Modeling and Model-based Control of Homogeneous

Charge Compression Ignition (HCCI) Engine Dynamics

Rolf Johansson

, Anders Widd

and Per Tunest˚al

Department of Automatic Control, Lund University, PO Box 118, SE22100 Lund, Sweden

Department of Energy Sciences, Div. Combustion Engines, Lund University

PO Box 118, SE22100 Lund, Sweden

Abstract. The Homogeneous Charge Compression Ignition (HCCI) principle

holds promise to increase efﬁciency and to reduce emissions from internal com-

bustion engines. As HCCI combustion lacks direct ignition timing control and

auto-ignition depends on the operating condition, control of auto-ignition is nec-

essary. Since auto-ignition of a homogeneous mixture is very sensitive to op-

erating conditions, a fast combustion phasing control is necessary for reliable

operation. To this purpose, HCCI modeling and model-based control with ex-

perimental validation were studied. A six-cylinder heavy-duty HCCI engine was

controlled on a cycle-to-cycle basis in real time using a variety of sensors, actu-

ators and control structures for control of the HCCI combustion in comparison.

The controllers were based on linearizations of a previously presented physical,

nonlinear, model of HCCI including cylinder wall temperature dynamics. The

control signals were the inlet air temperature and the inlet valve closing. A sys-

tem for fast thermal management was installed and controlled using mid-ranging

control. The resulting control performance was experimentally evaluated in terms

of response time and steady-state output variance. For a given operating point, a

comparable decrease in steady-state output variance was obtained either by in-

troducing a disturbance model or by changing linearization point. The robustness

towards disturbances was investigated as well as the effects of varying the pre-

diction and control horizons. Increasing the horizons had a very limited effect on

the closed-loop performance while increasing the computational demands sub-

stantially. As shown in the paper, modeling constitutes a necessary element for

embedded networked control design applied to HCCI combustion engine design.

1 Introduction

The motivation for studying the homogeneous charge compression ignition (HCCI) en-

gine principle is the promise of low levels of exhaust emissions with regards to NO

while still retaining an acceptable overall efﬁciency [15]. Pioneering efforts towards

this new engine principle—also called controlled auto-ignition (CAI)—were reported

in [42,57, 21,14,30]. Depending on the purpose, modeling of HCCI engine dynamics

may exhibit different complexity and format such as:

– Multi-zone models including chemical kinetics to simulate engine operation in a

large operating range;

Johansson R., Widd A. and Tunest

al P. (2009).

Modeling and Model-based Control of Homogeneous Charge Compression Ignition (HCCI) Engine Dynamics.

In Proceedings of the International Workshop on Networked embedded and control system technologies: European and Russian R&D cooperation,

pages 31-44

 SciTePress

– Multidimensional CFD for optimization of fuel injection and combustion chamber

design;

– Single-zone reduced-order dynamic models (for model-based control).

A signiﬁcant challenge with HCCI is the control of the combustion phasing, this is

essential in order to control the load, to obtain low fuel consumption and emissions. For

closed-loop control of the combustion phasing, feedback signals are necessary and in-

cylinder pressure feedback is, perhaps, the most straightforward approach. In practice,

the crank angle α of 50% burnt fuel (CA50 or α

or θ

) has proved to be a reliable

indicator of on-going combustion [41,6]. In closed-loop control of an HCCI engine,

several means to actuate the combustion phasing have been tested—e.g., dual fuels [41,

6,8], variable valve actuation (VVA) [1,8], variable compression ratio [15,27], and

thermal management [38, 28].

For control design purposes and embedded control design exploiting information

from networked sensors, appropriate models and system variables useful for feedback

control are needed. Previously, it was shown that physical modeling and system iden-

tiﬁcation can be used to obtain low-complexity models of the HCCI dynamics [58,7,

51]. For closed-loop HCCI engine operation, it was reported that the combustion phas-

ing can be stabilized by means of a PID controller [41]; LQG control [58]; and MPC

control [8].

