Abstract— This paper introduces the needs for applying

model-based control techniques to vehicle powertrain and

aftertreatment systems. A tutorial overview of model-based

control techniques and methodologies for modern powertrain

and aftertreatment systems is presented and compared with the

traditional approaches. The control-oriented powertrain and

aftertreatment system modeling techniques are also addressed

along with their real-time simulation requirement for HIL

(hardware-in-the-loop) simulations. The application examples of

the model-based control of internal combustion engine,

transmission, and aftertreatment systems are given in detail.

I. INTRODUCTION

Although substantial advances have been made in electric

vehicles in the forms of battery technology and electric

powertrain development, the market penetration of these

vehicles is currently marginal. Hybrid electric vehicles with

efficient, clean combustion engines are more likely to pave

the future transportation needs. According to a publication

from the European automotive manufacturer’s association

(ACEA), a realistic market share for new, electrically

chargeable vehicles is estimated in the range of 2 to 8% in the

next decade [1]. Furthermore, electrification of heavy-duty

vehicles and off-highway vehicles is currently far-fetched and

is primarily limited by the energy densities of batteries (1-2

MJ/kg) compared to those of conventional fuels (42-44

MJ/kg). As a result, internal combustion (IC) engines and the

respective powertrains will continue to dominate the ground

transportation sector for the foreseeable future and beyond.

IC engines, particularly in the transportation sector, have

undergone a series of regulatory constraints owing to their

enormous environmental and energy impacts. The fossil fuel

dependence of conventional IC engines has raised concerns

about sustainability of this technology leading to a gradual

adaptation to alternative and renewable fuels. The other

negative impact of IC engines is the CO2 emission and the

consequential climate change. Consequently, regulations are

in place for the greenhouse gas (GHG) emissions which

essentially require the engines to be more efficient. Finally,

the toxic emissions emitted following the combustion in

engines include nitrogen oxides (NOx), particulate matter

(PM) emissions, and products of incomplete combustion.

These emissions have been regulated for several decades

while the regulations continue to become increasingly

Guoming Zhu is with the Department of Mechanical Engineering and the

Department of Electrical and Computer Engineering, Michigan State

University, East Lansing, MI 48824 USA (e-mail: zhug@msu.edu).

Junmin Wang is with the Department of Mechanical and Aerospace

Engineering at The Ohio State University, Columbus, OH 43210 USA

(email: wang.1381@osu.edu).

stringent. Such requirements, sometimes conflicting, have led

to significant development in and complexity of the modern

IC engines, transmissions, and aftertreatment systems along

with continual refinements of their control systems. Despite

the long existence of such technologies, they are still evolving

in fast paces.

A. Traditional and modern engine control

As summarized above, engine systems are becoming

highly non-linear multi-variable systems with large cross-

coupling between sub-systems. Furthermore, the multi-mode

operation (cold start, after-treatment regeneration, different

combustion modes, etc.) and the several layers of constraints

placed on the actuators complicate the calibration effort and

the control system design. The conventional ‘experimental

mapping’ based calibration approach, where set-point maps

are generated during the development phase and multi-

dimensional interpolation is carried out during the

deployment stage, becomes increasingly time and resource

intensive. For instance, the shift from mechanical fuel

injection to common-rail injection system in diesel engines

has increased the calibration effort by multifold. Several

variables such as injection pressure, number of fuel injections

per cylinder per cycle, and the duty cycle of each injection

event can now be independently commanded, hence requiring

calibrations. It is pertinent to mention here that significant

efforts have been invested in standardization of calibration

(such as Design of Experiments) across engine platforms and

generations, at least within the same engine manufacturer.

Nevertheless, each new technology implemented in the

engine platform relates to an exponential increase in the

dimension of the operating maps and hence the calibration

effort.

The typical engine calibration process can be summarized

as shown in [2], where the process is governed by several

objective functions and constrains that include actuator

physical limitations and safe operating ranges. For instance,

the problem can be stated as an optimization problem to

minimize the emission species over a standard operating

regime. The minimization problem is constrained by the

engine torque output that is to be within the deviation limit

Zongxuan Sun is with the Department of Mechanical Engineering at

University of Minnesota, Minneapolis, MN 55455, USA (email:

zsun@umn.edu)

Xiang Chen is with the Department of Electrical and Computer

Engineering at University of Windsor, Windsor, Ontario, Canada N9B3P4

(email: xchen@uwindsor.ca).

Tutorial of Model-Based Powertrain and Aftertreatment System

Control Design and Implementation

Guoming Zhu, Junmin Wang, Zongxuan Sun, and Xiang Chen

2015 American Control ConferencePalmer House HiltonJuly 1-3, 2015. Chicago, IL, USA

978-1-4799-8684-2/$31.00 ©2015 AACC 2093

and the system input limitations within their respective

operating ranges.

Fig 1. Typical engine calibration process (adapted from [2])

Notwithstanding the aforementioned regulatory constraints

on IC engines and the resultant increase in hardware

complexity, the cost incentive of minimization of engine

hardware is significant. As a result, reduced calibration effort

along with very little sensor information is desired by the IC

engine community. Thus, a model-based feed-forward control

structure that is calibrated on the test bench and deployed in

the ECU (electronic control unit) is preferred. The increasing

on-board computing power and computer memory available

on modern ECUs further motivate this approach. Besides,

recall from [2] that many of the engine control demands can

be stated in the form of a constrained multi-input and multi-

output optimal control problems while considering the

interdependence of the many system variables. These

requirements of model-based engine control fit the

characteristics of model predictive control (MPC) wherein a

model-based optimal control input to the plant is computed

over a limited number of steps to minimize a pre-defined

constrained cost function. Only the control inputs

corresponding to the next sample time are sent to the actuator.

The control input prediction over a finite horizon is repeated

at every sample step while change of the plant state is

accounted for in the model-based prediction.

B. Traditional and modern aftertreatment system control

For IC engine powertrains of ground vehicle applications,

aftertreatment systems have become indispensable in order to

meet the increasingly stringent tailpipe emission regulations

worldwide. Several decades ago, the research and

development efforts on the engine aftertreatment control

system started with the celebrated three-way catalytic (TWC)

converters for gasoline engines. Because of the largely

homogeneous and stoichiometric combustion nature of the

gasoline engines, TWC has been the dominant and effective

aftertreatment option. Recently, promoted by the tightening

emission regulations on diesel engine vehicles, diesel engine

aftertreatment systems have been actively developed and used

for diesel engine powertrains. Different from these for

gasoline engines, the aftertreatment systems for diesel

engines are more diversiform due to the heterogeneous

combustion nature of the diesel engines and the high

complexities of the diesel exhaust gas treatments. Diesel

oxidation catalyst (DOC), diesel particulate filter (DPF), lean

NOx trap (LNT), selective catalytic reduction (SCR), and

other systems have emerged accordingly and combinations of

such devices are necessary in order to satisfactorily treat the

diesel exhaust gas. While the gasoline engine aftertreatment

control focus on the TWC operation alone, diesel

aftertreatment system control needs to be more holistic with

systematic considerations of the interconnected dynamics

among the different aftertreatment subsystems. Driven by the

growing concerns on the vehicle emissions, model-based

control methods have become the essential approaches for

operating both gasoline and diesel engine aftertreatment

systems under real-world driving conditions for reduced

tailpipe emissions.

C. Traditional and modern transmission control

Just as the internal combustion engine, traditional

transmission control has been conducted with extensive

calibrations. This is mainly due to the lack of precise models

and low cost sensors that can enable real-time model-based

feedback control. However the calibration based approach is

facing more challenges as the recent trend in transmission

systems has driven up the time and cost associated with the

calibration. There are two new changes in the transmission

system aimed at improving vehicle fuel efficiency and

reducing emissions. One is the introduction of different types

of transmissions to North America which is traditionally

dominated by automatic transmissions. The other is the

increasing number of gear ratios for transmissions. Four speed

transmissions have dominated the market for many years until

the introduction of five and six speed transmissions a few year

ago. Recently eight speed transmissions have been

introduced. The increasing number of different transmissions

and the gear ratios can drastically increase the burden for

control calibration. This calls for the need of control-oriented

model and model-based control. This paper will review

various types of transmissions and the modeling and control

approaches for the transmissions.

II. CONTROL-ORIENTED MODELING AND MODEL-BASED

CONTROL FOR ENGINE SYSTEMS

A. Requirements for modern engine control

The number of actuators and sensors of a modern engine is

increasing rapidly as the government regulations on vehicle

emissions and fuel economy get tight. This requires to apply

the model-based engine control. In general, engine control

can be roughly divided into two main groups: engine charge

management and fuel (combustion) control.

1) Charge air

The multifold advantages of EGR (exhaust gas

recirculation) resulting in its deployment in diesel and

gasoline engines have made the air-path and in-cylinder

charge control largely complex. In addition, the increasing

versatility of the air-path hardware such as dual-loop EGR

[3], multi-stage turbocharging [4] , and VVA (variable valve

actuation) [5] improves the ability of air-path control but the

control itself is highly non-linear and multi-variable.

Particularly in clean Low Temperature Combustion (LTC)

2094

cycles, significant charge dilution is achieved through EGR

and concurrent increase of intake boost is necessary for

increasing engine power density. Thus, control of the

turbocharging and EGR interaction is critical for stable

operation in LTC mode [6]. A significant amount of work has

been done on the characterization and coordinated control of

variable geometry turbocharging (VGT) and EGR for

conventional diesel engines [7]. A combination of the fairly

simple physical models and relatively cheap sensor

deployment provides opportunities for implementing modern

air-path control concepts [8].

2) Fuel and combustion

Traditional combustion in spark ignited (SI) or

compression ignited (CI) engines is considered to be highly

robust requiring very little intervention for stable operation.

However, newer clean combustion concepts such as LTC or

HCCI (homogenous charge compression ignition), are highly

sensitive to small changes in gas temperature, charge

composition and fuel quantity, and small variations in these

quantities may lead to unstable combustion. Reitz

summarized the research in diesel engine combustion and

presented the trends (in research) towards future clean

combustion technologies in [9]. These marginally stable

combustion systems require cycle-by-cycle control of fast

actuation hardware such as VVT (variable valve timing) [10]

or fuel delivery systems [11] that typically use in-cylinder

pressure measurement for feedback. Moreover, these

combustion concepts have limited operating range and

switching between modes is necessary to encompass the

entire engine map. For instance in diesel LTC, NOx and soot

emissions can be maintained below the desired limits with

different levels of EGR. At idle load, the emission targets can

be achieved using heavy EGR with conventional diesel

operation. For mid-load diesel HCCI or RCCI (reactivity

controlled compression ignition) may be feasible while full

load operation is feasible in conventional diesel operation or

in ethanol-diesel dual fuel mode. Asad et al demonstrated

cycle-by-cycle fuel injection control for mode switching

operation with minimum drivability or emissions impact [12].

B. Control-oriented engine models

1) HCCI single zone model

In [13], a control-oriented ordinary differential equation

engine model is proposed for studying HCCI engines using

ethanol fuel.

In this model, the initial condition of the compression

stroke is determined using the dynamic engine air-path

process. A two-step reaction mechanism is applied for the in-

cylinder combustion, where both the Arrhenius reaction rates

and heat transfer processes using Woschni’s correction were

taken into account. The model captures the basic

characteristics of HCCI combustion and predicts the ignition

timing reasonably close to the experimental results acquired

in [14]. However, as the model is only a single-zone model,

the assumption that the HCCI in-cylinder mixture is perfectly

homogeneous is not appropriate. Moreover, the suitability of

using Woschni’s model for HCCI heat transfer estimation has

not been justified.

The detailed model proposed in [13] can be found below.

The engine cylinder geometric volume change is defined in

time domain, and is expressed as: �� = ���� ( sin + �� ��� � ��� ������� ���� �)� (1)

where B is the cylinder bore, is the crank angle, a is half of

the stroke length and l is the connecting rod length. = ��, where � is the rotating speed of the crankshaft. The intake gas

mass flow is defined as:

��� =� ! "#$%�&'�()*+ , &&'-

� ./0 1 23�3� − 1 [1 − , &&'-(./��) ./0 ],9 &&' > , 23� + 1-

./ (./��)0 ;#$%�&'�()*+ (3�)� <0 , 23� + 1-

(./=�) <(./��)> ,9 &&' ≤ , 23� + 1-./ (./��)0 ;

(2)

And the exhaust gas mass flow is defined as:

�<� =� ! "#$%<&√() ,&'& -

� .�0 1 23<3< − 1 [1 − , &&'-(.���) .�0 ],9&'& > , 23< + 1-

.� (.���)0 ;#$%<&√() (3<)� <0 , 23< + 1-

(.�=�) <(.���)> ,9&'& ≤ , 23< + 1-.� (.���)0 ;

(3)

where &' is the intake manifold pressure, & is the cylinder

pressure, )*+ is the intake manifold temperature, and ) is the

cylinder temperature. ( is the gas constant and A is the cross-

sectional area of the corresponding valves, 3 is the gas

specific heat ratio and A$ is the gas discharge coefficient. The

rate of species concentration change is defined as: BC�D = BC� ,EFGD + BC� ,HFD (4)

where the BC�D is the rate change of moles species i per unit

volume and BC� ,EFGD ,

BC� ,HFD are the rate of change of moles

species i due to combustion and flow through the intake and

exhaust valves.

