Optimal catalyst temperature management of Plug-in Hybrid Electric Vehicles

Abstract

For driving cycles that require use of the engine (i.e. the trip distance exceeds the All Electric Range (AER) of a Plug-in Hybrid Electric Vehicle (PHEV) or a driving cycle demands power exceeding the battery peak power), the catalyst temperature management for reduced tailpipe emissions is a challenging control problem due to the frequent and extended engine shut-down and catalyst cool-down. In this paper, we develop a method to synthesize a supervisory powertrain controller (SPC) that achieves near-optimal fuel economy and tailpipe emissions under known travel distances. We first find the globally optimal solution using dynamic programming (DP), which provides an optimal control policy and state trajectories. Based on the analysis of the optimal state trajectories, a variable Energy-to-Distance Ratio (EDR) is introduced to quantify the level of battery state-of-charge (SOC) relative to the remaining distance. A novel two-dimensional extraction method is developed to extract engine on/off, gear-shift, and power-split control strategies as functions of both EDR and the catalyst temperature from the DP control policy. Based on the extracted results, an adaptive SPC that optimally adjusts the engine on/off, gear-shift, and power-split strategies under various EDR and catalyst temperature conditions was developed to achieve near-optimal fuel economy and emission performance.

Full text

Abstract—For driving cycles that require use of the engine (i.e.
the trip distance exceeds the All Electric Range (AER) of a
Plug-in Hybrid Electric Vehicle (PHEV) or a driving cycle
demands power exceeding the battery peak power), the catalyst
temperature management for reduced tailpipe emissions is a
challenging control problem due to the frequent and extended
engine shut-down and catalyst cool-down. In this paper, we
develop a method to synthesize a supervisory powertrain
controller (SPC) that achieves near-optimal fuel economy and
tailpipe emissions under known travel distances. We first find
the globally optimal solution using dynamic programming (DP),
which provides an optimal control policy and state trajectories.
Based on the analysis of the optimal state trajectories, a variable
Energy-to-Distance Ratio (EDR) is introduced to quantify the
level of battery state-of-charge (SOC) relative to the remaining
distance. A novel two-dimensional extraction method is
developed to extract engine on/off, gear-shift, and power-split
control strategies as functions of both EDR and the catalyst
temperature from the DP control policy. Based on the extracted
results, an adaptive SPC that optimally adjusts the engine on/off,
gear-shift, and power-split strategies under various EDR and
catalyst temperature conditions was developed to achieve
near-optimal fuel economy and emission performance.
I. INTRODUCTION
ECENTLY, Plug-in Hybrid Electric Vehicles (PHEVs)
received much attention as a promising technology to
lower ground transportation’s dependency on petroleum fuel
and to reduce CO2 emissions. The dramatic reduction in fossil
fuel consumption of the PHEV is achieved by substituting
fossil fuels with grid electricity. As an example, when the All
Electric Range (AER) of a PHEV is 30 miles, in theory it will
be possible to use little or no fossil fuel when the travel
distance is less than 30 miles, assuming the electric power
source is capable of satisfying the propulsion power need.
When the trip distance exceeds AER, and especially when
emissions are considered, the optimal control of the PHEV is
non-trivial–an optimal supervisory powertrain controller
(SPC) that minimizes fuel consumption while maintaining
catalyst temperature high for various trip distances is difficult
to design. In this study, we seek to develop a systematic
method for the synthesis of the SPC to achieve near-optimal
This work was supported by the General Motors.
Dongsuk Kum is with the General Motors R&D Center, Warren, MI
48090 USA (e-mail: dongsuk.kum@gm.com ).
Huei Peng is with the Department of Mechanical Engineering, G041 Lay
Automotive Laboratory, University of Michigan, Ann Arbor, MI 48109 USA
(corresponding author: e-mail: hpeng@umich.edu).
Norman K. Bucknor is with the General Motors R&D Center, Warren, MI
48090 USA (e-mail: Norman.k.bucknor@gm.com).
fuel economy (FE) and emission performance regardless of
trip distances, assuming that the trip distance information is
available. If not available, one of the best and simplest
strategies would be to use the vehicle’s average daily trip
distance.
The focus of past PHEV control studies has been on how to
use the available battery energy efficiently throughout the
driving cycle when the travel distance exceeds the AER.
Gonder and Markel proposed and compared three control
strategies, electric vehicle/charge sustaining (EV/CS),
engine-dominant, and electric-dominant strategy [1]. They
found fuel economy is sensitive to travel distances and driving
conditions, and suggested that the control strategy should be
switched from one to another to improve FE based on the
future driving information. A study by Sharer et al. performed
similar analysis on EV/CS, full engine power, and optimal
engine power strategies and reached similar conclusions [2].
When emissions are considered, the optimal control of the
PHEV becomes much more complex because the PHEV is
designed to dramatically reduce fuel consumption by frequent
and extended engine shut-down. A recent study by the authors
developed a systematic design method of an SPC that achieves
near-optimal fuel economy for a PHEV [3]. In this paper, we
build upon that work by applying the design method for
PHEVs.
II. PLUG-IN HYBRID ELECTRIC VEHICLE MODEL
A. Target PHEV
The target vehicle is a compact SUV with the
pre-transmission parallel hybrid configuration (Fig. 1). An
engine-disconnect clutch replaces the torque converter for
pure electric vehicle (EV) mode. Main design variables of the
PHEV are battery capacity and rated power of the battery and
motor/generator (M/G). In this study, the same battery
capacity and electric propulsion power of the previous study is
Optimal Catalyst Temperature Management of
Plug-in Hybrid Electric Vehicles
Dongsuk Kum, Huei Peng, and Norman K. Bucknor
R
Transmission
Battery
ClutchEngine
Electric
Motor
Transmission
Battery
ClutchEngine
Electric
Motor
Fig. 1. Schematic of a pre-transmission parallel hybrid electric vehicle
powertrain.
2011 American Control Conference
on O'Farrell Street, San Francisco, CA, USA
June 29 - July 01, 2011
978-1-4577-0079-8/11/$26.00 ©2011 AACC 2732