A fast and robust control of α

appears to be necessary in order to stabilize HCCI

engine control. It is also desirable that the load, peak cylinder pressure, peak rate of

cylinder pressure and emissions are controlled simultaneously. This is a multi-input

multi-output (MIMO) control problem where the controller has to be able to handle

constraints on several variables. In a comparison among several control methods, it

will be demonstrated that Model Predictive Control (MPC) control could be used with

favorable properties [4,35]. All of the actuators suggested have control constraints and

MPC has the beneﬁt of explicitly taking the constraints into account.

Whereas monitoring of α

or other methods to sense on-going combustion for

feedback control of an HCCI engine all rely on pressure sensors, these sensors may be

expensive. One candidate to replace pressure sensors is the use of electronic conductive

properties for the reaction zone [24]. This phenomenon is called ion current for which

no expensive sensor is needed. Ion current has been successfully used in closed-loop

control of SI engines [20]. The basic principle of ion current sensing is that a voltage

is applied over an electrode gap inserted into the gas volume (combustion chamber)

[24]. The common belief so far has been that ion current levels are not measurable for

the highly diluted HCCI combustion. However, a recent study shows that it is not the

dilution level in itself but the actual fuel/air equivalence ratio φ which is an important

factor for the signal level [22,58].

In this paper, we will report new modeling and experimental results on HCCI con-

trol, complementingour previously published results on control of a six-cylinderheavy-

duty engine, evaluating a variety of control methods (MPC and PID) and actuators

(VVA, dual fuel), and experimental results on HCCI control of a single-cylinder heavy-

duty engine evaluating a variety of sensors (in-cylinder pressure, ion current) [8,9, 7].

The purpose of this paper is to provide a survey of state-of-the-art HCCI engine

modeling with particular attention to control-oriented modeling relevant for networked

embedded system design. The structure of the paper is the following: An overview of

HCCI modeling is given with particular emphasis on modelingsuitable for model-based

control, followed by a model-based control description, discussion and conclusions.

2 HCCI Modeling

There are two often used methods to obtain models of HCCI engine dynamics suitable

for control; physical modeling [51] and modeling by means of system identiﬁcation

[7–9]. Physical modeling based on conservation laws and chemical kinetics has attrac-

tive intuitive component-based features but suffers from complexity issues with adverse

effects in application. Whereas system identiﬁcation has proved to be a very effective

modeling tool for prototyping, it may provide results hard to interpret from a physical

point of of view.

The purpose of modeling has an obvious inﬂuence on focus and the complexity of

modeling [33,19]. As modeling and simulation may easily become too detailed and

computationally expensive to serve purposes of model-based control, low-complexity

models and reduced-order models become relevant. A minimum requirement of phys-

ical modeling is explanation of the nature of the in-cylinder pressure traces where

adiabatic compression combines with fuel-dependent auto-ignition [43], [10], [23]. In

previous work, modeling choices involve aspects of chemical kinetics, cycle-to-cycle

coupling, in-cylinder concentrations of reactants, wall temperature dynamics, pressure

dynamics, and auto-ignition timing.

Modeling details fall into categories of single-zone models, multi-zone models,

multidimensional computational ﬂuid dynamics (CFD) models, sometimes combined

with exosystem simulation on the form of stochastic disturbances, load modeling, sen-

sor modeling. Both physical aspects and operational aspects require attention. Shaver

et al. singled out six distinct stages in modeling of HCCI engine operation—i.e., induc-

tion, compression, combustion, expansion, exhaust and residence in the exhaust man-

ifold [52,53,45]. As for stable operation, combustion phasing control design requires

appropriate models and system output variables usable for feedback control. Recently,

mode-transition operation and control of Diesel-HCCI and SI-HCCI engines and other

hybrid control aspects have received attention [54].