The in-cylinder mass change is equal to the difference of

the inflow and outflow mass, �� *+ and �� IJ respectively: KLKM = ∑ �� *+*+ − ∑ �� IJIJ (5)

Whereas the energy balance of the engine cylinder is defined

as: KOKM = P� −Q� + ∑ (�� *+*+ ℎ*+) − ∑ (�� IJℎIJ)IJ (6)

where P� is the rate of net heat transfer equals to the energy

generated from the combustion and the heat transfer through

the cylinder walls, Q� is the rate of mechanical work done by

the system, ℎ*+ is the enthalpy for the intake gas species and ℎIJ is the enthalpy of the exhaust gas species.

For ethanol fuel, the two-step reaction is in the form of: A<STU + 2(U< + 3.773Y<) → 2AU + 3S<U + 7.546Y< AU + �< U< → AU< (7)

As the engine running at different strokes, the mass of gas

transfer between the engine cylinder and manifolds would

change according to (2) and (3) where the flow rates equations

are developed based on compressible, steady state, one-

dimensional and isentropic flow analysis. The gas species

concentration would change due to chemical reaction and gas

exchange processes which happened between the cylinder and

2095

the manifolds and is described using (4). The mass and energy

balances of the engine cylinder are described using (5) and

(6). The combustion process is considered to take place close

to the top dead center of the cylinder and is approximated as

constant volume combustion which bears a two-step reaction

mechanism which is expressed by three-parameter Arrhenius

functional form in (7).

2) HCCI two-zone model

In order to improve the accuracy of the HCCI combustion

prediction, a two-zone HCCI combustion model is proposed

in [15] which the heterogeneity of the model is considered.

The change of in-cylinder condition is described by a two-

zone process where one zone is to represent the well-mixed

air-fuel charge and the other zone represents the unmixed

volume. The study shows that the size of the unmixed zone in

the model plays an important role in determination of the peak

cylinder pressure and temperature during combustion as well

as the start of combustion.

For the two-zone model, during the intake phase, the mass

transfer rate can be expressed as: �� M^( *) = _( *)#�`̅( *)�b#<%( *)/d#M (8)

where A is the surface area of the unmixed zone, #< is the

calibration constant based on the assumptions, _ is the

residual gas density, d#M is a dimensionless constant known

as turbulent Schmidt number, #� is a constant to be calibrated

and �b is the concentration of residual gas at the interaction

surface. The details of the two-zone model can be found

below.

The temperature during intake phase at both zones is

approximated using the following equations: )( *)e+L*JIK = )( fDg)(h(�ijk)h(�l) )+�� +0 (9)

)( *)L*JIK = L(�l)m(�l)�LnGolFpq(�l)m(�l)nGolFpqLolFpq(�l) (10)

where * the is the corresponding crank angle at which the

instance took place, n is the polytropic exponent which is used

by the author to model the heat transfer from the unmixed

zone to the mixed zone.

The temperature change of the unmixed and mixed zones

during compression phase can be described by: T( *)e+L*JIK= �e+L*JK( *��)As)e+L*JIK( *��) − t( *��)∆�v( *) − w( *)[�e+L*JIK( *��) − �� M^( *)∆�]As

(11) T( *)L*JIK= PL*JIK − t( *��)∆�x( *) + �L*JIK( *��)As)L*JIK( *��) + w( *)[�L*JIK( *��) + �� M^( *)∆�]As

(12)

where ∆�v( *) = [�e+L*JIK( *) − �e+L*JIK( *��)] ∆�x( *) = [�L*JIK( *) − �L*JIK( *��)] F( *) = �� M^( *)∆�Az)( *)e+L*JIK PL*JIK is the heat transfer to the cylinder walls from the

mixed zone while �� M^ is the mass transfer rate from unmixed

zone to mixed zone.

Heat transfer between the mixed and unmixed zone is not

considered here, thus the average in-cylinder temperature

during compression phase can be obtained using: T( *) = LolFpqm(�l)olFpq=LnGolFpqm(�l)nGolFpqLij{ (13)

The Arrhenius integral is used as the criterion for the start

of HCCI combustion: ARI = � %&�[U<]�[w���]��� ���∙�olFpq(�)� �l�ij{ (14)

where Ea is the activation energy for the auto ignition, A is a

scaling factor related to fuel composition. Equation (9) is used

to determine the volume of the current unmixed zone during

the compression phase. For the mixed zone, a generalized

formula for mass fraction burned curve is modeled by �(θ) = α��( ) + ��<( ) + (1 − � − �)��( ) (15)

each of the three functions xi is

�*( ) = 1 − ���l,����l∆�l -ol�/ ,� = 1, 2, 3 (16)

where the coefficients ai ,mi , factors α, β, and predicted burn

duration ∆ * are calibrated parameters of engine speed, load

and coolant temperature.

The energy conservation equation applied to the mixed

zone during combustion is: �L*JIK KeK� + & KDK� + P� = ����f��eI�P��D KJK� (17)

The combustion efficiency ����f is defined by matching the

indicated mean effective pressure (IMEP) simulated from

GT-Power model, P��D is the lower heating value of the fuel.

The temperature, pressure and volume of the mixed zone

during combustion can be solved by:

)L*JIK( *) = )L*JIK( *��) ∙ ��L*JIK( *��)�L*JIK( *) �+��

+ ����f��eI�P��D[�( *) − �( *��)] − P( *)�L*JIKAs

(18)

P( *) = P( *��) ∙ DolFpq(�l�/)DolFpq(�l) ∙ molFpq(�l)molFpq(�l�/) (19) �L*JIK( *) = �( *) − �e+L*JIK( *) (20)

After the combustion phase, the two-zones are assumed to

be well mixed instantaneously. The in-cylinder temperature

can be calculated by using (9), with the initial condition

obtained from )( I) = LolFpqm(�p)=LnGolFpqmnGolFpq(�p)Lij{ (21)

where the index e is the crank angle when the combustion

finishes.

3) SI and HCCI hybrid combustion model

HCCI combustion has the advantage to produce ultra-low

NOx and soot emissions with very high efficiency but suffers

from audible engine knocking at high load and misfire when

running at low load. To enjoy the advantages of the HCCI

combustion, other combustion technique such as SI

combustion can be used to replace the HCCI combustion at

certain conditions which are inappropriate for HCCI

combustion to operate. Yang and Zhu [16] introduce a

control-oriented zero-dimension mean value model which is

capable of modeling the SI, SI-HCCI, and HCCI combustion

as well as the transition between the combustion modes in an

SI engine. The combustion model starts with SI combustion,

2096

transits to HCCI combustion. The SI combustion was

modeled using the two-zone assumption for better HCCI start

of combustion estimation. The HCCI combustion is modeled

using one-zone combustion to speed up the computation.

This model can be implemented in hardware-in-the-loop

(HIL) simulations, and can produce comparable estimation as

the high-fidelity models.

In this model, the start of HCCI combustion is judged by

the Arrhenius integration (ARI) in the unburned zone: ARI = � %����bJ� ������ � �l�ij{ (22)

where �� and �b� are unburned fuel and oxidizer

concentrations, the exponents b and c are the influence

factors. R is the gas constant, A and the Arrhenius activation

energy Ea is obtained by matching the experimental burn rate.

For the SI phase, the fuel mass fraction burned is estimated

using Wiebe function: �( *) = 1 − ��&[− ¡�l��¢�∆� £L=�] (23)

where x is the mass fraction burned (MFB) of the fuel, * is

the crank angle position, ∆ the predicted burned duration, m

the Wiebe exponent, a is a parameter which depends on ∆ .

When ∆ is between 10% and 90% of MFB, a is: a = ¥[− ln(1 − 0.9)] /o�/ − [− ln(1 − 0.1)] /o�/©L=�(24)

The energy balance of the burned zone is: K(ª«I«)K� + t KD«K� + P� = �¬fℎ��D­� KJK� + Kª«K� ℎ® (25) ­�, �� and �� represents the mass, volume, internal energy

of the burned zone respectively. P� is the heat transfer from

the burned zone, P� = �P and P will be provided in (30). ­�

is the total trapped in-cylinder fuel mass for the given cycles,

P is the gas pressure of the two-zones, ℎ��D is the lower

heating value of the fuel, ℎ® is the specific enthalpy of the

unburned zone, �¬f is the combustion efficiency due to

incomplete combustion.

The energy balance of the unburned zone is defined by: K(ª¯I¯)K� + t KD¯K� + P® = Kª¯K� ℎ® (26)

­® , �® , �® are the mass, volume and internal energy of

unburned zone respectively. P® is the heat transfer from the

unburned zone where P® = (1 − �)P.

For both burned and unburned zone, the gas mixtures are

considered as ideal gases. For the burned zone: hD«°m« = ­� = �­M (27) ­M is the total mass of gas in the two-zones, )� is the burned

zone temperature and R is the gas constant.

For the unburned zone: hD¯°m¯ = ­® = (1 − �)­M (28)

where )® is the unburned zone gas temperature. The total

cylinder volume therefore is expressed as: �� + �® = � (29)

where V is the current transient cylinder volume.

The heat transfer between the gas and the cylinder wall is

calculated using Woschni correlation model: P( *) = %�ℎ�[)( *��) − )�] (30)

and ℎ� = ±²���t�³�)'.´µ��.T<�/YI (31)

where B is the cylinder bore, w is the gas flow velocity and it

is a function of engine speed YI, A is the contact area between

the gas and the cylinder wall, )� is the average temperature

of the cylinder wall, ± and l are model calibration parameters.

Gas temperature T in (30) and (31) is averaged temperature in

both zones and is expressed as: ) = J�¶«m«=(��J)�¶¯m¯J�¶«=(��J)�¶¯ (32)

where As is the specific heat for constant volume.

For the HCCI phase, the combustion chemical reaction

process is ruled by a single rate Arrhenius equation: AR = %����bJ� ������ (33)

where AR is the rate of unburned fuel consumption while the

other parameters used are the same as the ones in (22).

During the fast combustion phase, the fuel MFB can be

estimated by a Wiebe function: �( *) = 1 − ��&[− ¡�l��¢k·{{i∆�·{{i £L=�] (34)

a, m and the combustion duration ∆ ���f are all functions of

engine speed, load and coolant temperature.

The in-cylinder gas pressure and temperature are determined

by: )( *) = )( *��)(�( *��)�( *) )(¸��)+ ����f­�ℎ��D[�( *) − �( *��)] − P( *)­MAs

(35)

and t( *) = t( *��) D(�l�/)D(�l) m(�l)m(�l�/) (36)

where ¹ is the average heat capacity ratio of the in-cylinder

charge, ����f is the function of engine speed and fuel mass

and is calibrated using data from the high fidelity GT-Power

model. The compression phase uses (35) and (36) to model

the process with x=0.

4) HCCI with variable valve actuation modeling

Re-inducted exhaust gas from the previous cycle is one

method to initiate HCCI combustion. Reference [17] presents

a model which accounts for the entire HCCI process with

variable valve actuation (VVA). The model captures the

chemical kinetics of HCCI and is relatively simple. The start

of HCCI combustion is estimated using the integration of a

single global reaction represented by the Arrhenius rate

expression, which reflects the importance of temperature and

reactant concentration in the initiation of the start of

combustion. The model also included the trapping and re-

induction process of exhaust gas at the exhaust manifold

which enhances its ability to predict the transient

characteristics of HCCI combustion.

In this model, the in-cylinder volume and its derivative is

represented by: � = �� + ��º»¼�� (½�¾� + �¾� − �¾� cos − Á½�¾�< − �¾�< Â�Ã< )

(37)

�� = ��º»¼� �º»¼�� ��� �� Ä1 + �¾� ����Á�º»¼� ��º»¼� Å*+��Æ (38)

2097

where is the crank angle, �¾� is half of the stroke, ½�¾� is

the length of the connecting rod, ²�¾� is the bore diameter, �� is the cylinder clearance volume.