used, and parameters of the vehicle are summarized in Table I.
B. PHEV Model
The authors previously developed a simplified three-state
HEV model to efficiently evaluate fuel economy and tail-pipe
emissions for supervisory control purposes [4]. This model
focuses on the effect of various engine operations on the
energy flow and the catalytic converter thermal dynamics
while fast dynamics (e.g. intake manifold filling and motor
dynamics) are neglected. Also, low-level controls such as
Air/Fuel ratio and spark timing are assumed pre-designed for
optimal cold-start performance. In the state space
representation, the PHEV model is described as follows.
),( uxfx =

(1)
where x is the state vector [vehicle speed, state-of-charge
(SOC), and catalytic converter temperature], and u is the
control input vector [engine torque, engine on/off, motor
torque, gear selection, and friction brake]. Due to limited
space, readers are referred to [4]-[7] for more details.
III. OPTIMAL SUPERVISORY CONTROL VIA DP
Both instantaneous and horizon optimization methods are
used to solve the HEV optimal control problem for fuel
economy [7]-[10]. However, optimality of the instantaneous
optimization method no longer holds for PHEV optimization
especially when emissions are considered. Two reasons for
this are i) tailpipe emissions heavily depend on the warm-up of
the catalyst temperature and ii) PHEVs are designed to
significantly reduce fuel consumption by frequent and
extended engine shut-downs, which may lead to catalytic
converter cool-down below the light-off temperature.
Therefore, a horizon-based approach must be used to solve the
combined fuel and emissions optimization of the PHEV, and a
DP problem is formulated and solved in the following section.
A. DP Problem Formulation
The DP problem of the PHEV is different from that of the
HEV because PHEVs are designed to deplete the battery
energy whereas HEVs must sustain SOC. Table II summarizes
variables and their grids of the PHEV DP problem, which
consists of two control inputs and two dynamic states, whereas
vehicle velocity (V) and power demand (Pdem) are specified by
the driving cycle.
The LA-92 cycle, a high-power cycle, is selected to ensure
that the engine turns on even for trips shorter than the AER,
otherwise the optimal control solution is trivial (i.e. only use
the battery). For extended travel distances, the LA-92, a 10
mile cycle, is repeated to generate 20 mile and 30 mile cycles,
which significantly reduces computation time by reusing the
cost tables during the backward optimization process. Note
that the engine-off command is included in this DP problem
by augmenting Teng grid with -1. The friction brake command
is set to maximize recuperation, and the M/G torque (Tm/g)
control variable is eliminated by the drivability constraint.
engdemigm
TTT −=
,/
(2)
where Ti,dem is torque demand at the transmission input.
The optimal control problem is formulated as follows
Minimize
∑
−
=