2.1 Fuel Modeling

The necessity of developing a practical iso-octane mechanism for HCCI engines was

presented after various different experiments and currently available mechanisms for

iso-octane oxidation being reviewed and the performance of these mechanisms applied

to experiments relevant to HCCI engines being analyzed [48,39]. A skeletal mecha-

nism including 38 species and 69 reactions was developed, which could predict satis-

factorily ignition timing, burn rate and the emissions of HC, CO and NO

for HCCI

multi-dimensional modeling [39]. Comparisons with various experiment data including

shock tube, rapid compression machine, jet-stirred reactor and HCCI engine indicate

good performance of this mechanism over wide ranges of temperature, pressure and

equivalence ratio, especially at high pressure and lean equivalence ratio conditions. By

applying the skeletal mechanism to a single-zone model of an HCCI engine, it was

found that the results were substantially identical with those from the detailed mecha-

nism developed by Curran et al. [18] but the computing time was reduced greatly [39].

A model for the auto-ignition of hydrocarbons applicable to 3D internal combus-

tion engine calculations was proposed [16]. The limits of classical methods using an

auto-ignition delay are investigated when cool ﬂame phenomena are present. A method

based on tabulated reaction rates was presented to capture the early heat release in-

duced by low temperature combustion. Cool ﬂame ignition delay when present and

cool ﬂame fuel consumption are also tabulated. The reaction rate, fuel consumption,

and cool ﬂame ignition delay tables were built a priori from complex chemistry calcu-

lations. The reaction rates, which directly depend on instantaneous changes of thermo-

dynamic conditions, were then integrated during the 3D engine calculation. The model

is ﬁrst validated through comparisons with complex chemistry calculations in constant

and variable volume conﬁgurations where good agreement was found. The model was

applied both to a Diesel computation with spray injection and residual gases, and to

a Diesel-HCCI conﬁguration. Comparisons with experimental results showed that the

auto-ignition essential features were well reproduced in these cases [16].

The combination of CFD computations with detailed chemistry leads to excessive

computation times, and is not achievable with current computer capabilities. A reduced

chemical model for n−heptane is described, in view of its implementation into a CFD

simulation code [37]. Firstly, the reduction process to get to the 61-step mechanism

is detailed and then the 26-step mechanism is described; this further reduction is car-

ried out under various conditions that include a range of interest in engine applications.

Validation work in reference to the original detailed mechanism and two reduced mech-

anisms was published in the literature, focusing on the prediction of ignition delay times

under constant as well as variable volume conditions [37]. A good and accurate repro-

duction of both ignition delay times and heat release was reported to be reached with

the 26-step model [37].

Despite the rapid combustion typically experienced in HCCI, components in fuel

mixtures do not ignite in unison or burn equally. In experiments and modeling of blends

of diethyl ether (DEE) and ethanol, the DEE led combustion and proceeded further to-

ward completion, as indicated by

C-isotope tracing [36]. A numerical model of HCCI

combustion of DEE and ethanol mixtures supports the isotopic ﬁndings. Although both

approaches lacked information on incompletely combusted intermediates plentiful in

HCCI emissions, the numerical model and

C-tracing data agreed within the limita-

tions of the single-zone model. Despite the fact that DEE is more reactive than ethanol

in HCCI engines, they were sufﬁciently similar and prevented incidence of a large elon-

gation of energy release or signiﬁcant reduction in inlet temperature required for light-

off, both desired effects for the combustion event. This ﬁnding suggests that, in general,

HCCI combustion of fuel blends may have preferentialcombustion of some of the blend

components [36].

2.2 Auto-Ignition Modeling

Whereas HCCI engines have been shown to have higher thermal efﬁciencies and lower

and soot emissions than spark ignition engines, the HCCI engines experience very

large heat release rates which can cause too rapid an increase in pressure. One method

of reducing the maximum heat-release rate is to introduce thermal inhomogeneities,

thereby spreading the heat release over several crank angle degrees [55]. Direct numer-

ical simulations (DNS) showed that both ignition frontsand deﬂagration-likefronts may

be present in systems with such inhomogeneities [17]. Here, an enthalpy-based ﬂamelet

model was presented and applied to four cases of varying initial temperature variance.