The mass flow rate of the gas exchange between the

manifolds and the cylinder are:

�� = �ÇÈ�zÉ�°mÉ (z�hÉ)� .⁄ Ë <..�� Ì1 − ¡z�hÉ£(.��)/.ÍÎ�/< (39)

for subsonic flow Ï&m &'⁄ > [2/(3 + 1)]./(.��)Ð; and �� = �ÇÈ�zÉ�°mÉ √3 Ñ <.=�Ò(.=�)/<(.��) (40)

for choked flow Ï&m &'⁄ ≤ [2/(3 + 1)]./(.��)Ð, where %° is

the valve effective open area, &' is the upstream stagnation

pressure, )' is the downstream stagnation temperature, &m is

the downstream stagnation pressure.

The rate of change of the gas species concentration is: ÓÔ�*Õ = KKM ¡BlD £ = B� lD − D� BlD� = ³* − D� BlD� (41)

i is the index for the kind of the species,Y* is the number of

moles of the species i, ³* , is change of moles of species i per

unit volume, and is defined as: ³* = BlD (42) ³* is contributed by the change of moles due to combustion, ³^J+,* and due to flow through the VVA controlled valves ³s��sIÅ,*, thus ³* = ³^J+,* +³s��sIÅ,* (43)

The rate of moles change rate for species i for the flow

through valves can be found to be: ³s��sIÅ,* = ³*�,* + ³I�,* − ³�I,* (44)

where

³*�,* = Ö*,*�� *��­Q*

³I�,* = ÖI,*�� I��­Q*

³�I,* = Ö�,*�� �I�­Q*

Note that Ö*,*, ÖI,* and Ö�,* are the mass fraction of species i in

the inlet, exhaust manifold and in the cylinder respectively.

The mass fraction of the species i in-cylinder, Ö�,* is

constantly changing and is expressed as: Ö�,* = [×l]ªØl∑[×l]ªØl (45)

The in-cylinder gas temperature is derived using the first

law of thermodynamics, for the cylinder the first law of

thermodynamics is: K(Lºeº)KM = P�� −Q�� +�� *�ℎ* +�� I�ℎI −�� �Iℎ� (46) �� is the mass of species in the cylinder, �� *� is the mass of

species transfer rate from the intake manifold to the cylinder, �� I� is the mass of species transfer rate from the exhaust

manifold to the cylinder, �� �I is the mass of species transfer

rate from the cylinder to the exhaust manifold, �� is the in-

cylinder internal energy, P�� is the heat transfer rate into the

cylinder, Q�� = &�� is the in-cylinder work output rate, ℎ*, ℎI, ℎ� is the enthalpy of species in the intake manifold, the

exhaust manifold and the cylinder respectively. P�� = −ℎv�%Å() − )����) (47) %Å is the in-cylinder surface area and )���� is the average

cylinder wall temperature.

ℎv� = 194.7&'.Ù(A��vh)'.Ù²�¾��'.<)�'.µµ (48) �vh is the mean piston velocity, A� takes the value 6.18 during

gas exchange and 2.28 for compression, combustion and

expansion.

The enthalpy is related to the internal energy and is expressed

as: ℎ� = �� + &� ��⁄ (49)

Equations (46) and (49) can be combined to get: K(Lºeº)KM = P�� − &�� +�� *�ℎ* +�� I�ℎI −�� �Iℎ� (50)

Expand the enthalpy shows the contribution of each species

inside the cylinder ��ℎ� = S� = ∑Y*ℎx�,* (51)

here Y* is the moles of species i in the cylinder, S� is the total

enthalpy of all species in cylinder, and ℎx�,* is the molar

enthalpy of species i in the cylinder.

Equations (41) and (51) can be combined to have: K(LºÚº)KM = �Ï∑ÓÔ�*Õ ℎx�,* + )∑[ÔÛ]#̂z,Û())� Ð + �� ∑[Ô*]ℎx�,* (52)

The in-cylinder pressure and pressure change rate is defined

as: & = ∑[Ô*]() (53) &� = z∑[×� l]∑[×l] + zm�m (54)

The in-cylinder mass and its change rate is: �� = �∑[Ô*]­Q* (55) �� � = �� ∑[Ô*]­Q* + �∑ÓÔ�*Õ­Q* (56)

The in-cylinder temperature derivative therefore can be

expressed as: )� = Ý� �D∑[×� l]ÚÞº,l�D� ∑[×l]ÚÞº,l=°mD[×� l]=∑L� ÚDÏ∑[×l]�ß,l(m)�°∑[×l]Ð (57)

the ∑�� ℎ = �� *�ℎ* +�� I�ℎI −�� �Iℎ� , equation (46) to (57)

covers the thermodynamic modeling of the engine cylinder.

The exhaust manifold model is used to describe

thermodynamic characteristics of the re-inducted exhaust gas.

This model is defined differently based on the crank angle

range and can be described by: EVO < < 720: �� I = �� �I (58) 0 < < å�A: �� I = −�� I� (59) EVC < < å�U: �� I = −Lp,�j{�Lp,EpçODg�OD� � (60)

The thermodynamics for the gas in the exhaust manifold

follows: K(Lpep)KM = P�I −Q�I +�� �Iℎ� −�� I�ℎI (61) �I is the internal energy of the product gas in the manifold, P�I is the manifold heat transfer rate, Q�I is the boundary work

for the control mass.

The exhaust volume is defined as �I = Lp°mpªØpz�èo (62) ­QI is the molecular weight of the major combustion

products.

The manifold heat transfer model is: P�I = −ℎvI%I()I − )�L�*I+M) (63) ℎvI is the convection coefficient of exhaust over area %I.

The exhaust gas temperature is dependent on the internal

energy, if pressure is given as constant ambient pressure, then

the temperature can be expressed as: )I = é(�I|&�ML) (64)

2098

The exhaust enthalpy is expressed as: ℎI = �I + ()I (65)

Combining equations (61) to (65), the governing function for

the internal energy of the gas in the exhaust manifold is: �� I = �Lp. [�� �I(ℎ� − ℎI) + ℎvI%I()�L�*I+M − )I) (66)

Equations (58) to (66) complete the modeling for the exhaust

manifold characteristics.

Propane is used as the fuel for this model, thus the global

combustion chemical reaction process can be modeled as: ∅A�SÙ + 5U< + 18.8Y< → 3∅AU< + 4∅S<U + 5(1 − ∅)U< + 18.8Y< (67)

∅ = 1 is for stoichiometric process and ∅ < 1 indicates a

lean burn reaction.

HCCI combustion is assumed to start when the in-cylinder

temperature reaches the threshold value. From then on, the

rate of propane reaction is approximated using a Wiebe

function:

) ≥ )MÚ: ³�î�ï = [�î�ï]lDl�� �(L=�)(���l∆� )oD∆� ðñòÌ�(���l∆� )o�/Í (68)

) < )MÚ ∶ ³�î�ï = 0 (69) * , �* and [A�SÙ]* represents the crank angle, volume and

propane concentration respectively at the point when

combustion start. ∆ indicates the duration of combustion, a

and m indicates the shape of the Wiebe function.

By observation, from (67), we can derive the reaction rates

for the other reactants: ³g� = 5³�î�ï (70) ³B� = 0 (71) ³�g� = −3³�î�ï (72) ³��g = −4³�î�ï (73)

Equations (38), (42), (57)-(60), (66) and (68)-(73) complete

the nonlinear differential equation set for the model after the

temperature reaches the threshold value.

In the real combustion reaction, numerous sub-reactions

would take place during the transition from reactants to

products. In this model, this process is simplified assuming

the start of combustion is modeled with a single global

reaction rate which is mathematically represented as an

integration of an Arrhenius reaction rate. The integrate

reaction rate is represented as: �(( = � %)+exp(− O�°m)'fDg [A�SÙ]�÷[U<]�÷/�� (74)

As the integrated Arrhenius rate exceeds one threshold, the

rate of propane reaction would follow the same Wiebe

function used previously in the temperature threshold

approach. Thus:

�(( ≥ �((MÚ: ³�î�ï = [�î�ï]lDl�� �(L=�)(���l∆� )oD∆� ðñòÌ�(���l∆� )o�/Í (75)

�(( < �((MÚ: ³�î�ï = 0 (76) % , O�° , ø , ùø and n are the parameters determined from

experimental propane combustion kinetics.

C. Engine model-based control

MPC is a technique developed in the 1980s [18] for

realizing the multiple input and multiple output control of a

complex linear plants with states and control constraints. The

method was first successfully applied to systems with slow

dynamics behaviors. MPC provides an approximate “receding

horizon” solution, where the receding horizon optimal control

inputs to the plant is calculated within limited steps which

minimize the cost function under constraints. However, only

the values calculated at the next available time are used. This

process is repeated at every sample. Considering the actual

change of the state of the plant [19], the MPC creates a closed

loop control. MPC control strategy has been applied to a

number of engine control applications. In this section, a

number of the MPC control examples will be presented.

Sliding-mode, extremun-seeking, and linear parameter-

varying (LPV) gain-scheduling control techniques are also

used to control engine and its actuating subsystems.

1) VVA MPC control

VVA can significantly improve the fuel economy, reduce

the exhaust emissions, and increase the power output of

internal combustion engines.

Paper [20] presents an MPC for an electro-pneumatic valve

actuator used on engine VVA. Both the exhaust valve actuator

model and the in-cylinder pressure model have been

developed and are explained in [21]. MPC technique is used

to improve the repeatability of the VVA actuation. The model

parameters are first identified using a model reference

adaptive scheme and then a closed-loop valve lift and closing

timing control are formulated to generate the feed forward

estimated valve timings based on the identified parameters.

The close-loop control is used to eliminate the steady-state

error. The block diagram of this control structure can be found

in [21].

Fig 2: Control system architecture for reference [21]

2) MPC air-to-fuel ratio control for gasoline engines

Air-to-fuel ratio (AFR) affects the fuel efficiency, emission

reduction and performance improvement of an internal

combustion engine. In [23], an AFR model for gasoline

engine is constructed using neural network modeling

technique.

Fig 3. Control system scheme for [23]

The model is calibrated on-line to adjust its nonlinear

dynamics and the parameter uncertainties. Based on this

adaptive model, MPC strategy is used to maintain the in-

Control-oriented

model

MIT rule

[22]

Feedforward

Calculation

Actuation

Calculation

PI controlSolenoid signal

constructionValve plant

Actuation

timing

+

+

+

+

+

-

+

-

Desired

valve

actuation

DriverFilter

Nonlinear

optimization

Engine

simulation

Neural

Network

model

Fuel injection

quantity

+

+

+

-

-

Se

tpo

int

Engine

output

2099

cylinder AFR at stoichiometric level as the engine load and

speed changes. The trained adaptive model is used to predict

the engine output for a certain sampling times, an optimizer

then minimizes the proposed cost function which is

constructed as a combination of the differences between the

desired and predicted AFR and fuel injection quantity. The

MPC then locates the optimal model predicted fuel injection

quantity within one sampling period. The optimal injection

amount is applied for the control and the whole process is

repeated for the next sampling time. The control scheme of

this work can be found in [23].

3) MPC Exhaust gas recirculation valve position control

EGR technique is used for diesel engines for the purpose of

reducing NOx emissions in the engine exhaust. Paper [31]

presents an MPC method for EGR valve position control

which is an important mean for achieving accurate EGR

manipulation. A two-state EGR valve model is designed in

this work where the model parameters are determined through

experiment measurement and the valve plate position is

defined as the output from the model. The future steps of the

plant output as well as the corresponding control input are

derived from the MPC controller in advance at every step. The

MPC control structure can improve the response time and

accuracy of the EGR valve positioning. The structure of this

control scheme can be found in Fig 1.

Fig 1. System control scheme for [31]

4) Sliding mode AFR ratio control

In order to promote the fuel efficiency as well as reducing

the emissions from gasoline engines, a duel fuel system with

gasoline port fuel injection (PFI) and ethanol direct injection

(DI) controlling strategy is presented in [24]. The control aim

is to vary the PFI and DI fuel injection rate thus to maintain

the engine AFR ratio at a desired level, while at the same time

regulate the PFI fueling to the total fueling ratio at a desired

value.

A multiple input and multiple output (MIMO) sliding mode

controller with state estimator was developed based on a

simplified AFR model. The state estimator provides the

controller with state information in real-time from accessible

measurements due to limited sensor availability. The control

scheme of this work can be found in [24].

