing emissions

Basic mo del

The air path of a typical engine is depicted in Figure An asso ciated lump ed parameter

phenomenological mo del suitable for developing an online cylinder air charge estimator

is now describ ed Let P V T and m b e the pressure in the intake manifold psi volume of

the intake manifold and runners liters temp erature R and mass lbm of the air in the

intake manifold resp ectively Invoking the ideal gas law and assuming that the manifold

air temp erature is slowly varying leads to

d RT

P MAF CylN P T T

a EC i

dt V

where MAF is the actual mass air ow metered in by the throttle R is the molar gas

a

constant CylN P T T is the average instantaneous air ow pump ed out of the intake

EC i

manifold by the cylinders as a function of engine sp eed N RPM manifold pressure engine

o o

co olant temp erature T R and air inlet temp erature T R It is assumed that b oth

EC i

MAF and CylN P T T have units of lbmsec

a EC i

The dep endence of the cylinder pumping or induction function on variations of the engine

co olant and air inlet temp eratures is mo deled empirically by page as

v

mapping

u

T T

u

i

EC

t

CylN P T T CylN P

EC i

mapping

T

EC

T

i Hot Wire Probe Electronic Circuit Throttle

Intake Manifold Runner

Intake Valve

Exhaust

Valve

Figure Schematic of Air Path in Engine

o

where the sup erscript mapping denotes the corresp onding temp eratures R at which the

function CylN P is determined based on engine mapping data An explicit pro cedure for

determining this function is explained in Subsection

Cylinder air charge p er induction event CAC can b e determined directly from In

steady state the integral of the mass ow rate of air pump ed out of the intake manifold over

two engine revolutions divided by the number of cylinders is the air charge per cylinder

Since engine sp eed is nearly constant over a single induction event and the time in seconds



for two engine revolutions is a go o d approximation of the inducted air charge on a per

N

cylinder basis is given by

CylN P T T lbm CAC

EC i

nN

where n is the number of cylinders

The nal element to be incorp orated in the mo del is the mass air ow meter The

imp ortance of including this was demonstrated in For the purp ose of achieving rapid

online computations a simple rst order mo del will b e used

d

MAF MAF MAF

m m a

dt

where MAF is the measured mass air ow and is the time constant of the air meter

m

Substituting the left hand side of for MAF in yields

a

RT d d

P MAF MAF CylN P T T

m m EC i

dt V dt

RT

To eliminate the derivative of MAF in the ab ove equation let x P MAF This

m m

V

yields

RT RT d

x MAF CylN x MAF T T

m m EC i

dt V V

Cylinder air charge is then computed from as

RT

CAC CylN x MAF T T

m EC i

nN V

Note that the eect of including the mass air ow meters dynamics is to add a feedforward

term involving the mass air ow rate to the cylinder air charge computation When

and reduce to an estimator which ignores the air meters dynamics or equivalently

treats the sensor as b eing innitely fast

Determining Mo del Parameters

The pumping function CylN P can be determined on the basis of steadystate engine

mapping data Equip the engine with a high bandwidth manifold absolute pressure sensor

and exercise the engine over the full range of sp eed and load conditions while recording

the steadystate v alue of the instantaneous mass air ow rate as a function of engine sp eed

and manifold pressure For this purp ose any external exhaust gas recirculation should be

disabled Atypical data set should cover every RPM of engine sp eed from to

RPM and every half psi of manifold pressure from psi to atmosphere For the purp ose

of making these measurements it is preferable to use a laminar air ow element as this

the will in addition allow the calibration of the mass air ow meter to be veried Record

engine co olant and air inlet temp eratures for use in The function CylN P can be

represented as a table lo okup or as a p olynomial regressed against the ab ove mapping data

In either case it is common to represent it in the following functional form

CylN P N P N

The time constant of the air meter is b est determined by installing the meter on a ow

bench and applying step or rapid sinusoidal variations in air ow to the meter Metho ds

for tting an approximate rst order mo del to the data can be found in any textb o ok on

classical control Atypical value is ms Though not highly recommended avalue for

the time constant can b e determined byonvehicle calibration if an accurate determination

of the pumping function has b een completed This is explained at the end of Subsection