This model used a mean scalar dissipation rate to model mixing between regions of

higher and lower enthalpies. The predicted heat-release rates agree well with the heat

release rates of the four DNS cases. The model was shown to be capable of capturing

the combustion characteristics for the case in which combustion occurs primarily in the

form of spontaneous ignition fronts, for the case dominated by deﬂagration-type burn-

ing, and for the mixed mode cases. The enthalpy-based ﬂamelet model shows consid-

erably improved agreement with the DNS results over the popular multi-zone model,

particularly, where both deﬂagrative and spontaneous ignition are occurring, that is,

where diffusive transport is important [17]. Another fuel model is the Shell model used

for auto-ignition below [26]. Further contributions on auto-ignition modeling can be

found in [47].

2.3 Thermal Modeling and Auto-Ignition

HCCI combustion is often achieved without a completely homogeneous mixture. In

order to derive a control-relevant model, however, we might ﬁrstly proceed by assum-

ing that the mixture is homogeneous, thus allowing a single-zone cylinder model [5].

Such assumptions may be justiﬁed by laser-diagnostic measurements in our experi-

mental set-up [46]. To reproduce the effects relevant for combustion phasing control

it is required that the auto-ignition model captures the effects on ignition delay (induc-

tion time) of varying species concentrations, temperature trace, and fuel quality. Several

alternative approaches are possible for modeling the instant of auto-ignition for fuels.

High-complexity models—e.g., (Primary Reference Fuels (PRF), 857 species, 3,606

reactions, CHEMKIN/LLNL) [56]—have been used to model complete combustion. In

addition to ignition prediction, such models are also aimed at describing intermediate

species and end product composition. Reduced chemical kinetics models, e.g., (PRF

fuels, 32 species, 55 reactions, CHEMKIN) [60], have also been proposed, where re-

actions with little inﬂuence on the combustion have been identiﬁed and removed. For

simulation of multi-cycle scenarios it is necessary to keep the model complexity low in

order to arrive at reasonable simulation times. An attractive and widespread alternative

is to use the Shell model [26], which is a lumped chemical kinetics model using only

ﬁve representative species in eight generic reactions. This model is aimed at prediction

of auto-ignition rather than describing the complete combustion process. Compression

ignition delay may also be described by empirical correlations, such as the knock inte-

gral condition

t=0

= 1 (1)

where t

is the instant of ignition and τ is the estimated ignition time (ignition delay)

at the instantaneous pressure and temperature conditions at time t, often described by

Arrhenius type expressions [29,49]. A drawback is that dependence on species concen-

trations is normally not regarded. An integral condition with concentration dependence

was used in [50,51] in a similar study for propane fuel, where also auto-ignition models

based on very simple reaction mechanisms were evaluated. Alternatives to physical or

physics-based models are to use system identiﬁcation to obtain models or to use empir-

ical look-up tables. The latter gives insufﬁcient physical insight, and require substantial

efforts to calibrate. In this work, the Shell model was chosen to describe the process of

auto-ignition. A static model is then used to describe the major part of the actual com-

bustion and corresponding heat release. The result from the Shell model was compared

to results from an integrated Arrhenius rate threshold model and the Planet mechanism

model [3, 2]. To the purpose of detailed treatise, modeling of the cylinder, auto-ignition,

integrated Arrhenius threshold, combustion, and heat transfer are now provided:

Cylinder Gas Model—First Law of Thermodynamics. The cylinder gas dynamics

are described by conservation laws such as the the ﬁrst law of thermodynamics

δQ

= (1 +

)pdV +

V dp + δQ

(2)

where p is the cylinder pressure, V the volume, R

the universal gas constant, c

− R

the speciﬁc heat capacity, and n the molar substance amount contained in the

cylinder. The time derivatives of Q

and Q

denote rates of heat released by the

combustion process and heat ﬂowing from the wall, respectively.

Gas Properties. The gas is described as a mixture of dry air and fuel, and the combus-

tion products are nitrogen, carbondioxide and water. Speciﬁc heat for each species i is

described by NASA polynomial approximations of JANAF data

p,i

(T ) =

j=1

i,j

j−3

(3)

where M

is the molar mass of species i and T is the cylinder temperature [12, 25].