∆⋅+∆⋅+⋅+
+−⋅
=
1
0
2
/
2
min
)0,max(
N
koffonk
kk
EGrHC
FCSOCSOC
J
λγβ
α
(3)
Subject to
max,min,
max,/,/min,/
max,,min,
max,,min,
min
battbattbatt
GMkGMGM
ekee
ekee
k
PPP
TTT
TTT
SOCSOC
≤≤
≤≤
≤≤
≤≤
≥
ωωω
(4)
The emission regulations emphasize eliminating cold-start
HC for gasoline engines, thus let us focus on HC in this study.
Due to numerical difficulties of implementing the minimum
SOC constraint, the max(SOCmin–SOCk,0) term is added in the
cost function, and α must be adjusted to prevent SOC
dropping below the minimum SOC while using electric energy
as much as possible. It was found that α is quite insensitive to
β, and no adjustment is necessary when all other coefficients
vary. Penalties on engine on/off (ΔEon/off) and gear-shift (ΔGr)
events are applied to improve drivability and to promote
separation of engine on/off and gear selections for the
extraction process in Section IV.
B. Results and Analysis
Fig. 2 shows a DP solution that balances fuel economy and
emission performance for a 30 mile cycle. The optimal SOC
trajectory depletes uniformly such that the final SOC barely
touches the minimum SOC. Also, note that hydrocarbon
emissions are kept low by fast catalyst warm-up and
maintaining catalytic converter temperature (Tcat) above 600K
to ensure high converter efficiency.
Fig. 3 shows two Pareto-curves that represent the trade-off
between fuel consumption (FC) and HC for the 20 mile and 30
mile cycles. Note that the 20 mile cycle has a higher FC/HC
TABLE
II
VARIABLES AND GRID OF THE PHEV DP PROBLEM FOR FUEL AND EMISSION
REDUCTION
Variable Grid
Stage (k)
Time
[0:1:N (final time)]
Control (u)
Engine Torque (Teng)
[-1, 0:5:210] Nm
Gear (Gr) [1 2 3 4]
State (x)
SOC
[0.2:0.01:0.9]
Catalyst Temperature (Tcat)
[300:40:700, 900] K
TABLE
I
VEHICLE PARAMETERS OF THE PHEV-20
Vehicle
Curb weight: 1597 kg
SI Engine
2.4L, 4 Cylinder
127kw@5300 rpm (170 hp)
217Nm@4500 rpm (160 lb-ft)
Transmission
Automated Manual Transmission
4 speed, Gear Ratio: 2.95/1.62/1/0.68
AC Motor
Rated power: 40 kW
Max Torque: 300 Nm
NiMH Battery
Capacity: 7.75 kw-hr
Max Power: 40 kW
# of Modules: 100
Nominal Voltage: 7.5 volts/module
2733

sensitivity than the 30 mile cycle and sacrifice more fuel to
reduce HC. The main reason is that there is sufficient electric
energy for the 20 mile cycle, and the increased engine-load
and engine-on time for higher Tcat and conversion efficiency
leads to increase in FC that was originally unnecessary when
emissions were not considered. The SULEV emission
standard (FTP-75 cycle) is shown as a reference.
An important trend was observed from the optimal SOC
trajectories. Figure 4 shows the optimal SOC trajectory of the
30 mile cycle with respect to distance. It can be seen that SOC
depletes at a constant rate when plotted on a Distance vs. SOC
plane, and this holds for all SOC and distance conditions. This
is an important finding because if all optimal solutions behave
in this manner this slope can be used to inform the controller
how much electric energy is available and how fast the battery
should be depleted for optimal performance. This is the key
idea of the adaptive SPC illustrated in the following sections.
IV. COMPREHENSIVE EXTRACTION OF DP SOLUTION
A. Introduction of Energy-to-Distance Ratio (EDR)
From the previous section, we observed that the SOC vs.
distance slope of the optimal solutions remain near-constant
throughout the cycle. Let us quantify this slope as
remrem d
SOCSOC
d
SOCSOC minmin
1
tan −
≈







−
=−
θ
(5)
where tan-1 can be removed under the small angle assumption,
when the unit of distance is in miles, and SOC ranges from 0 to
1. Note that
max
θθ
≤
(6)
where
035.0
20
2.09.0
tan
1
max
=