Mo del Discretization and Validation

The estimator and must b e discretized for implementation In engine mo dels an

event based sampling scheme is often used For illustration purp oses the discretization

will b e carried out here for a V the mo dications required for other congurations will be

evident Let k be the recursion index and let t be the elapsed time in seconds per

k

 

degrees of crankangle advancement or revolution that is t sec where N is the

k k

 N

k

current engine sp eed in RPM Then can b e Euler integrated as

RT RT

k  k 

MAF CylN x MAF T T x x t

mk  k  k  mk  EC i k k  k

V V

The cylinder air charge is calculated by

RT

k

MAF T T CAC t CylN x

mk EC i k k k k

V

and need only be computed once per crankangle degrees

The accuracy of the cylinder air charge mo del can be easily validated on an engine

dynamometer equipp ed to maintain constant engine sp eed Apply very rapid throttle tip

ins and tipouts as in Figure while holding the engine sp eed constant If the mo del

parameters have b een prop erly determined the calculated manifold pressure will accurately

track the measured manifold pressure Figure illustrates one such test at RPM The

dynamic resp onses of the measured and computed values match up quite well There is

some inaccuracy in the quasisteady state values at psi this corresp onds to an error in

the pumping function CylN P at high manifold pressures so in this op erating condition

it should be reevaluated 100

80

60

40

Throttle Position 20

0 0 0.5 1 1.5 2 2.5 Seconds

0.15

0.1

0.05 MAF in LBm per Sec 0 0 0.5 1 1.5 2 2.5

Seconds

Figure Engine Op erating Conditions at Nominal RPM

From Figure it can be seen that the air meter time constant has been accurately

identied in this test If the value for in had b een chosen to o large then the computed

manifold pressure would be leading the measured manifold pressure conversely if were

to o small the computed value would lag the measured value

Eliminating AF Maldistribution through Feedback Control

Airfuel ratio maldistribution is evidenced by very rapid switching of the EGO sensor on

an engineeventbyengineevent basis Such cylindertocylinder AF maldistribution can

result in increased emissions due to shifts in the closed lo op AF setp oint relative to the

TWC The trivial control solution which consists of placing individual EGO sensors in

each exhaust runner and wrapping indep endent PI controllers around each injectorsensor

pair is not acceptable from an economic p oint of view technically there would also be

problems due to the nonequilibrium condition of the exhaust gas immediately up on exiting

the cylinder This subsection details the development of a controller which eliminates AF

maldistribution on the basis of a single EGO sensor per engine bank The controller is

develop ed for the left bank of the engine 14 __ MAP Computed

12 -- MAP Measured

10

8

6 Manifold Pressure in PSI 4

2

0 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Seconds

Figure Comparison of Measured and Computed Manifold Pressure

Basic Mo del

A control oriented blo ck diagram mo del for the AF system of the left bank of an eight

cylinder engine is depicted in Figure The mo del evolves at an engine sp eeddep endent

sampling interval of crankangle degrees consistent with the cylinder geometry one

exhaust event o ccurs every degrees of crankshaft rotation The engine is represented by

d

injector gains G through G and pure delay z which accounts for the numb er of engine

events that o ccur from the time that an individual cylinders fuel injector pulsewidth is

computed until the corresp onding exhaust valve op ens to admit the mixture to the exhaust

manifold The transfer function Hz represents the mixing pro cess of the exhaust gases from

the individual exhaust p orts to the EGO sensor lo cation including any transp ort delay The

switchingtyp e EGO sensor is represented by a rst order transfer function followed by a

preload switch nonlinearity

Note that only cylinders through are inputs to the mixing mo del Hz This is due to

the fact that the separate banks of the V engine are controlled indep endently The gains and

delays for cylinders through corresp ond to the right bank of the engine and are included

in the diagram only to represent the ring order Note furthermore that cylinders and Exhaust -d G1 z E (k) Runners and 1 Induction-to- -d Power Stroke G3 z E (k) 3 Lag -d G7 z E (k) 14.64 7 η(k) Y(k) -d G2 +1 u(k) z E (k) 1 − 2 H(z) τ + ++ 14.64 1 -d s+1 −1 G6 z E (k) Τ 6 Exhaust G5 -d Manifold EGO SENSOR z E (k) 5 Mixing G4 -d z E (k) 4 -d G8 z E (k) 8 T = 90¡ ENGINE and EXHAUST