The mixture speciﬁc heat is then

(T ) =

p,i

(T ) (4)

where n

is the mole of species i.

Shell Auto-ignition Model. The Shell auto-ignition model for hydrocarbon fuels [26],

, is based on a general eight-step chain-branching reaction scheme with lumped

species: The hydrocarbon fuel RH, radicals

R, intermediate species Q, and the chain

branching agent B.

RH + O

−→ 2

R (initiation) (5)

−→

R + products and heat (propagation cycle) (6)

−→

R + B (propagation forming B) (7)

R + Q

−→

R + B (propagation forming B) (8)

−→ out (linear termination) (9)

−→

R + Q (propagation forming Q) (10)

−→ out (quadratic termination) (11)

−→ 2

R (degenerate branching) (12)

Auto-ignition is described by integrating the time variations of species concentrations

from the beginning of the compression stroke.

= 2



[RH][O

] + k

[B] − k

[



− f

[

R] (13)

d[B]

= f

[

R] + f

[Q][

R] − k

[B] (14)

d[Q]

= f

[

R] − f

[Q][

R] (15)

d[O

]

= −gk

[

R] (16)

The species

R, Q, and B are not considered in thermodynamiccomputations for the gas

mixture. The stoichiometry is approximated by assuming a constant CO/ CO

ratio, ν,

for the completecombustionprocess, with oxygen consumptiong = 2[a(1−ν)+b/4]/b

mole per cycle. The heat release from combustion is given by

= k

qV [

R] (17)

where q is the exothermicity per cycle for the regarded fuel. The propagation rate coef-

ﬁcient is described as

= (

p,1

]

p,2

p,1

[RH]

)

−1

(18)

To capture dependence of induction periods on fuel and air concentrations the terms f

, and f

are expressed as

= f

◦

]

[RH]

(19)

Rate coefﬁcients and rate parameters k

and f

◦

are then described by Arrhenius rate

coefﬁcients

= A

exp



−E



, f

◦

= A

exp



−E



(20)

We usethe acronymFuelMEP to denote the mean effectivepressure calculated from the

quantity of fuel injected. Calibrated parameters for a number of fuels, including a set of

Primary Reference Fuels (PRF), are found in the literature [26]. PRFx is a mixture of n-

heptane and iso-octane, where the octane number x is deﬁned as the volume percentage

of iso-octane. Parameters for PRF90 were used in the simulations. Auto-ignition was

deﬁned as the crank angle where the explosive phase of combustion starts.

Integrated Arrhenius Rate Threshold. The Arrhenius form can be used to determine

the rate coefﬁcient describing a single-step reaction between two molecules [62]. The

single-step rate integral condition is based on the knock integral with

IVC

1/τ dθ/w (21)

1/τ = A exp(−E

/(R

T ))[Fuel]

]

(22)

where θ is the crank angle and θ

IVC

is the crank angle of the inlet valve closure. The

integral condition describes a generalized reaction of fuel and oxygen and this is an

extreme simpliﬁcation of the large number of reactions that take place during combus-

tion. The empirical parameters A, E

, a, b and K

are determined from experiments.

Values for n-heptane and iso-octane from [62] were used in the comparison below with

A = 4.65 · 10

, E

= 15.1, a = 0 .25, b = 1.5, K = 1.6 · 10

. Auto-ignition was

deﬁned as the crank angle where the integral condition has reached the threshold K

Sensitivity analysis of integrated Arrhenius rate thresholding was made by Chiang and

Stefanoupolou [32].

Combustion. When auto-ignition is detected by the Shell model or the Integrated Ar-

rhenius Rate Threshold, the completion of combustion is described by a Wiebe function

[65].

(θ) = 1 − exp



−a(

θ − θ

∆θ

)

m+1



(23)

where x

denotes the mass fraction burnt, θ is the crank angle, θ

start of combustion,

∆θ is the total duration, and a and m adjustable parameters that ﬁx the shape of the

curve. The heat release is computed from the rate of x

and the higher heating value of

the fuel.

