tutorial of model-based powertrain and aftertreatment system … · 2018-05-16 · and the system...
TRANSCRIPT
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: [email protected]).
Junmin Wang is with the Department of Mechanical and Aerospace
Engineering at The Ohio State University, Columbus, OH 43210 USA
(email: [email protected]).
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:
Xiang Chen is with the Department of Electrical and Computer
Engineering at University of Windsor, Windsor, Ontario, Canada N9B3P4
(email: [email protected]).
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