CONTROLLER 1

Τ

Figure Control Oriented Blo ck Diagram of AF Subsystem

exhaust within degrees of one another whereas cylinders and exhaust degrees

apart Since the exhaust stroke of cylinder is not complete b efore the exhaust stroke of

cylinder commences for any exhaust manifold conguration there will be mixing of the

exhaust gases from these cylinders at the point where the EGO sensor samples the exhaust

gas We will adopt the notation that the sampling index k isamultiple of degrees that

alue is xk is the quantity x at k degrees moreover if we are lo oking at a signals v

during a particular point of an engine cycle then we will denote this by xk j which is

x at k j degrees or x at the j th event of the k th engine cycle The initial time

will be taken as k at top dead center TDC of the compression stroke of cylinder

The basic mo del for a V or a four cylinder engine is simpler see

A dynamic mo del of the exhaust manifold mixing is dicult to determine with current

technology This is b ecause a linear AF measurement is required and currently such

sensors have a slow dynamic resp onse in comparison with the time duration of an individ

ual cylinder event Hence standard system identication metho ds break down In a

mo del structure for the mixing dynamics and an attendant mo del parameter identication

pro cedure compatible with existing lab oratory sensors is provided This is outlined next

The key assumption used to develop a mathematical mo del of the exhaust gas mixing is

that once the exhaust gas from any particular cylinder reaches the EGO sensor the exhaust

of that cylinder from the previous cycle two revolutions has b een completely evacuated from

the exhaust manifold It is further assumed that the transp ort lag from the exhaust port of

180 DEGREES 720 DEGREES = ONE ENGINE CYCLE

Sample Time 8k-48k-3 8k-2 8k-1 8k 8k+1 8k+2 8k+3 8k+4 8k+5 8k+6 8k+7 8k+8 8k+9 8k+10 8k+11 8k+12

INTAKE COMPRESSION POWER EXHAUST INTAKE COMPRESSION POWER EXHAUST CYLINDER 1

EXHAUST INTAKE COMPRESSION POWER EXHAUST INTAKE COMPRESSION POWER EXHAUST CYLINDER 3

EXHAUST INTAKE COMPRESSION POWER EXHAUST INTAKE COMPRESSION POWER CYLINDER 7

POWER EXHAUST INTAKE COMPRESSION POWER EXHAUST INTAKE COMPRESSION POWER CYLINDER 2

POWER EXHAUST INTAKE COMPRESSION POWER EXHAUST INTAKE COMPRESSION CYLINDER 6

COMPRESSION POWER EXHAUST INTAKE COMPRESSION POWER EXHAUST INTAKE COMPRESSION CYLINDER 5

COMPRESSION POWER EXHAUST INTAKE COMPRESSION POWER EXHAUST INTAKE CYLINDER 4

INTAKE COMPRESSION POWER EXHAUST INTAKE COMPRESSION POWER EXHAUST INTAKE

CYLINDER 8

Figure Timing Diagram for Cylinder Engine

any cylinder to the sensor lo cation is less than two engine cycles With these assumptions

and with reference to the timing diagram of Figure a mo del for the exhaust mixing

dynamics may be expressed as relating the AF at the sensor over one crankangle

degree p erio d b eginning at k as a linear combination of the airfuel ratios admitted to the

exhaust manifold by cylinder during the exhaust strokes o ccurring at times k k

and k by cylinder at k k and k by cylinder at k k and

y k and by cylinder atk k and k This relationship is given b

k

E k



a k a a a

   

E k



E k



a a k a a

   

E k



k

E k E k

 

a a

 

E k E k

 

E k E k

 

a a

 

E k E k

 

where is the actual AF at the pro duction sensor lo cation E is the exhaust gas AF

n

from cylinder n n and a is the time dep endent fraction of the exhaust gas from

n

cylinder n contributing to the air fuel ratio at the sensor It follows from the key assumption

that only of the co ecients in equation can b e nonzero Sp ecicallyevery triplet

fa k a k a k g has at most one nonzero element This will b e exploited in the

n n n

mo del parameter identication pro cedure

Determining Mo del Parameters

d

The pure delay z is determined bythetyp e of injection timing used op en or closedvalve

and do es not vary with engine sp eed or load Atypical value for closedvalve injection timing

is d The time constant of the EGO sensor is normally provided by the manufacturer if

not it can b e estimated b y installing it directly in the exhaust runner of one of the cylinders

and controlling the fuel pulsewidth to cause a switch from rich to lean and then lean to rich