Fig 4. Control structure for [24]

5) Extremum seeking

Besides model-based control strategies, non-model-based

control method has also becoming more popular in the realm

of engine control research due to its practical advantage in

real-time application. Extemum seeking (ES) is a model-less

gradient based optimization method that has become very

popular recently after its local stability have been proved in

2000 [25]. The method utilizes a sinusoidal signal to perturb

the input to a dynamic plant. The output of the plant is first

high pass filtered to remove the DC offset and then the

gradient estimate in the output is demodulated by multiplying

the signal to a sinusoidal dither signal. The gradient

information is then extracted by low pass filtering the

demodulated output to remove all the components that are

harmonic of the sinusoidal signal. The gradient is then pushed

to its extremum using a gradient descent algorithm.

Fig 5. Extremum seeking architecture

In [26], ES was used to tune cam timing and spark timing

to improve the brake specific fuel consumption (BFSC) for a

variable cam timing engine. Reference [27] introduced an

approach where ES was used for the fuel consumption

optimization of an HCCI engine. The authors used a

temperature-control valve to adjust the in-cylinder gas

temperature, thus altering the auto-ignition of the

homogenous cylinder charge and hence the combustion

timing. ES was applied to perturb the combustion-timing set-

point to optimize the fuel consumption. The set-point was

then used to tune the PID parameters for the valve controller.

ES was also applied in [28], where the engine performance

index was minimized by controlling the throttle position. An

ES implementation of spark timing modulation for

maximizing the steady state EGR amount with guaranteed

combustion stability can be found in [29]. In [30], ES is used

to locate the optimum intake oxygen concentration for which

a diesel engine can reach a point where both its emissions and

the engine combustion efficiency would compromise to a

satisfactory level.

6) LPV control

LPV gain-scheduling control [35] was used to control the

engine air-to-fuel ratio (AFR) [32], variable valve timing

(VVT) actuator [33], and engine throttle position [34]. The

advantage of the LPV control is that the parameter dependent

gains can be obtained during the control design, which

eliminates (or significantly reduces) the control calibration

effort.

Engine

model

Target state

calculator

Sliding mode

controller

+

-

Desired AFR,

PFI ratio

AFR, PFI

ratioTarget state

calculator

Mass air

flow rate

2100

III. CONTROL-ORIENTED MODELING AND MODEL-BASED

CONTROL FOR AFTERTREATMENT SYSTEMS

The ground vehicle engine emission aftertreatment systems

have experienced a long and inventive development for

several decades [36]. As the primary means of converting the

harmful engine-out emissions into environmentally-friendly

species, aftertreatment systems have become necessary and

crucial parts for both diesel and gasoline vehicle powertrains.

For gasoline engines, the three-way catalyst (TWC) has been

the dominant and very effective aftertreatment system. Diesel

engines’ aftertreatment systems are multifarious including

diesel oxidation catalyst (DOC), diesel particulate filter

(DPF), selective catalytic reduction (SCR) system, and lean

NOx trap (LNT), etc. The complex physical processes and

chemical reactions occurring within such aftertreatment

systems naturally make them nonlinear and multivariable

dynamic systems, and highlight the significance of model-

based aftertreatment control systems. This section briefly

describes some recent progresses on control-oriented

modeling and model-based control for engine aftertreatment

systems.

A. Control-oriented modeling for aftertreatment systems

The chemical reactions and physical processes that occur in

engine aftertreatment systems are quite complex and involved.

Detailed and computational models describing the chemical

reaction kinetics, flow, and thermo-physical phenomena in

engine exhaust aftertreatment systems have been coming forth

since about a half century ago when catalytic converters were

introduced for vehicle applications [37]-[41]. Such models can

provide insightful and detailed understanding and

mathematical descriptions on the chemical reactions, mass

transfer, and heat transfer processes in the catalysts in one-

dimensional and multi-dimensional fashions. From the real-

time, model-based control and estimation viewpoints,

aftertreatment system models that describe the main dynamics

and characteristics of the catalysts in ordinary differential

equations (ODE) are desirable and tractable for the designs of

aftertreatment system control, estimation, and fault diagnosis

algorithms. In this subsection, emphasis will be therefore

placed on the control-oriented models of the mainstream

aftertreatment systems for Diesel and gasoline engine

applications.

1) SCR system operating principles

For diesel vehicle tailpipe NOx emission reductions, urea-

SCR (selective catalytic reduction) systems have recently

evolved as the leading choice in medium-to-heavy-duty

applications and popular option in light-duty applications.

The fundamental NOx reduction mechanism of urea-SCR

systems is to supply ammonia (NH3) for catalytically

converting the engine-out nitrogen oxides (NOx) into nitrogen

(N2) and water (H2O). For safety and toxicity concerns in

mobile applications, Diesel exhaust fluid (DEF) containing

32.5% aqueous urea and 67.5% deionized water is used to

provide ammonia to the SCR catalysts. The urea solution that

is injected upstream of SCR needs to go through a urea-to-

ammonia conversion process that typically includes urea

solution evaporation (77), thermal decomposition of solid

urea (78), and hydrolysis of isocyanic acid (HNCO) (79),

respectively [42].

( )2 2 2 2 2NH CO NH liquid NH CO NH xH O

∗− − → − − + (77)

2 2 3NH CO NH HNCO NH∗− − → + (78)

2 3 2H O HNCO NH CO+ → + . (79)

Next, the ammonia adsorption to the SCR catalyst and the

ammonia desorption from the catalyst may happen

simultaneously, as described by reaction (80) in [40].

3 3freeNH NHθ ∗+ ↔ (80)

where the forward reaction and reverse reaction represent the

ammonia adsorption and desorption, respectively; freeθ

denotes the free catalyst sites. One of the important variable

for SCR systems is the SCR ammonia coverage ratio, 3NH

θ ,

which is defined as (81):

3 3NH NHMθ = Θ (81)

where 3NH

M indicates the total amount of ammonia adsorbed

on the catalyst sites; Θ denotes the ammonia storage capacity

of the catalyst.

The SCR catalytic deNOx reactions can be described by the

following three reactions of different reaction rates [43]:

3 2 2 24 4 4 6NH NO O N H O∗ + + → + (82)

3 2 2 22 2 3NH NO NO N H O∗ + + → + (83)

3 2 2 24 3 3.5 6NH NO N H O∗ + → + (84)

At high exhaust temperatures (>450 °C), ammonia can

undesirably react with oxygen and be oxidized into N2 via

reaction (85) [43], and NO oxidation may occur as well.

3 2 2 24 3 2 6NH O N H O∗ + → + (85)

As far as the performance of SCR systems, both tailpipe

NOx and NH3 emissions are concerned. However, lowering

tailpipe NOx emissions and lowering tailpipe NH3 emissions

are naturally conflictive. High SCR ammonia coverage ratio

can increase the NOx reduction efficiency and reduce the

tailpipe NOx emissions, but may cause high tailpipe NH3 slip.

Low SCR ammonia coverage ratio may help to reduce the

tailpipe NH3 slip, but cannot sufficiently reduce the NOx

emissions. Such a contradictory feature of the SCR operation

also forms one of the fundamental challenges for the real-time

control of SCR systems.

2) SCR control-oriented models

Several control-oriented models for urea-SCR systems

have been developed in the past decade. In order to yield the

models in the form of ordinary differential equations (ODEs),

a common assumption employed in the SCR system control-

oriented modeling work is to treat the SCR as a continuous

stirred tank reactor (CSTR) in which all the states are

homogeneous [44]-[47]. Schӓr et al. proposed a two-state

control-oriented SCR model including temperature dynamics

and ammonia coverage ratio by ODEs [44]. In [45],

Devarakonda et al. developed a four-state control-oriented

SCR model with both NO and NO2 being considered as states.

A more complete SCR control-oriented model was recently

developed in [47] with experimental validation. This model

considers the aforementioned reactions as well as the urea-to-

2101

ammonia conversion process with the assumption that the

injected urea is completely converted into ammonia upstream

of the SCR at high enough temperatures. Arrhenius equations

are used to model the reaction rates and a first-order dynamics

is employed to approximate the urea-to-ammonia conversion

process. Based on the mass conservation law, this five-state

model is expressed as

2 3 2 3 2

2 3 2 2 2

2

3 3 3 3

3

3

3

3

11 2 5 ,2

12 5 ,2

14 4 2 ,

,

[ (1 ) ]

(

F FNO O NH NO NO NH NO O NO NO inV V

NOF F

NO NO NH NO O NO NO inV VNO

F FNH F NH R NH NH inV V V

NH

NHNH

NH in

rC C V r C C V r C C V C CC

r C C V r C C V C CC

C r r CC

C

θ θ

θ

θ θ δ

θθ

− Θ − Θ − − +

− Θ + − +

− Θ − + + Θ + = −

ɺ

ɺ

ɺ

ɺ

ɺ

3 2 2 2 3

3

2 2

4 3 1 4 2 1 2 4

,

)

2

, 1,2,3,4 ,4 ,5EiRT

F NH O R NO O NO NO F NH

AdBlueNH in

urea

i i

r C V r C V r rC C V r C C V r C V

uC

N F

r K e i F R

δ δ

τα α

−

+ + + + +

− +

= =

(86)

in which, *

C represent the concentrations of gas species, F is

the gas flow rate, V is the SCR catalyst volume, T is the

temperature, Ei and Ki are the activation energy and rate

constant of Arrhenius reaction model, δ is the ammonia

desorption efficiency, α is the inverse of time constant, τ is

the mass fraction of urea in the urea solution, Nurea is the

atomic number of urea, and uAdBlue is the mass injection rate

of urea. The model parameters were identified by minimizing

the least-squares errors of the measured and model-predicted

NO, NO2, and NH3 concentrations in various SCR operations

using Genetic Algorithm.

3) DOC and DPF control-oriented models

In addition to the diesel NOx treatment devices, DOC and DPF (or catalytically coated DPF with integrated SCR capability) are two other indispensable components for Diesel aftertreatment systems with DOC’s main function as oxidizing CO, HC, and organic fraction of diesel particulates and DPF’s main function being the reduction of tailpipe PM emissions. As the oxygen in diesel exhaust gas is excessive, the DOC CO and HC oxidation efficiencies are usually quite high as long as the temperature is above the light-off temperature (200 ºC). Because DOC and DPF are typically placed upstream of the NOx treatment devices, their dynamics on gas temperature, oxygen concentration, and NO/NO2 ratio are of particular interests from the downstream system operation and tailpipe emission viewpoints. In [48]-[50], several control-oriented DOC and DPF models are generated to describe these dynamics in a tractable fashion. By utilizing the Eley-Rideal mechanism to describe the chemical reactions inside a DOC and treating a DOC as an ideal combustion chamber, the temperature dynamics for DOC solid materials and exhaust gas passing through the DOC can be formulated as (87) and (88), respectively [48].

( )( )

( )( )

( ) ( )

( )

1 2

1

,

2

1

1

DOC DOC

out

g DOCDOC

DOC DOC

outDOCg DOC exh ambDOC

v DOC

DOC

T K T K

hAmcK H

mc mc

qmc H T hA T

hK

mc

= +

= − − +

− − +

=

ɺ

ɺ

ɺɺ

(87)

, ,

, ,

, ,exp

DOC DOC

g outlet DOC DOC exh DOC DOC

v DOC v DOC

v DOC c DOC DOC

DOC

g

q qT T T T H

h h

h A LH

mc

= + + − −

= −

ɺ ɺ

ɺ

(88)

where, TDOC is the lumped temperature of DOC solid

materials, Tg,outlet,DOC is the gas temperature at DOC outlet,

Texh is the engine-out exhaust gas temperature, Tamb indicates

the ambient temperature, (mc)DOC is the product of DOC

overall mass and specific heat, ( )out

DOChA is the product of

convective heat transfer coefficient and outer surface area of

the DOC, hv,DOC represents the volumetric convective heat

transfer coefficient, Ac,DOC is the cross-sectional area of a

DOC, DOCqɺ represents the specific heat release rate due to the

chemical reactions. The values of those parameters can be

identified from experimental data. For example, Fig. 6 shows

that the model with calibrated parameter values can predict

the actual DOC-out gas temperature well during transient

engine operations.

Fig. 6. Comparison between modeled and measured DOC-out gas

temperature [48].

In [51], a simplified DPF model was developed to describe

the thermal response. Such a model was modified by

including the heat generation from the chemical reactions

inside a DPF, and a control-oriented model of DPF solid and

gas temperature dynamics was proposed in [48] based on the

energy conservation as given by Equations (89) and (90).