Heat Transfer. Heat is transfered by convection and radiation between in-cylinder

gases and cylinder head, valves, cylinder walls, and piston during the engine cycle.

In this case the radiation is neglected. This problem is very complex, but a standard

solution is to use the Newton law for external heat transfer

= h

(T − T

) (24)

where Q

is the heat transfer by conduction, A

the wall area, T

the wall temper-

ature, and the heat-transfer coefﬁcient h

given by the Nusselt-Reynolds relation by

Woschni [66]

= 3.26B

−0.2

0.8

−0.55

(2.28S

)

0.8

(25)

where S

is the mean piston speed and B is the bore.

3 Experiments

Detailed reviews of experimental set-up and conditions are given in [8, 9, 11].

0 200 400 600 800 1000 1200 1400

−2

Cycle Index [−]

[Deg]

0 200 400 600 800 1000 1200 1400

560

580

600

Cycle Index [−]

IVC

[Deg]

0 200 400 600 800 1000 1200 1400

110

120

130

Cycle Index [−]

[C]

Data Set Point

0 200 400 600 800 1000 1200 1400 1600

[Deg]

0 200 400 600 800 1000 1200 1400 1600

560

580

IVC

[Deg]

0 200 400 600 800 1000 1200 1400 1600

110

120

130

[C]

Data Set Point

0 200 400 600 800 1000 1200 1400 1600 1800

2.5

3.5

x 10

Cycle Index [−]

IMEP

[Pa]

Engine Speed

Fuel Energy

EGR Level

Fig.1. Results of consecutive set-point changes (upper) and response to disturbances (lower)

[63].

A cycle-resolved model of HCCI presented in [64] was used to design model pre-

dictive controllers. The controlled output was the crank angle of 50 % burnt fuel (here

denoted θ

). The control signals were the inlet air temperature and the crank angle of

inlet valve closing. A fast thermal management system was used to obtain fast intake

temperature actuation.

As witnessed by Fig 1, successful model-based control was accomplished both for

setpoint tracking and disturbance rejection.

4 Conclusions

In addition to aspects of modeling related to thermodynamics, chemical combustion

kinetics, and engine operation, careful attention is required for control-oriented com-

bustion modeling and the interactions among dynamics, control, thermodynamics and

chemical combustion properties. Modeling of engine-load transients as well as ther-

mal transients also belong to this important domain of modeling (Fig. 1). Progress in

this area is important and necessary for successful and robust control such as model-

predictive control.

Within the project a cycle-resolved, physics-based, model of HCCI has been de-

veloped. The model includes a low-complexity model of the cylinder wall temperature

dynamics in order to capture the relevant time-scales of transient HCCI when only small

amounts of hot residuals are trapped in the cylinder. The temperature evolution of the

gas charge is modeled as isentropic compression and expansion with three heat transfer

events during each cycle.

Recently, research focused on design and evaluation of model predictive controllers

based on linearizations of the model. The considered control signals were the inlet

valve closing and the intake temperature. Simulations were used for the initial control

design and the resulting controller was tested experimentally. The control performance

was evaluated in terms of response time to set-point changes and the resulting output

variance.

It was found that a comparable decrease in the output variance in some operating

points could be achieved either by introducing a disturbance model or by changing

linearization. All tested set-pointchanges were accomplishedwithin 20 engine cycles or

less. Only minor changes to the intake temperature were required for moderate changes.

The closed-loop system showed good robustness towards disturbances in engine speed,

injected fuel energy, and the amount of recycled exhaust gases.

Acknowledgements

This research was supportedby the CompetenceCenter of Combustion Processes(KCFP)

Project Closed-LoopCombustion Control, Swedish Energy Administration (Ref. 22485-

1).

This research was partially done in the framework of the HYCON Network of Ex-

cellence, contract number FP6-IST-511368.

The authors would like to thank Johan Bengtsson, Daniel Blom, Kent Ekholm,

Bengt Johansson, Maria Karlsson, Petter Strandh for cooperation on HCCI modeling

and control.

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