A typical average value of these two times is ms

The rst step towards identifying the parameters in the exhaust mixing mo del is to

determine which one of the parameters fa k a k a k g is the p ossibly nonzero

n n n

element this can be uniquely determined on the basis of the transp ort delay between the

op ening of the exhaust valve of each cylinder and the time of arrival of the corresp onding

exhaust gas pulse at the EGO sensor The measurement of this delay is accomplished by

installing the fast switching typ e EGO sensor in the exhaust manifold in the pro duction

lo cation and carefully balancing the AF of each cylinder to the stoichiometric value Then

apply a step change in AF to each cylinder and observe the time delay The results of a

typical test are given in The transp ort delays will change as a function of engine sp eed

In addition they may and load and thus should be determined at several op erating p oints

not be a multiple of degrees A practical metho d to account for these issues through a

slightly more sophisticated sampling schedule is outlined in

At steady state equation reduces to

k

E k



k

E k



A

mix

E k



k

E k



k

where

P P

a j a j

 

j  j 

A

mix

P P

a j a j

 

j  j 

This leads to the second part of the parameter identication pro cedure in which the values of

the summed co ecients of equation may b e identied from steady state exp eriments

p erformed with a linear EGO sensor installed in the pro duction lo cation Then knowing

which of the co ecients is nonzero equation may be evaluated

Install a linear EGO sensor in the pro duction lo cation Then the measured AF resp onse

y k to the sensor input k is mo deled by

w k w k k

y k w k

T

L

where e is the time constant of the linear EGO sensor and T is the sampling

L

interval that is the amount of time per degrees of crankangle advance It follows

that the combined steady state mo del of exhaust mixing and linear EGO sensor dynamics is

Y Q A E

s mix

where

y k

E k



y k

E k



E Y

E k



y k

E k



y k

and

 

 

Q

s



    

     

Next carefully balance each of the cylinders to the stoichiometric AF and then oset

each cylinder succesively AF rich and then AF lean to assess the eect on the AF at

the sensor lo cation At each condition let the system reach steady state and then record Y

and E over three to ten engine cycles averaging the comp onents of each vector in order to

y in the combustion pro cess This minimize the impact of noise and cycle to cycle variabilit

   

will provide input AF vectors E E E and output AF vectors Z Y Y where

the overbar represents the averaged value The least squares solution to is then given

by

 T T 

A Q Z E E E

mix

s

The identied co ecients of A should satisfy two conditions the entries in the

mix

matrix lie in the in terval the sum of the entries in any row of the matrix is

unity These conditions corresp ond to no chemical pro cesses o ccurring in the exhaust system

which could mo dify the AF between the exhaust valve and the EGO sensor Inherent

nonlinearities in the linear EGO sensor or errors in the identication of its time constant

often lead to violations of these conditions In this case the following x is suggested For

each row of the matrix identify the largest negative entry and subtract it from each entry

so that all are nonnegative then scale the row so that its entries sum to one

Assembling and Validating the State Space Mo del

A state space mo del will b e used for control law design The combined dynamics of the AF

system from the fuel scheduler to the EGO sensor is shown in Figure The co ecients

k k arise from constructing a state space representation of and thus are

 

directly related to the a k j In particular they are p erio dic with period equal to one

n x8 x9 x24 u(k) G(k) z -8 z -1 z -1 ... z -1

Induction-to-Power κ (k) κ (k) κ (k) Stroke 1 2 16 + EGO Fuel Scheduling Sensor x -T/τ 25 ++ ++ -1 ... 1-e ++ z η(k) y(k) -T/τ

e

Figure Perio dically Time Varying Mo del of Engine Showing State Variable Assignments

engine cycle Figure provides an example of these co ecients for the mo del identied in

Assigning state variables as indicated the state space mo del can b e expressed as

κ κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) κ (k) k 1(k) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0 00000a (1,1) 000 0 0 0 0 a6(1,1) a7(1,1) a8(1,1) a5(1,2)

1 00a (2,1) 0a (2,1) 000 a (2,1) 0 0 0 0 0 0 0 6 7 8 a5(2,2)

2 0 0 a (3,1) 0 a (3,1) 0 0 0 0 0 0 0 0 0 a8(3,0) 6 7 a5(3,2)

3 0 a (4,0) 0 0 a (4,1) 0 a (4,1) 0 0 0 0 0 0 0 0 8 6 7 a5(4,2)

4 0 0 a (5,0) 0 0 a (5,1) 0 a (5,1) 0 0 0 0 0 0 0 8 6 7 a5(5,2)

5 0 00a (6,0) 00a (6,1) 0 a (6,1) 0 0 0 0 0 0 8 6 7 a5(6,2)