2102

( )( )( )

( )( )

( )( )

( ) ( ) ( )

( )

3 4 5

3

4

, ,

5

1 1

1

1 1

DPF DOC DPF

g

DOC DPF

DPF

out

g DPFDPF

DPF DPF

out DOC DPFamb g DPF exh DOC DOCDPF

v DOC v DPF

DPF

T K T K T K

mcK H H

mc

hAmcK H

mc mc

q qhA T mc H T H H

h hK

mc

= + +

= − −

= − − +

+ − + − −

=

ɺ

ɺ

ɺ

ɺ ɺɺ

(89)

, , , ,

, ,

, ,exp

DPF DPFg outlet DPF DPF g outlet DOC DPF DPF

v DPF v DPF

v DPF c DPF DPF

DPF

g

q qT T T T H

h h

h A LH

mc

= + + − −

= −

ɺ ɺ

ɺ

(90)

where, TDPF is the DPF solid temperature, Tg,outlet,DPF is the

DPF outlet gas temperature, (mc)DPF is the product of overall

mass and specific heat of a DPF, ( )out

DPFhA denotes the

product of heat transfer coefficient and outer surface of a

DPF, hv,DPF represents the volumetric convective heat transfer

coefficient, Ac,DPF is the cross-sectional area of a DPF, DPFqɺ

denotes the volumetric heat release rate due to chemical

reactions. The parameter values can be acquired through

parameter identification and optimization using the

experimental data. For instance, Fig. 7 demonstrates that the

model can well capture the DPF-out gas temperature

dynamics in comparison with the measured gas temperature.

Fig. 7. Comparison between modeled and measured DPF-out gas temperature

[48].

As the oxygen concentration in diesel exhaust gas has

influential effect on in-cylinder combustion and engine-out

emissions through both high-pressure and low-pressure EGR

loops, it is meaningful to model the oxygen concentration

dynamics throughout the DOC and DPF from engine-

aftertreatment system control, estimation, and fault diagnosis

perspectives. By considering the chemical reactions relevant

to oxygen in a DOC and a DPF and under the CSTR

assumption, control-oriented models for DOC and DPF

oxygen concentration dynamics were developed and

experimentally validated in [50] as shown in the following

equations (91) and (92).

2 2 2 2

,2 ,2 ,2 ,2

,2 ,3 ,2 ,2

2 2 2 2

in out oxi red

O O O O

V V r RC C C C

V V V V= − − +ɺ ɺ

ɺ (91)

2 2 2 2

,2 ,1 ,1 ,1

,1 ,2 ,1 ,1

1 1 1 1

out out oxi red

O O O O

V V r RC C C C

V V V V= − − +ɺ ɺ

ɺ (92)

where, the subscripts “1”, “2”, and “3” represent the DPF,

DOC, and exhaust manifold, respectively; ,*inVɺ and ,*outVɺ are

volume flow rates at the inlet and outlet of the DOC and DPF,

respectively; 2 ,*OC denotes the oxygen concentration, *V is

the volume of the DOC or DPF; ,*oxir is the DOC or DPF

oxygen reaction rate coefficient, and ,*redR denotes the

reaction rate due to reduction inside the DOC or DPF.

Fig. 8. Comparison between modeled and measured DOC-out oxygen

concentration [50].

These parameters can be identified based on experimental

data. Comparisons between the measured and modeled

oxygen concentrations at DOC and DPF outlets as in Fig. 8

and Fig. 9 demonstrate that the models can capture the oxygen

concentration dynamics well.

Fig. 9. Comparison between modeled and measured DPF-out oxygen

concentration [50].

Another important variable for the diesel aftertreatment

systems, particularly for DPF and SCR, is the ratio of

NO2/NOx in the exhaust gas. While majority of the NOx in

diesel exhaust is NO, higher NO2/NOx ratio is preferable from

0 500 1000 1500 2000 2500 30000

5

10

15

20

Time (sec)

Co

ncen

trati

on

(%

)

Aft. DOC O2 (test)

Aft. DOC O2 (model)

0 500 1000 1500 2000 25000

5

10

15

20

Time (sec)

Co

ncen

trati

on

(%

)

Aft. DPF O2 (test)

Aft. DPF O2 (model)

2103

both NO2-assisted DPF regeneration and SCR NOx reduction

viewpoints [54], [55]. Due to the NO oxidation in the DOC

and NO2 consumption in the DPF, the NO2/NOx ratio changes

along the diesel aftertreatment components. Unfortunately,

the current commercial NOx sensors cannot differentiate NO

or NO2 but only measure the lumped NOx concentration in the

exhaust gas. Thus control-oriented models that can describe

the dynamics of NO and NO2 concentrations in DOC and DPF

would be quite useful for the control of downstream SCR

systems. With an empirical model characterizing the engine-

out NO and NO2 concentrations and the CSTR assumption,

the NO and NO2 related chemical reactions in DOC and DPF

are considered in the control-oriented models developed in

[49]. Such models also assume that the exhaust gas NOx

consists of only NO and NO2, and the total NOx concentration

does not change through the DOC or DPF. Thus, the models

only need to describe the dynamics of the NO concentration

as shown in Equations. (93) and (94).

, , ,in DOC oxi red

NO DOC NO in NO DOC

DOC in DOC DOC

F T R RC C C

V T V V

= − − +

ɺ (93)

( )2,

, , ,

C NODPF DPFinNO DPF NO in NO DPF

DPF DPF in DPF

RP p TFC C C

V P T V

+ ∆ = − +

ɺ (94)

where, VDOC and VDPF are the volumes of DOC and DPF,

respectively; Fin is the engine exhaust gas volume flow rate;

*T are the temperatures; Roxi and Rred are the reaction rates of

oxidation and NO2 reduction in the DOC; PDPF is the DPF

downstream pressure and p∆ is the differential pressure

across DPF; 2,C NOR is the reaction rate of the NO2-assisted

DPF regeneration. Such model parameters were identified

based on experimental data using the Genetic Algorithm. The

comparisons between the measured and modeled DOC-out

and DPF-out NO and NO2 concentrations during transient

engine operations are shown in Fig. 10 and Fig. 11 where

good agreements are observed.

Fig. 10. Comparisons between the measured and modeled DOC-out NO and

NO2 concentrations [49].

Fig. 11. Comparisons between the measured and modeled DPF-out NO and

NO2 concentrations [49].

4) TWC control-oriented models

On the gasoline engine side, the three-way catalyst (TWC)

converters have been the dominant aftertreatment systems

studied in the field. Complex phenomenal models based on

chemical and thermo-fluid principles and simplified kinetic

models based on reactions have been developed.

For the real-time control and diagnosis purposes, gas

storage dominated dynamic models which are accurate and

simple enough have also been developed. Most of control-

oriented TWC models consist of only nonlinear oxygen

storage dynamics. In [56] and [57], Brandt et al. proposed and

experimentally evaluated a simplified TWC model which

consists of a steady-state efficiency submodel, brick

temperature dynamic model, and oxygen storage dynamic

model without considering the effects of feedgas, catalyst

temperature and space velocity. Peyton-Jones et al. developed

a simplified oxygen storage dynamic model for a TWC

converter by incorporating the effects of space velocity which

is capable of accurately describing the response of catalysts

during transient operations [58]. Furthermore, to improve the

prediction of conversion efficiency under rich condition and

avoid distortion of post-catalyst exhaust gas oxygen (EGO)

sensor signals, an extended control-oriented TWC model

explicitly considering both oxygen storage dynamics and

reversible catalyst deactivation dynamics was proposed and

experimentally validated in [59]. In [60] and [61], the authors

offered two control-oriented TWC models with the fraction

of oxygen sites and air-fuel ratio at the catalyst outlet being

the state variables which are suitable for real-time control

purpose during and after the warm-up phase, respectively. To

predict the essential features of TWC such as the oxidant and

reductant emissions, the total oxygen storage capacity, and

the fractional oxidation state, over a wide range of engine

operation in real-time, an accurate low-dimensional TWC

model consisting of seven ODEs was developed and

experimentally validated recently in [62]. Also a simple

catalyst aging model was proposed to update the catalyst

storage capacity in the literature. In [63], a control-oriented

multi-cell TWC model was proposed and experimentally

validated for a TWC converter under different driving

conditions. This model can potentially be utilized to describe

the oxygen storage distribution across the axial direction.

Dawson et al. developed and validated simplified TWC

models which are capable of distinguishing healthy TWC

from aged TWC in [64].

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Time (sec)

Aft.DOC NO, (Model, ppm)

Aft. DOC NO2, (Model, ppm)

Aft. DOC NO, (Meas., ppm)

Aft. DOC NO2, (Meas., ppm)

DPF Load (ECU, hPa/(m3/sec))

0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

Time (sec)

PP

M

After DPF NO (Meas)

After DPF NO2 (Meas)

After DPF NO (Model)

After DPF NO2 (Model)

2104

B. Model-based estimation and control

The primary purpose of the abovementioned engine

aftertreatment system control-oriented models is to serve for

the designs of real-time aftertreatment control and fault-

diagnosis systems to reduce the tailpipe emissions during

real-world vehicle operations. Because the observers and

controllers designed are based on such control-oriented

models that contain physically-meaningful parameters of the

actual aftertreatment systems, the model-based estimation and

control algorithms can have excellent generalizability among

different platforms. In this section, some observer and

controller design examples of using such control-oriented

models are briefly described.

1) Model-based estimation of diesel aftertreatment systems

Due to the high complexities associated with the chemical

reactions, physical processes, and structural characteristics of

diesel engine aftertreatment systems, many system states and

signals are not directly measureable or too expensive to

measure in production vehicles. Model-based observers thus

are instrumental for providing the necessary information for

real-time control and diagnosis systems. As the aftertreatment

system dynamics are generally featured by time-varying and

nonlinear characteristics, synergistic combinations of the

estimation theory with insight into the aftertreatment system

characteristics may offer effective approaches.

In [49], an observer was designed to estimate the DOC-out

and DPF-out NO and NO2 concentrations with the total NOx

concentration being the measurement. The convergence of the

estimation errors is proved using the Lyapunov analysis to

study the time-varying parameter characteristics of the DOC

and DPF control-oriented models (93) and (94). Following the

similar thought process, in [48] and [50], two observers were

designed for estimating the DOC and DPF gas and solid

temperatures as well as the DOC-out and DPF-out oxygen

concentrations based on the control-oriented models

mentioned earlier, respectively. The convergences of the

estimation errors are also guaranteed by analyses using

Lyapunov method incorporating the characteristics of the

model structures and time-varying parameters. As an example

of these observers, Fig. 12 indicates that the estimated DOC-

out NO and NO2 concentrations can match with the measured

ones very well.

Fig. 12. Comparison of the measured and observer-estimated DOC-out NO

and NO2 concentrations [49].

For urea-SCR systems, there are two important variables

that certainly require accurate real-time estimations. One is

the SCR catalyst ammonia coverage ratio, 3NH

θ , which as

shown in equation (86) has a pivotal influence on both the

SCR NOx reduction and SCR ammonia slip, but cannot be

measured by any sensors. The other variable is the actual NOx

concentration in the presence of NH3 due to the NOx sensor

ammonia cross-sensitivity. In [65]-[67], sliding-mode

observers and gain-scheduled observer were developed based

on the SCR control-oriented models like the one in equation

(86) to estimate the SCR ammonia coverage ratio in real-time.

Simulations and indirect experimental measurements were

used to demonstrate the effectiveness of such observers. Two

different extended Kalman filter based methods for estimating

the actual NOx concentrations in the presence of NH3 are

offered in [68] and [69], where one approach uses both the

NOx sensor and NH3 sensor, and another approach only

utilizes two NOx sensors of different cross-sensitivity factors

for reduced cost. Experimental results show that such

methods can well correct the NOx sensor outputs in the

presence of both NOx and NH3.

C. Model-based control for diesel aftertreatment systems

Real-time controls of the diesel aftertreatment systems,

particularly the NOx treatment systems, are crucial because of

the highly transient engine operations and increasingly

stringent tailpipe emission regulations. Various different

model-based SCR control methods have been proposed in

literature [70]-[73], [75]. The naturally conflicting

requirements on simultaneously reducing tailpipe NOx and

NH3 emissions as mentioned earlier for SCR systems make

the urea dosing control quite challenging. Among several

others, one of the fundamental issues for SCR control is how

to control the ammonia coverage ratio distribution profile

along the SCR longitudinal axial direction, which can

significantly affect the SCR NOx reduction and NH3 slip

performance. Based on the SCR operation principles, it would

be ideal to have the ammonia coverage ratio high upstream of

SCR and low downstream of SCR in order to achieve high

NOx conversion efficiency and low tailpipe ammonia slip.