6 0 a (7,0) 00a (7,0) 0 0 a (7,1) 0 0 0 0 0 0 0 7 8 6 a5(7,2)

7 00a (8,0) 00a (8,0) 000a (8,1) 0 0 0 0 00

7 8 6 a5(8,2)

Figure Time Dep endent Co ecients for Figure

xk Ak xk B k uk

y k C k xk

This is an p erio dic SISO system

For control design it is convenient to transform this system via lifting to a linear

T

timeinvariant MIMO system as follows Let x k xk Y k y k yk

T

U k uk uk Then

xk Axk BU k

Y k C xk DU k

where A AA AA

B AA AB AA AB AB B

C

C A

C

C A A

C A A

C B

D

C A AB C A AB

C A AB C A AB C B

Normally D is identically zero b ecause the time delay separating the input from the sensor

is greater than one engine cycle Since only cylinders through are to b e controlled the B

and D matrices may be reduced by eliminating the columns that corresp ond to the control

variables for cylinders through This results in a system mo del with inputs and

outputs

Additional data should b e taken to validate the identied mo del of the AF system An

example of the exp erimental and mo deled resp onse to aunit step input in AF is shown in

Figure

Control Algorithm for ICAFC

The rst step is to check the feasibility of indep endently controlling the AF in the four



cylinders This will be p ossible if and only if the mo del with all of the injector

gains set to unity has full rank at dc no transmission zeros at To evaluate this

compute the dcgain of the system



G C I A B D

dc

Since the mo del is asymptotically stable it is automatically stabilizable and detectable



Physically this corresp onds to b eing able to use constant injector inputs to arbitrarily adjust the AF

in the individual cylinders needs necessary ber mo del be y b will system side are the alues should b e no larger or the regulation problem F input hardw dc the G of the on k cylinders k BU done V on all be k a redesign k trol x can A U con then t This k Y setp oin k k to o large alue decomp osition SVD of x step U tegrators in next ratio is individual four e to the If the with hiev Comparison of Actual and Mo deled Step Resp onse for Cylinder Num e ac ted to four pro ceeding order augmen Figure the In to b e b efore to b e feasible the ratio of the largestthan to four the to fourth v largest singular v and then compute the singular v latter the do Model Response, A/F Input Command, volts Sensor Output, volts 13.00 13.50 14.00 14.50 15.00 -0.20 0.00 0.20 0.40 0.60 0.50 0.60 0.70 0.80 0.80 o T 00 0. 600 0. 10. 10. 10. 20. 20. 20. 00030. 3600.0 3300.0 3000.0 2700.0 2400.0 2100.0 1800.0 1500.0 1200.0 900.0 600.0 300.0 0.0 3600.0 3300.0 3000.0 2700.0 2400.0 2100.0 1800.0 1500.0 1200.0 900.0 600.0 300.0 0.0 3600.0 3300.0 3000.0 2700.0 2400.0 2100.0 1800.0 1500.0 1200.0 900.0 600.0 300.0 0.0 MODELED vs.ACTUALSTEPRESPONSEforCYLINDER6 side k DU output k Crank Angle,degrees Crank Angle,degrees Crank Angle,degrees the x C on or ariable v trol con new the is k V where

comp onents of Y which are to be regulated to stoichiometry must be selected One way to

do this is to cho ose four comp onents of Y on the basis of achieving the best numerically

conditioned dcgain matrix when the other four output comp onents are deleted Denote the

resulting reduced output by Y k Then integrators can be added as

xk Ax k BU k

W k W k Y k

m

Y k C xk DU k

where Y is the error b etween the measured value of Y and the stoichiometric setp oint

m

In either case it is nowvery easy to design a stabilizing controller by a host of techniques

presented in this handb o ok For implementation purp oses the order of the resulting con

troller can normally be signicantly lowered through the use of mo del reduction metho ds

Other issues dealing with implementation are discussed in such as how to incorp orate the

switching asp ect of the sensor into the nal controller and how to prop erly schedule the com

puted control signals Sp ecic examples of such controllers eliminating AF maldistribution

are given in and

Idle Sp eed Con trol

Engine idle is one of the most frequently encountered op erating conditions for city driving

The quality of idle sp eed control ISC aects almost every asp ect of vehicle p erformance

such as fuel economy emissions drivability etc The ISC problem has b een extensively

studied and a comprehensive overview of the sub ject can be found in

The primary ob jective for idle sp eed control is to maintain the engine sp eed at a desired

setp oint in the presence of various load disturbances The key factors to b e considered in its

design include

Engine sp eed setp oint To maximize fuel economy the reference engine sp eed is

scheduled at the minimum that yields acceptable combustion quality accessory drive

requirements and noise vibration and harshness NVH prop erties As the automotive

industry strives to reduce fuel consumption by lowering the idle sp eed the problems

asso ciated with the idle quality suchasallowable sp eed dro op and recovery transient

combustion quality and engine vibration etc tend to b e magnied and thus put more

stringent requirements on the p erformance of the control system

Accessory load disturbances Typical loads in to days automobile include air con

ditioning power steering power windows neutraltodrive shift alternator loads etc

Their characteristics and range of op eration will determine the complexity of the con

trol design and achievable p erformance

Control authority and actuator limitations The control variables for ISC are air

ow regulated by the throttle or a bypass valv e and spark timing Other variables

such as AF also aect engine op eration but AF is not considered as a control

variable for ISC b ecause it is the primary handle on emissions The air bypass valve

or throttle and spark timing are sub ject to constraints imp osed by the hardware itself

as well as other engine control design considerations For example in order to give

spark enough control authority to resp ond to the load disturbances it is necessary

to retard it from MBT to provide appreciable torque reserve On the other hand

y asso ciated with the retarded spark which in theory can be there is a fuel penalt

comp ensated by the lower idle sp eed allowed by the increased control authority of

spark The optimal tradeo however diers from engine to engine and needs to be

evaluated by taking into consideration combustion quality and the ignition hardware

constraints the physical time required for arming the coil and ring the next spark

imp oses a limitation on the allowable spark advance increase between two consecutive

events

Available measurement Typically only engine sp eed is used for ISC feedback

Manifold absolute pressure MAP or inferred MAP is also used in some designs Ac

cessory load sensors such as the air conditioning switch neutraltodrive shift switch

power steering pressure sensor etc are installed in manyvehicles to provide informa

tion on load disturbances for feedforward control

Variations in engine characteristics over the entire op erating range The

ISC design has to consider dierent op erational and environmental conditions such

as temp erature altitude etc To meet the p erformance ob jectives for a large eet of

vehicles throughout their entire engine life the control system has to b e robust enough

to incorp orate changes in the plant dynamics due to aging and unittounit variability

The selection of desired engine setp oint and spark retard is a sophisticated design trade

o pro cess and is beyond the scop e of this article The control problem addressed here is

the sp eed tracking problem which can be formally stated as For a given desired engine

speed setpoint design a control ler which based on the measured engine speed generates

commands for the air bypass valve and spark timing to minimize engine speed variations

from the setpoint in the presence of load disturbances A schematic control system diagram

is shown in Figure

Air Bypass Valve Position

Intake Manifold

Engine Coolant Air Charge Temperature Temperature Electronic Control Unit Ignition Timing

Engine Speed

Figure SensorActuator Conguration for ISC

Engine Mo dels for ISC

An engine mo del which encompasses the most imp ortant characteristics and dynamics of

engine idle op eration is given in Figure It uses the mo del structure develop ed in and

consists of the actuator characteristics manifold lling dynamics engine pumping charac

teristics intaketop ower stroke delay torque characteristics and engine rotational dynamics

EGR is not considered at idle The assumption of sonic ow through the throttle generally

A/F Load Spark Torque

Rotational MAF Dynamics

uP- K - K N f (u) + Cyl(N,P) Delay fT + a S Je S Air Bypass Manifold Engine Engine

Valve Filling Pumping Torque

Figure Nonlinear Engine Mo del

satised at idle has led to a much simplied mo del where the air ow across the throttle

is only a function of the throttle p osition The dierential equations describing the overall

dynamics are given by

MAF f u

a

P K MAF m

m

m CylN P

J N T T

e q L

rt t T t f mt Nt

q T

u duty cycle for the airbypass valve

r AF ratio

where

spark timing in terms of crank angle degrees b efore top dead center

T load torque

L

J and K in are two engine dep endent constants where J represents the engine

e m e

rotational inertia and K is a function of the gas constant air temp erature manifold

m

volume etc Both J and K can b e determined from engine design sp ecications and given

e m

in the engine mo del equals approximately nominal op erating conditions The time delay

degrees of crankangle advance and thus is a sp eed dep endent parameter This is one

reason that mo dels for ISC often use crank angle instead of time as the indep endentvariable