However, in all the control-oriented SCR models, the states

including the ammonia coverage ratio are assumed

homogeneous inside an SCR without differentiating the actual

state variations along the SCR axial direction in order to keep

the resultant models in the forms of ODE. This modeling

deficiency inherently limits the performance of SCR control

systems. In [71], [75]-[76], control and optimization methods

were developed to achieve approximated SCR ammonia

coverage ratio distribution profile control by using two SCR

cans connected in series. By inserting sensors in the SCR

catalyst or splitting the catalyst into two cans, such SCR

control approaches try to control urea dosing rate such that the

ammonia coverage ratio of the upstream SCR can be high for

high NOx conversion efficiency while keeping the ammonia

coverage ratio of the downstream SCR can below a low upper

bound to constrain the tailpipe ammonia slip. Experimental

results have shown that such a two-can SCR control strategies

can significantly improve the SCR operational performance

in terms of simultaneous reductions of the tailpipe NOx and

NH3 emissions in comparison to urea dosing control methods

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

Time (sec)

PP

M

After DOC NO, Meas.

After DOC NO2, Meas.

After DOC NO, Est.

After DOC NO2, Est.

2105

do not consider the ammonia coverage ratio distribution

profile.

1) Model-based control for gasoline TWC

Model-based controls of TWC converters have been

broadly studied in the past a couple of decades. In [77],

Balenovic et al. proposed a popular cascade dual-loop model-

based control method for a TWC converter with the oxygen

storage controller in the outer loop for calculating the

reference lamda signal and air-fuel ratio engine controller (an

internal model control strategy) in the inner loop for

controlling the relative storage level in the catalyst. Schallock

et al. developed a nonlinear model predictive catalyst

controller which was implemented within a multi-rate cascade

control structure which allows sufficient time for solving

dynamic optimization during real-time implementation in

[78]. In [79], a model-predictive air-fuel ratio controller was

proposed to optimize the oxygen storage capacity by allowing

deviation from stoichiometric operation without significant

post-catalyst emissions for minimizing both vehicle

emissions and fuel consumption during transient operation.

Meanwhile, a number of studies have been focused on the air-

fuel ratio control systems of SI engines because an accurate

control for stoichiometric feed gas air-fuel ratio is important

for emissions reductions [80]. Other studies are focused on

the on-board diagnostic of automotive TWC converters. In

[81], Dawson et al. developed a model-based diagnostic

method for monitoring the health of automotive TWCs by

recognizing the change of coefficients in the adapted models

via an information synthesis technique. The model-based

diagnostic algorithm was verified successfully using

experimental data. An integrated model-based control and

diagnostic system where the adaptive gain in the control

system can be utilized to reflect the catalyst health was

developed in [82]. The benefit of this approach is that it does

not require complex entry condition and thus significantly

reduces the calibration burden.

IV. CONTROL-ORIENTED MODEL AND MODEL-BASED

CONTROL FOR TRANSMISSION SYSTEMS

A. Introduction to the transmission systems

With the latest CAFE regulation, technical innovations are

required for both engines and transmissions to significantly

improve the efficiency and reduce emission [83], [84]. In

theory, transmissions are not needed if the engine can provide

the required speed and torque for the vehicle in real-time with

high efficiency. Unfortunately the engine operation range is

not a direct match with the vehicle operation and its efficiency

varies significantly as a function of the speed and torque. In

order to transfer the engine torque to the vehicle with the

desired ratio smoothly and efficiently, various transmissions

are designed [85]. The most common automotive

transmissions are manual transmission (MT) and step gear

automatic transmission (AT). Other types of transmissions

include automated manual transmission (AMT), dual clutch

transmission (DCT), continuously variable transmission

(CVT), and hybrid transmission.

Manual transmissions are controlled by the driver and don’t

require automatic control. Automatic transmissions conduct

gear shift automatically and require complex controls [85].

The control problem becomes more challenging as more

speeds (gear ratios) are used in the automatic transmissions in

recent years. The gear shift in AT is realized by shifting a set

of clutches actuated with fluid power. So the dynamics of the

fluid power actuation system and the clutches are critical to

shift quality.

The automated manual transmission is designed based on

the MT architecture. Actuators are added to select the gears

and engage or disengage the clutch that connects the

transmission to the engine. Such automation greatly reduces

the complexity of operating the MT and still maintains its

high efficiency. However the torque interruption still exists

during the AMT gear shift where the clutch has to disengage

to disconnect the engine and the transmission. To reduce or

eliminate the torque interruption, dual clutch transmissions

(DCT) were introduced. DCT uses two input clutches – one

for odd gears and one for even gears. DCTs can transmit

torque continuously during the shift by coordinating the two

input clutches. For AMTs and most DCTs, they don’t use the

torque converter between the engine and the transmission and

therefore the clutch control is critical to ensure driveline

vibration is not triggered.

Continuously variable transmissions (CVT) [86] allows the

engine to operate at speed and load conditions independently

from the speed and load requests of the vehicle by varying the

transmission ratio continuously. This feature enables the

engine to operate in the optimal region independent of the

vehicle speed to maximize the fuel efficiency and reduce

emissions. Different types of CVT have appeared in the

market. The belt and chain drive CVTs use the hydraulic

piston to control the sheave position and thus the input-output

ratio. Toroidal traction drive transmissions (TCVT) [87] have

been examined by many manufacturers as promising

alternatives to chain or belt CVTs. TCVTs offer a larger

torque capacity and a quicker ratio change capability. A half-

toroidal CVT system is unstable under open-loop operation

and hence a speed ratio control system is necessary[88],[89].

Hybrid transmissions [90], [91]are designed to combine the

engine power and the alternative power (eletrical or fluid

power) for hybrid vehicles. A key architecture for hybrid

transmission is the power split hybrid. There are two main

catergories for the power split transmission. One is the

electrically variable transmissions (EVT) [90]and the other is

the hydro-mechincal transmission (HMT)[91]. The EVT

employs eletrical motor and genratror with one or two sets of

planetary gears to form the power split architecture. The HMT

uses hydraulic motor and pump with the planetary gear sets to

form the hybrid transmission. The EVT splits the engine

power into the mechanical path and the eletrical path and then

combine them to propel the vehicle. Such power split will

provide an extra degree of freedom for optimizing the engine

operating condition independent from the vehicle operation.

The HMT operates in a similar fashion.

B. Control-oriented transmission system modeling

Transmission models often consist of the modeling of the

gear ratio mechanics and the modeling of the gear shift

mechanism [85]. Transmission models are typically

2106

combined with the engine model and the vehicle model to

simulate the overall powertrain performance.

The gear ratio mechanics describes the gear ratios by

connecting different nodes of the planetary gear sets. This will

effectively generate different ratios between the engine and

the vehicle. For hybrid transmissions, the speed and torque

relationship between the sun gear, the carrier, and the ring

gear is critical to realize the power split function and therefore

needs to be modeled.

The gear shift mechanisms can be divided into two

categories: the hydraulically actuated system and the

electrically actuated system. For ATs, hydraulically actuated

clutches are used to connect different nodes of the planetary

gear sets. During the gear shift, one clutch (off-going clutch)

will be disengaged, and another clutch (on-coming clutch)

will be engaged. This is called the clutch to clutch shift

technology. The coordination of the on-coming clutch torque

and the off-going clutch torque is critical to the shift quality.

So the modeling of the electro-hydraulic actuation system and

the clutch dynamics are needed [83], [92], [93].

Fig 13. Schematic of the transmission clutch

As shown in Fig. 13, the dynamics of an electro-

hydraulically actuated clutch can be modeled as[93]:

1 2x x=ɺ

2 2

2 1 0

1[ ( )

( , ) ( )]

p r c atm p

p

drag r c res p

x A P P P D xM

F P P x F x x

= × × + − −

− + − +

ɺ

(95)

2

( )[ ( , ) ]r

r r p

PP Q u P A x

V

β= −ɺ

where x1 is the clutch piston displacement, x2 is the clutch

piston velocity, Mp is the effective mass of the piston, Ap is

the piston surface area, Dp is the clutch damping coefficient,

Patm is the atmospheric pressure, xp0 is the return spring

preload. Pc is the centrifugal force induced pressure generated

from the rotation of the clutch assembly. Fres is the

displacement dependent resistance force. During the clutch

fill, the resistance force comes from the return spring. During

the clutch engagement, the resistance force is due to the

squeezing of the clutch pack. Fdrag is the piston seal drag

force, which is dependent on the piston motion. Pr is the

clutch chamber pressure. V is the chamber volume and β is the

effective bulk modulus. Q is the incoming flow rate and it is

often controlled with a solenoid valve.

This model contains several nonlinearities. The drag force

is dependent on the clutch motion as well as the clutch

chamber pressure that expands the piston seal against the wall.

The fluid bulk modulus is a function of the chamber pressure,

especially at the low pressure range and with high air

entrapment. The clutch resistance force during the clutch

engagement is typically a nonlinear function of the clutch

displacement and can also vary as a function of temperature.

Those nonlinear dynamics are difficult to model precisely and

require robust control to enable precise and robust

performance.

For hybrid transmissions, besides the gear ratio mechanics

and the gear shift mechanism, the alternative power source

also needs to be modeled, such as the motor, generator and

the battery [85]. Again control-oriented models are needed for

the alternative power sources so that they can be used for

control design purpose and for real-time simulation.

C. Model-based transmission control

Transmission control is mainly concerned with the

transmission shift scheduling and gear ratio shift control. The

shift scheduleing [94], [95]determines when to shift and to

which gear (the new gear ratio). This is necessary since all

transmissions except MT will determine the gear ratio

automatically in real-time. Traditionally the shift shceduling

is designed based on the gas padel position and the vehcile

speed. More factors are being considered to better coordinate

the transmission ratio with the engine operation to improve

fuel consumption and reduce emissions. The transmisison

gear ratio shift control is targeted to achieve a smooth shift

from the current gear to the new gear ratio based on the shift

scheduling. For CVTs, it is shifted from one ratio to another

rather than a discrete step gear ratio. The gear ratio shift

depends heavily on the specific shift mechanism of the

transmissions. For ATs and CVTs, and many AMTs and

DCTs, such shift mechanism is conducted with fluid power

system[96]. The controlling of the fluid power system

(pressure, flow) and the clutch is critical to realize the high

shift quality. For ATs, the control is achieved by a

combination of open loop, closed loop and event based

controls. Part of the challenge for realizing complete feedback

control is the availability of low cost and reliable sensors.

Traditionally calibration has been the key method for

designing and tuning the transmission control. This method

becomes more time consuming today due to the increasing

number of transmission speeds and the high number of

various types of transmissions. Model-based transmision

control is necessary to further improve system performance

and reduce the development time. To achieve this objective,

research work on hardware (sensors and actuators), control

oreinted model development and advanced control

methodologies is required. Several examples inlcude

feedback loop in the transmisison hydraulic control module

and the pressure based clutch feedback control.

One example of the pressure based clutch control [93] is to

imbed a pressure sensor in the clutch chamber and close the

loop with a sliding mode control due to its ability to handle

Clutch

Seal

Piston

Return

Spring

p p

Wave

Plate

Piston

Seal

Clutch

Piston

Return

SpringClutch

Packs

Pr

x 1

Q

2107

nonlinear dynamics and system uncertainty. The idea is to

control the imcoming flow to the clutch chamber through a

solenoid valve so that the chamber pressure will track a

desired pressure profile. The preesure based control will

ensure a precise clutch fill as well as the clutch engagement.

Define the tracking error e2 as the difference between the

desired pressure trajectory r and the actual measurement Pr.

2 re P r= − (96)

And define another error term e1, the derivative of which is

equal to e2.

1 2e e=ɺ (97)

With the pressure dynamics in (95), we have

2

2 2 1

2 1 2

( )[ ( , ) ( , ) ] ( )

( ) ( ) ( )( , ) ( ) ( , )

r

r

r r p r

r r r

r p r r

e P r

PQ u P u P A x P r

V

P P PQ u P A x r P u P

V V V

β

β β β

= −

= + ∆ − + ∆ −

= − − + ∆ + ∆

ɺɺ ɺ

ɺ

ɺ

(98)

where ∆1(Pr) represents the model uncertainty of the pressure

dynamics, and ∆2(u, Pr) represents the model uncertainty of

the control valve dynamics. Bounds of the uncertainty terms

can be obtained experimentally.

Define the sliding surface S as:

1 1 2S k e e= + (99)

where k1 is a weighting parameter. Then the controller can be

designed as:

1 2 2 2

( )ˆ ˆ{ [ ] ( , ) ( ), }

( )

r p

r r

r

P AVu U k e x r P x sign S P

P V

βγ

β= − × − × − +ɺ

(100)

where U is the mapping from flow rate to the control voltage

of the solenoid valve, 2x̂ is the estimate of x2, and 2ˆ( , )

rP xγ is

the controller gain. Experimental implementation of the

sliding mode control has achieved precise pressure control

over the entire process of the clutch fill and clutch

engagement as shown below [93] in Fig. 14.