Additionally most engine control activities are event driven and synchronized with crank

dM dP dM dP

p osition the use of and instead of resp ectively tends to have a linearizing

d d dt dt

eect on the pumping and torque generation blo cks

Performing a standard linearization pro cedure results in the linear mo del shown in Figure

with inputs u T the change of the bypass valve duty cycle spark and load

L

torque from their nominal values resp ectively and output N the deviation of the idle

sp eed from the setp oint The time delay in the continuoustime feedback lo op usually

complicates the control design and analysis tasks In a discretetime representation however

Δδ 0.1058 ΔTL Manifold Engine

Dynamics Delay Dynamics

Δ - u 7.89 -0.04s + + 34.96 + 11.15 + Δ - 0.195 s + 1 e 0.227 s + 1 N

0.00093

Engine

Pumping

Figure Linearized Mo del for Typical Cylinder Engine

n

the time delay in Figure corresp onds to a rational transfer function z where n is an

integer that dep ends on the sampling scheme and the number of cylinders It is generally

more convenient to accomplish the controller design using a discretetime mo del

Determining Mo del Parameters

In the engine mo del of the nonlinear algebraic functions f f Cyl describ e char

a T

acteristics of the air bypass valve torque generation and engine pumping blo cks These

functions can be obtained b y regressing engine dynamometer test data using least squares

or other curve tting algorithms The torque generation function is develop ed on the engine

dynamometer by individually sweeping ignition timing AF and mass ow rate regulated

by throttle or air bypass valve p osition over their exp ected values across the idle op erating

sp eed range For atypical eight cylinder engine the torque regression is given by

T f MAFN r

q T

MAF N r MAF



N r MAF N MAF r

MAF N r N r

The steadystate sp eedtorque relation to spark advance is illustrated in Figure

30

27

N=1000rpm 24

21

18 N=680rpm

Engine torque(ft-lb) 15

12

9

6 3 6 9 12 15 18 21 24 27 30 33 36

Spark(degrees BTC)

Figure SparkTorque Relation for Dierent Engine Sp eeds with AF

For choked ie sonic ow the bypass valves static relationship is develop ed simply by

exercising the actuator over its op erating envelop e and measuring mass airow using a hot

wire anemometer or volume owby measuring the pressure drop across a calibrated laminar

ow element The dynamic elements in the linearized idle sp eed mo del can be obtained by

linearizing the mo del in Subsection or they can b e estimated byevaluating small step

resp onse data from a dynamometer In particular the intake manifold time constant can b e

validated by constant sp eed sonic ow throttle step tests using a suciently high bandwidth

sensor to measure manifold pressure

ISC Controller Design

The ISC problem lends itself to the application of various control design techniques Many

dierent design metho dologies ranging from classical such as PID to mo dern such as

LQG H adaptive etc and nonconventional such as neural networks and fuzzy logic



designs have been discussed and implemented The mathematical mo dels describ ed in

Section and commercially available software to ols can b e used to design dierent control

strategies dep ending on the implementors preference and exp erience A general ISC system

with b oth feedforward and feedback comp onents is shown in the blo ck diagram of Figure

Load Disturbance Load Sensor

Air Bypass Valve Feed Forward Control

Desired Engine Speed Error Air Engine Speed

+ Air Bypass Valve + - + Engine Speed Feedback Control

Spark Spark

Feedback Control

Figure General ISC System with Feedforward and Feedback Elements

Feedforward control design

Feedforward control is considered as an eective mechanism to reject load disturbances

esp ecially for small engines When a disturbance is measured most disturbance sensors used

in vehicles are ono typ e control signals can b e generated in an attempt to counteract its

eect A typical ISC strategy has feedforward only for the air bypass valve control and

the feedforward is designed based on static engine mapping data For example if an air

conditioning AC switch sensor is installed an extra amount of air will be scheduled to

prevent engine sp eed dro op when the AC compressor is engaged The amount of feedforward

control can b e determined as follows At the steady state since P N the available engine

torque to balance the load torque is related to the mass air ow and engine sp eed through

T f MAFN r

q T

By estimating the load torque presented to the engine by the measured disturbance one

can calculate for xed AF ratio and spark the amount of air that is needed to maintain

the engine sp eed at the xed setp oint The feedforward control can be applied either as a

multiplier or an adder to the control signal

Feedforward control intro duces extra cost due to the added sensor and software complex

ityandthus it should b e used only when necessary Most imp ortantly it should not b e used

to replace the role of feedback in rejecting disturbances since it also do es not address the

problems of op erating condition variations miscalibration etc

Feedback design

Feedback design for ISC can b e pursued in many dierentways Two philosophically dierent

approachesareusedindeveloping the control strategy One is the singleinput singleoutput

SISO approach which treats the air and spark control as separate entities and designs one

lo op at a time When the SISO approach is used the natural separation of time scale in the

air and spark dynamics spark has a fast resp onse compared to air ow which has a time lag

due to the manifold dynamics and intaketop ower delay suggests that the spark control b e

closed rst as an inner lo op Then the air control as an outer lo op is designed by including

the spark feedback as part of the plant dynamics Another approach is to treat the ISC as

amultiinput singleoutput or when the manifold pressure is to b e controlled a multiinput

multioutput MIMO problem Many control strategies such as LQoptimal control and

H have been develop ed within the MIMO framework This approach generally leads to a



co ordinated air and spark control strategy and improved p erformance

Despite the rich literature on ISC featuring dierent control design metho dologies PID

control in combination with static feedforward design is still viewed as the control structure

of choice in the automotive industry In many cases controllers designed using advanced

theory such as H and LQR are ultimately implemented in the PID format to reduce



complexity and to app end engineering content to design parameters A typical pro duction

ISC feedback strategy has a PID for the air bypass valve or throttle control and a simple

prop ortional feedback for the spark control This control conguration is dictated by the

following requirements At steady state the spark should return to its nominal value

indep endent of the load disturbances Zero steadystate error has to b e attained for step

disturbances

Calibration of ISC

Control system development in the automotive industry has b een traditionally an empirical

pro cess with heavy reliance on manual tuning As engine control systems have b ecome more

complex b ecause of increased functionality the oldfashioned trialanderror approach has

proved inadequate to achieve optimum p erformance for interactively connected systems The

trends in to days automotive control system development are in favor of more mo delbased

design and systematic calibration Tools intro duced for p erforming systematic invehicle

calibration include dynamic optimization packages which are used to search for optimal

parameters based on a large amount of vehicle data and controller netuning techniques

Given the reality that most ISC strategies implemented in vehicles are of PID typ e we

discuss two PID tuning approaches that have proved eective in ISC calibration

The rst metho d is based on the sensitivity functions of the engine sp eed with resp ect to

the controller parameters Let K be a generic controller parameter p ossibly vector valued

and supp ose that we want to minimize a p erformance cost function J N a commonly

used function for J is J N by adjusting K Viewing N as a function of K and

N N

noting that we have

K K



N N N



K K K J K K J K N

K K K

According to Newtons metho d K which minimizes J is given by



 

N N N

K N

K K K

N

By measuring the sensitivity function we can use a simple gradient metho d or to

K

iteratively minimize the cost function J The controller gains for the air and spark lo ops can

b e adjusted simultaneously The advantages of the metho d are that the sensitivity functions

are easy to generate For the ISC calibration the sensitivity functions of N with resp ect to

PID controller parameters can b e obtained by measuring the signal at the sensitivity p oints

as illustrated in Figure

Load Disturbance

Desired e PID Air Engine +- Engine Speed (K p,,Ki K d ) Model Spark K s

PID control for ISC Load Disturbance

PID Air Engine

(K p,,Ki K d ) Model ∂N ∂Kp

K s ++ e

Sensitivity points for proportional spark-loop control

∂N ∂Kp K e ∂N p ∂Ki z Engine ++ ++ z - 1 K i + Model Spark z - 1 z K d ∂N ∂Kd K s

Sensitivity points for PID air-loop control

Figure SensitivityPoints for Calibrating PID Idle Sp eed Controller

It should be pointed out that this oline tuning principle can be used to develop an

online adaptive PID control scheme referred to as the MIT rule in the adaptive control

literature The sensitivity function metho d can also be used to investigate the robustness

N

of the ISC system with resp ect to key plant parameters by evaluating where K is the

p

K

p

plant parameter vector

The second metho d is the wellknown ZieglerNichols PID tuning metho d It gives aset

of heuristic rules for selecting the optimal PID gains For the ISC applications mo dications

havetobeintro duced to accommo date the time delay and other constraints Generallythe

ZieglerNichols sensitivity metho d is used to calibrate the PID air feedback lo op after the

prop ortional gain for the spark is xed

Acknowledgment

The authors would like to acknowledge their many colleagues at Ford and the University of

Michigan who contributed to the work describ ed in this article with sp ecial thanks to Dr

P aul Moraal of Ford

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