Fig 14. Pressure tracking performance during clutch fill and cluthc

engagement For hybrid transmission control, it is furthe integrated with

the engine control. To operate the power split hybrid

transmission, coordination between the engine operation, the

motor and generator operation is necessary[97],[98]. The

hybrid control consists of mainly two level. The high level

determines the energy distribution between the engine and the

alternative power source so that the overall fuel efficiency is

achieved. The lower level controls the actuators (engine,

motor, generator) to achieve the desired operting points

determined by the high level control. Again model-based

control and optimization are need to reduce the development

time and improve system performance and efficiency.

V. CONCLUSION

This paper provides a tutorial overview of model-based

control techniques and methodologies for powertrain and

aftertreatment systems adopted in the automotive industry and

academia. The control requirements of modern vehicular

systems, such as engines, aftertreatment systems, and

transmissions, are presented and their increasing complexities

are highlighted, indicating that with the ever-increasing

powertrain complexity model-based control becomes a

necessity. The paper covers selected control-oriented models

for engines, transmissions, and aftertreatment systems and

their associated model-based control applications.

REFERENCES

[1] ACEA position paper on electrically chargeable vehicles, European

Automobile Manufacturers’ Association, November 2012, Retrieved

from:http://www.acea.be/publications/article/position-paper-

electrically-chargeable-vehicles, (Retrieved on August 2014)

[2] D. Alberer, H. Hjalmarsson, and L. Re, “Identification for Automotive

Systems,” Lecture Notes in Control and Information Sciences, vol 418,

pp 1-10, 2012.

[3] M. Zheng, G. T. Reader, and G. J. Hawley, “Diesel Engine Exhaust Gas

Recirculation—A Review on Advanced and Novel Concepts,” J.

Energy Conversion and Management, vol 45, no 6, pp. 883–900, 2004.

[4] A. G. J. Lewis, C. J. Brace, S. Akehurst, J. Turner, A. Popplewell, S.

Richardson, and S.W. Bredda, “Ultra Boost for Economy : Realizing a

60% downsized engine concept,” IMechE Internal Combustion

Engines: Performance, Fuel Economy and Emissions Conference,

London, 2013.

[5] C. Kuruppu, A. Pesiridis, and S. Rajoo, "Investigation of Cylinder

Deactivation and Variable Valve Actuation on Gasoline Engine

Performance," SAE Technical Paper 2014-01-1170, 2014.

[6] P. Divekar, U. Asad, X. Han, X. Chen, and M. Zheng, "Study of

Cylinder Charge Control for Enabling Low Temperature Combustion

in Diesel Engines," J. Eng. Gas Turbines Power, vol 136, no 9, 2014.

[7] M. J. Van Nieuwstadt, I. Kolmanovsky, P. Moraal, A. Stefanopoulou,

M. Jankovic, "EGR-VGT control schemes: experimental comparison

for a high-speed diesel engine," Control Systems, IEEE, vol.20, no.3,

pp.63,79, 2000.

[8] J. Shutty, H. Benali, and L. Daeubler, “Air System Control for

Advanced Diesel Engines,” SAE Paper No. 2007-01-0970, 2007.

[9] R. Reitz, “Directions in Internal Combustion Engine Research,”

Combust. Flame, vol 160, no 1, pp. 1–8, 2013.

[10] C. Guardiola, B. Pla, D. Blanco-Rodriguez, and P. Bares, "Cycle by

Cycle Trapped Mass Estimation for Diagnosis and Control," SAE Int.

J. Engines vol 7, no 3, pp 1523-1531, 2014.

[11] X. Han, P. Divekar, M. Zheng, U. Asad, and X. Chen, “Enabling of low

temperature combustion via active injection control in a diesel engine,”

Combustion Institute - Canadian Section Spring Technical Meeting,

2014.

[12] U. Asad, P. Divekar, X. Chen, M. Zheng, and J. Tjong, "Mode

Switching Control for Diesel Low Temperature Combustion with Fast

Feedback Algorithms," SAE Int. J. Engines vol 5, no 3, 2012.

[13] F. Sun, X. Chen, D. Ting, A. Sobiesiak, “Modeling operation of HCCI

Engines fuelled with ethanol”, Proceedings of the American Control

Conference, pp.1003,1009, 2005.

29.4 29.6 29.8 30 30.2 30.4 30.6 30.8

2

3

4

5

6

7

time (second)

pre

ssure

(bar)

Real Pressure

Reference

End of engagement

Slipping control

Clutch Fill

2108

[14] M. Christensen, B. Johansson, “Influence of Mixture Quality on

Homogeneous Charge Compression Ignition,” SAE Technical Paper

982454, 1998.

[15] S. Zhang, G. Zhu, and Z. Sun, "A Control-Oriented Charge Mixing and

Two-Zone HCCI Combustion Model," IEEE Transactions on Vehicular

Technology , vol.63, no.3, pp.1079,1090, 2014.

[16] X. Yang and G. Zhu, “A control-oriented hybrid combustion model of

a homogeneous charge compression ignition capable spark ignition

engine” J Automotive Eng, vol 226, no 10, pp 1380-1395.

[17] G. M. Shaver, J. Christian Gerdes, M. J. Roelle, P. A. Caton and C. F.

Edwards, “Dynamic modeling of residual-affected homogeneous

charge compression ignition engines with variable valve actuation”, J

of Dynamic Systems, Measurement, and Control, vol. 127, no 3, 2004.

[18] C. E. Garcia and A. M. Morshedi, “Quadratic programming solution of

dynamic matrix control QDMC,” Chemical Engineering

Communications vol 46, pp73–87, 1986.

[19] J. B. Rawlings “Tutorial overview of model predictive control,” IEEE

Control Systems Magazine, 2000.

[20] J. Ma, G. Zhu, and H. Schock, "Adaptive control of a pneumatic valve

actuator for an internal combustion engine," IEEE Transaction on

Control System Technology, Vol. 19, No. 4, July, 2011, pp. 730-743

(DOI: 10.1109/TCST.2010.2054091).

[21] J. Ma, G. Zhu, and H. Schock, "A dynamic model of an electro-

pneumatic valve actuator for internal combustion engines" ASME

Journal of Dynamic Systems, Meas. Control, vol.132, pp. 021007,

2010.

[22] K.J. Astrom and B. Wittenmark, “Adaptive control,” 2nd ed. Boston,

MA, Addison-Wesley, 1995.

[23] S. W. Wang, D. L. Yu, J. B. Gomm, G. F. Page, and S. S. Douglas,

“Adaptive neural network model-based predictive control for air-fuel

ratio of SI engines”, Engine applications of artificial intelligence, vol

19, no 2, 2006.

[24] S. Pace and G. Zhu, “Sliding mode control of both air-to-fuel and fuel

ratios for a dual-fuel internal combustion engine”, J. Dyn. Sys., Meas.,

Control, vol 134, pp 031012, 2012.

[25] M. Krstic and H. Wang, “Stability of extremum seeking feedback for

general nonlinear dynamic systems”, Automatica, vol 36, no 4, pp 595-

601, 2000.

[26] D. Popovic, M. Jankovic, S. Magner, and A. Teel, “Extremum seeking

methods for optimization of variable cam timing engine operation,”

IEEE Transactions on Control Systems Technology, vol 14, pp 398-

407, 2006.

[27] N. J. Killingsworth, S. M. Aceves, D. L. Flowers, F. Espinosa-Loza,

and M. Krstic, “HCCI engine combustion-timing control: optimizing

gains and fuel consumption via extremum seeking,” IEEE Transactions

on Control Systems Technology, 17:1350-1361, 2009.

[28] S. Sugihira, K. Ichikawa, and H. Ohmori, “Starting speed control of SI

engine based on online extremum control,” SICE Annual Conference,

2569-2573, 2007.

[29] I. Haskara, G. Zhu, and J. Winkelman, “Multivariable EGR/spark

timing control for IC engines via extremum seeking,” American

Control Conference, 2006.

[30] Q. Tan, P. Divekar, X. Chen, M. Zheng, and Y. Tan, “Exhaust gas

recirculation control through extremum seeking in a low temperature

combustion diesel engine”, American Control Conference (ACC),

2014, vol., no., pp.1511,1516, 4-6 June 2014.

[31] N. Rajaei, X. Han, X. Chen, and M. Zheng, "Model Predictive Control

of Exhaust Gas Recirculation Valve," SAE Technical Paper 2010-01-

0240, 2010.

[32] A. White, J. Choi, R. Nagamune, and G. Zhu, “Gain-scheduling control

of port-fuel-injection process,” IFAC Journal of Control Engineering

Practice, 19 (2011), pp. 380-394.

[33] A. White, Z. Ren, G. Zhu, and J. Choi, “Mixed H∞ and H2 LPV control

of an IC engine hydraulic cam phase system,” IEEE Transaction on

Control System Technology, Vol. 21, Issue. 1, 2013, pp. 229-238 (DOI

10.1109/TCST.2011.2177464).

[34] S. Zhang, J. Yang, and G. Zhu, “LPV modeling and mixed H2/H∞

control of an electronic throttle,” IEEE/ASME Transaction on

Mechatronics (DOI: 10.1109/TMECH.2014.2364538).

[35] A. White, G. Zhu, and J. Choi, Linear Parameter Varying Control for

Engineering Applications, Springer-Verlag London Limited, 2013.

[36] T. Johnson, “Vehicular Emissions in Review,” SAE International

Journal of Engines, Vol. 7, issue 3, pp. 1207 – 1227, 2014.

[37] J. Vardi and W. Biller, “Thermal behavior of exhaust gas catalytic

convertor,” Industrial & Engineering Chemistry Process Design and

Development, Vol. 7, pp. 83 – 90, 1968.

[38] J. C. Kuo, Cr. Morgan, and H. G. Lassen, “Mathematical modeling of

CO and HC catalytic converter system,” SAE Paper 710289, 1971.

[39] E. Tronconi, I. Nova, C. Ciardelli, D. Chatterjee, B. Bandl-Konrad, and

T. Burkhardt, “Modeling of an SCR catalytic converter for diesel

exhaust after treatment: dynamic effects at low temperature,” Catalysis

Today, Vol. 105, pp. 529 – 536, 2005.

[40] I. Nova and E. Tronconi (eds.), Urea-SCR Technology for DeNOx

After Treatment of Diesel Exhausts, Springer, New York, 2014.

[41] A. G. Konstandopoulos, E. Skaperdas, E. Papaioannou, D. Zarvalis, and

E. Kladopoulou, “Fundamental studies of Diesel particulate filters:

transient loading, regeneration and aging,” SAE Paper 2000-01-1016,

2000.

[42] S. D. Yim, S. J. Kim, J. H. Baik, I. Nam, Y. S. Mok, J. Lee, B. K. Cho

and S. H. Oh, "Decomposition of Urea into NH3 for the SCR Process,"

Ind Eng Chem Res, vol. 43, pp. 4856-4863, 2004.

[43] M. Koebel, M. Elsener, and M. Kleemann, "Urea-SCR: a promising

technique to reduce NOx emissions from automotive diesel engines,"

Catalysis Today, vol. 59, pp. 335-345, 2000.

[44] C. M. Schӓr, C. H. Onder, and H. P. Geering, “Control-oriented model

of an SCR catalytic converter system,” SAE Paper No. 2004-01-0153,

2004.

[45] M. Devarakonda, G. Parker, J. H. Johnson, V. Strots, and S. Santhanam,

"Model-Based Estimation and Control System Development in a Urea-

SCR Aftertreatment System," SAE Int. J. Fuels Lubr. Vol. 1, Issue. 1,

pp. 646-661, 2008.

[46] D. Upadhyay M. Van Nieuwstadt, “Modeling of a urea SCR catalyst

with automotive applications,” Proceedings of ASME 2002 IMECE,

New Orleans, USA, 17-22 November, 2002, pp. 707-713.

[47] M.-F. Hsieh and J. Wang, “Development and Experimental Studies of

a Control-Oriented SCR Model for a Two-Catalyst Urea-SCR System,”

Control Engineering Practice, Vol. 19, Issue 4, pp. 409 - 422, 2011.

[48] P. Chen and J. Wang, "Control-Oriented Modeling and Observer-based

Estimation of Solid and Gas Temperatures for a Diesel Engine

Aftertreatment System," ASME Transactions Journal of Dynamic

Systems, Measurement and Control, Vol. 134, Issue 6, 061011 (12

pages), 2012.

[49] M.-F. Hsieh and J. Wang, "NO and NO2 Concentration Modeling and

Observer-Based Estimation across a Diesel Engine Aftertreatment

System," ASME Transactions Journal of Dynamic Systems,

Measurement, and Control, Vol. 133, Issue 4, 041005 (13 pages), 2011.

[50] P. Chen and J. Wang, "Oxygen Concentration Dynamic Model and

Observer-Based Estimation through a Diesel Engine Aftertreatment

System," ASME Transactions Journal of Dynamic Systems,

Measurement, and Control, Vol. 134, Issue 3, 031008 (10 pages), 2012.

[51] D. Rumminger, X. Zhou, K. Balakrishnan, L. Edgar, and A. Ezekoye,

“Regeneration Behavior and Transient Thermal Response of Diesel

Particulate Filters,” Proceedings of the SAE 2001 World Congress,

SAE paper No. 2001-01-1342, 2001.

[52] A. Maiboom, X. Tauzia, and J. Hétet, “Influence of high rates of

supplemental cooled EGR on NOx and PM emissions of an automotive

HSDI diesel engine using an LP EGR loop,” International Journal of

Energy Research, Vol. 32, pp. 1383 – 1398, 2008.

[53] H. Peng, Y. Cui, L. Shi, and K. Deng, “Effects of exhaust gas

recirculation (EGR) on combustion and emissions during cold start of

direct injection (DI) diesel engine,” Energy, Vol. 33, pp. 471 – 479,

2008.

[54] K. C. Premchand, J. H. Johnson, S. Yang, A. P. Triana, and K. J.

Baumgard, “A Study of the Filtration and Oxidation Characteristics of

a Diesel Oxidation Catalyst and a Catalyzed Particulate Filter”, 2007

SAE World Congress, SAE paper 2007-01-1123, 2007.

[55] D. Chatterjee, T. Burkhardt, M. Weibel, E. Tronconi, I. Nova, and C.

Ciardelli, “Numerical Simulation of NO/NO2/NH3 Reaction on SCR-

Catalytic Converters: Model Development and Applications”, SAE

2006 World Congress, SAE 2006-01-0468.

[56] E. Brandt, Y. Wang, and J. Grizzle, “A simplified three-way catalyst

model for use in on-board SI engine control and diagnostics.”

Proceedings of the ASME Dynamic System and Control Division 61

(1997): 653-659.

[57] E. Brandt, Y. Wang, and J. Grizzle, “Dynamic modeling of a three-way

catalyst for SI engine exhaust emission control,” Control Systems

Technology, IEEE Transactions on 8.5 (2000): 767-776.

2109

[58] J. Peyton Jones, J. Roberts, P. Bernard, and R. Jackson, “A simplified

model for the dynamics of a three-way catalytic converter,” SAE Paper

2000-01-0652, SAE, 2000.

[59] J. Peyton Jones, “Modeling combined catalyst oxygen storage and

reversible deactivation dynamics for improved emissions prediction,”

SAE Paper 2003-01-0999, SAE, 2003.

[60] G. Fiengo, L. Glielmo, S. Santini, and G. Serra, “Control-oriented

models for TWC-equipped spark ignition engines during the warm-up

phase.” Proceedings of the American control conference, pp. 1761 –

1766, 2002.

[61] G. Fiengo, L. Glielmo, and S. Santini, “On-board diagnosis for three-

way catalytic converters,” International Journal of Robust and

Nonlinear Control, Vol. 11: 1073-1094, 2001.

[62] P. Kumar, I. Makki, J. Kerns, K. Grigoriadis, M. Franchek, and V.

Balakotaiah, “A low-dimensional model for describing the oxygen

storage capacity and transient behavior of a three-way catalytic

converter,” Chemical Engineering Science, vol. 73, pp. 373-387, 2012.

[63] M. Tomforde, et al., “A Post-Catalyst Control Strategy Based on

Oxygen Storage Dynamics,” SAE Paper 2013-01-0352, SAE, 2013.

[64] B. Dawson, M. Franchek, and K. Grigoriadis, “Data Driven Simplified

Three-Way Catalyst Health Diagnostic models: Experimental Results,”

ASME 2007 International Mechanical Engineering Congress and

Exposition. American Society of Mechanical Engineers, 2007.

[65] H. Zhang, J. Wang, and Y.Y. Wang, "Nonlinear Observer Design of

Diesel Engine Selective Catalytic Reduction Systems with NOx Sensor

Measurements," IEEE/ASME Transactions on Mechatronics (in press),

2014 (DOI: 10.1109/TMECH.2014.2355039).

[66] H. Zhang, J. Wang, and Y.Y. Wang, "Robust Filtering for Ammonia

Coverage Estimation in Diesel Engine Selective Catalytic Reduction

(SCR) Systems," ASME Transactions Journal of Dynamic Systems,

Measurement, and Control, Vol. 135, Issue 6, 064504 (7 pages), 2013.

[67] M.-F. Hsieh and J. Wang, “Observer-Based Estimation of Selective

Catalytic Reduction (SCR) Catalyst Ammonia Storage,” Journal of

Automobile Engineering, Proceedings of the Institution of Mechanical

Engineers, Part D, Vol. 224, No. 9, pp. 1199 - 1211, 2010.

[68] M.-F. Hsieh and J. Wang, "Design and Experimental Validation of an

Extended Kalman Filter-based NOx Concentration Estimator in

Selective Catalytic Reduction System Applications," Control

Engineering Practice, Vol. 19, Issue 4, pp. 346 - 353, 2011.

[69] P. Chen and J. Wang, "A Novel Cost-effective Robust Approach for

Selective Catalytic Reduction State Estimations Using Dual Nitrogen

Oxide Sensors," Journal of Automobile Engineering, Proceedings of

the Institution of Mechanical Engineers, Part D, Vol. 229, No. 1, pp. 83

– 96, 2015.

[70] C. M. Schar, C. H. Onder, and H. P. Geering, “Control of an SCR

catalyst converter system for a mobile heavy-duty application,” IEEE

Trans. Contr. Syst. Technol., vol. 14, no. 4, pp. 641–652, 2006.

[71] M.-F. Hsieh and J. Wang, “Adaptive and efficient ammonia storage

distribution control for a two-catalyst selective catalytic reduction

system,” ASME Transactions Journal of Dynamic Systems,

Measurements, and Control, vol. 134, no. 1, 011012, 2012.

[72] T. McKinley and A. Alleyne, “Adaptive model predictive control of an

SCR catalytic converter system for automotive applications,” IEEE

Transactions on Control Systems Technology, 20(6):1533-1547, 2012.

[73] M. Devarkonda, G. Parker, J. Johnson, and V. Strots, “Model-based

Control System Design in a Urea-SCR Aftertreatment System Based on

NH3 Sensor Feedback,” International Journal of Automotive

Technology, Vol. 10, No. 6, pp. 653−662, 2009.

[74] Q. Song and G. Zhu, “Model-based Closed-loop Control of Urea SCR

Exhaust Aftertreatment System for Diesel Engine”, Proceedings of the

SAE 2002 World Congress, SAE 2002-01-0287, 2002.

[75] M.-F. Hsieh and J. Wang, "A Two-Cell Backstepping Based Control

Strategy for Diesel Engine Selective Catalytic Reduction Systems,"

IEEE Transactions on Control Systems Technology, Vol. 19, No. 6, pp.

1504 - 1515, 2011.

[76] H. Zhang, J. Wang, and Y.Y. Wang, “Optimization of the Ammonia

Coverage Ratio References in Diesel Engine Two-Can Selective

Catalytic Reduction Systems via Nonlinear Model Predictive Control,”

Journal of Automobile Engineering, Proceedings of the Institution of

Mechanical Engineers, Part D, Vol. 228, No. 12, pp. 1452 – 1467, 2014.

[77] M. Balenovic, A. C. P. M. Backx, and J. H. B. J. Hoebink, “On a model-

based control of a three-way catalytic converter,” SAE Paper 2001-01-

0937. SAE Technical Paper, 2001.

[78] R. Schallock, K. Muske, and J. Peyton-Jones, “Model predictive

functional control for an automotive three-way catalyst,” SAE Paper

2009-01-0728. SAE Technical Paper, 2009.

[79] K. Muske and J. Peyton Jones. "Multi-objective model-based control

for an automotive catalyst." Journal of Process Control 16.1: 27-35,

2006.

[80] B. Ebrahimi, R. Tafreshi, H. Masudi, M. Franchek, J. Mohammadpour,

and K. Grigoriadis, “A parameter-varying filtered PID strategy for air-

fuel ratio control of spark ignition engines,” Control Engineering

Practice, vol. 20, pp. 805 – 815, 2012.

[81] B. Dawson, M. Franchek, K. Grigoriadis, R. McCabe, M. Uhrich, and

S. Smith, “Automotive three-way catalyst diagnostics with

experimental results,” Journal of Dynamic Systems, Measurement, and

Control, Vol. 133, 051008, 2011.

[82] J. Peyton-Jones, I. Makki, and K. Muske, “Catalyst diagnostics using

adaptive control system parameters,” SAE Paper 2006-01-1070, SAE

Technical Paper, 2006.

[83] Z. Sun and K. Hebbale, “Challenges and Opportunities in Automotive

Transmission Control”, Proceedings of the 2005 American Control

Conference, Portland, OR, pp.3284-3289, June, 2005.

[84] G. Wagner, “Application of Transmission Systems for Different

Driveline Configurations in Passenger Cars”, SAE Technical Paper

2001-01-0882.

[85] Z. Sun and G. Zhu, “Design and Control of Automotive Propulsion

Systems”, CRC press, 2015.

[86] M. Kluger and D. Fussner, “An Overview of Current CVT

Mechanisms, Forces and Efficiencies”, SAE Technical Paper 970688.

[87] M. Raghavan and S. Raghavan, "Kinematic and dynamic analysis of the

half-toroidal traction drive variator," Proceedings of the 2002 Global

Powertrain Congress, Detroit, MI, September 24-27, 2002.

[88] H. Tanaka and M. Eguchi, “ Stability of a Speed Ratio Control Servo-

Mechanism for a Half-Toroidal Traction Drive CVT,” JSME

International Journal, Series C, Vol. 36, No. 1, 1993.

[89] K. V. Hebbale and M. E. Carpenter, "Control of the Geared Neutral

Point in a Traction Drive CVT," Proceedings of the 2003 American

Control Conference, Denver, CO, 2003.

[90] M. Ehsani, Y. Gao, and J. Miller, “Hybrid electric vehicles: architecture

and motor drives”, Proceedings of the IEEE, Vol. 95, No. 4, 2007: pp.

719–728.

[91] J. Van de Ven, M. W. Olson, and P. Y. Li, "Development of a hydro-

mechanical hydraulic hybrid drive train with independent wheel torque

control for an urban passenger vehicle", IFPE 2008, Las Vegas, NV,

2008.

[92] X. Song, A. Mohd Zulkefli, Z. Sun, and H. Miao, “Automotive

Transmission Clutch Fill Control Using a Customized Dynamic

Programming Method”, ASME Transactions on Journal of Dynamic

Systems, Measurement and Control, Vol. 133, 054503, September,

2011.

[93] X. Song and Z. Sun, “Pressure Based Clutch Control for Automotive

Transmissions Using a Sliding Mode Controller”, IEEE/ASME

Transactions on Mechatronics, Vol. 17, No. 3, pp.534-546, June, 2012.

[94] G. Qin, A. Ge, and J. Lee, "Knowledge-Based Gear-Position Decision,"

IEEE Transactions on Intelligent Transportation Systems, Vol. 5, No.

2, June 2004.

[95] M. Kawai, H. Aruga, K. Iwatsuki, T. Ota, and T. Hamada,

“Development of Shift Control System for Automatic Transmission

Using Information From a Vehicle Navigation System”, SAE Technical

Paper 1999-01-1095.

[96] X. Song, Z. Sun, X. Yang, and G. Zhu, “Modeling, Control, and

Hardware-in-the-Loop Simulation of an Automated Manual

Transmission”, Proceedings of the IMechE, Part D, Journal of

Automobile Engineering, Vol. 224, No. 2, pp.143-160, 2010.

[97] C. C. Lin, H. Peng, J. W. Grizzle, and J. Kang, “Power management

strategy for a parallel hybrid electric truck”, IEEE Transactions on

Control Systems Technology, Vol.11, No.6, 2003: pp. 839-849.

[98] Y. Wang, H. Zhang, and Z. Sun, “Optimal Control of the Transient

Emissions and the Fuel Efficiency of a Diesel Hybrid Electric Vehicle”,

Proceedings of the IMechE, Part D, Journal of Automobile

Engineering, 227 (11), pp.1546-1561, 2013.

2110