−
=
−
θ
(AER=20 for PHEV20).
Thus, we can normalize θ such that
1
max
≤≡
θ
θ
θ
(7)
Note that AER and θmax may change with driving style or
driving cycle. Fig. 5 illustrates the Energy-to-Distance Ratio
(EDR), θ, on the SOC vs. distance plane and optimal SOC
trajectories for a few sample
θ
values.
1=
θ
indicates
sufficient electric energy available (or EV mode), and
0=
θ
indicates a depleted battery (or charge-sustaining mode).
B. Comprehensive Extraction Method
In an earlier study [4], a comprehensive extraction method
that utilizes all of the optimal control information found from
DP is proposed to learn and design the optimal cold-start
strategy of HEVs. For PHEV control, this extraction method
10 3020
0.2
0.9
SOC
Distance
0.7
0.4
10 3020
0.2
0.9
SOC
Distance
0.7
0.4
θ
ΔSOC
d
rem
0=
θ
667.0=
θ
)(1
max
θθθ
==
Fig. 5. Geometrical definition of EDR (θ) on the Distance vs. SOC plane.
0100 200 300 400 500 600 700
0
5
10
15
20
25
Fuel cons umpti on vs. HC
Fuel Consum ption [g]
HC [mg/mile]
20 miles
30 miles
β= 500
β= 700
β= 0
β= 2000
β= 200
SULEV Standard (FTP)
β= 1000
0100 200 300 400 500 600 700
0
5
10
15
20
25
Fuel cons umpti on vs. HC
Fuel Consum ption [g]
HC [mg/mile]
20 miles
30 miles
β= 500
β= 700
β= 0
β= 2000
β= 200
SULEV Standard (FTP)
β= 1000
Fig. 3. Trade-off between fuel consumption and HC for 20 mile and 30
mile cycles.
0510 15 20 25 30
0.2
0.4
0.6
0.8
Distanc e [mil e]
SOC
Fig. 4. Optimal SOC trajectories on a Distance vs. SOC plane.
0500 1000 1500 2000 2500 3000 3500 4000
0.2
0.4
0.6
0.8
SOC
0500 1000 1500 2000 2500 3000 3500 4000
0
2
4
Speed [20m ph]
Fuel
rate
[g/s ec]
Fuel
rate
V [20m ph]
engine-on
0500 1000 1500 2000 2500 3000 3500 4000
400
600
800
1000
Cataly st Tem p [K]
0500 1000 1500 2000 2500 3000 3500 4000
0
50
100
time [ sec]
weighted HC [m g/mile]
η
[%]
HC
engine
HC
tail
η HC
0500 1000 1500 2000 2500 3000 3500
4000
0.2
0.4
0.6
0.8
SOC
0500 1000 1500 2000 2500 3000 3500
4000
0
2
4
Speed [20m ph]
Fuel
rate
[g/s ec]
Fuel
rate
V [20m ph]
engine-on
0500 1000 1500 2000 2500 3000 3500
4000
400
600
800
1000
Cataly st Tem p [K]
0500 1000 1500 2000 2500 3000 3500
4000
0
50
100
time [ sec]
weighted HC [m g/mile]
η
[%]
HC
engine
HC
tail
η HC
light-o ff temp.
30 miles, β=500
Fig. 2. DP simulation results for the 30-mile LA-92 cycle at β = 500.
(α=4e3, γ=0.02, λ=0.05)
2734

is expanded to a two-dimensional space (EDR and Tcat)
because the control strategy of PHEVs must be properly
adjusted depending on the EDR as well as the catalyst
temperature. For example, the optimal cold-start control
strategy for a high EDR condition (e.g. EV mode) should be
different from that for a low EDR condition (e.g. charge
sustaining strategy).
Suppose that DP stores the optimal control policy in the
form of uk
*(Tcat, SOC), where values of uk
* are stored for all
state grid points at each time step k. Then, all uk
* elements can
be grouped together by
θ
and Tcat as shown in Fig. 6. The
rectangular box represents the optimal control policy uk
* in a
state and time space, where x1 is Tcat and x2 is SOC, and k
indicates the time step. Each node in the box contains the
optimal control information for the given state (x1,x2) and time
step k. The following algorithm converts uk
* into three
decoupled optimal control strategies, engine on/off (uon/off
*),
gear-shift (uGear
*), and Power Split Ratio (PSR) (uPSR
*), where
PSR is defined as
dem
eng
P
P
PSR ≡
(8)
Prior to the extraction algorithm, a designer must choose β
that balances fuel economy and HC emissions and obtain uk
*
for the chosen β. In this study, β = 500 of the 30 mile cycle is
selected for a distinct cold-start strategy. The two-dimensional
extraction algorithm is described as follows:
a) Choose Tcat = 300K.
b) Let time step k = 1 and obtain optimal control policy uk
*.
c) Obtain driving cycle information (Pdem, Twheel, V, drem) at
k = 1, where drem is the remaining distance.
d) If Twheel < 0, store engine-off and EV gear information
into
( )
catwheeloffon
TTVu ,,,
/
θ
∗
,
( )
catdemioffon
TTNu ,,,
/
θ
∗
, and
( )
catdemEVGear
TPVu ,,,
θ
∗
matrices, and skip e) through g).
Otherwise, continue to e).
e) For all SOC grid points at the chosen Tcat, compute
θ
and convert uk
* into two separate optimal control signals,
gear selection (ugear
*) and engine torque (Teng
*). uon/off
*
can be simply obtained by checking whether Teng
* = -1 or
not.
f) Find the optimal Tdem
* and Ni
* using ugear
*, and compute
∗
∗
∗
=
dem
eng
PSR
T
T
u
g) Store all uon/off
*, uPSR
*, and uGear
* values into matrices to
obtain
( )
catwheeloffon
TTVu ,,,
/
θ
∗
,
( )
catdemioffon
TTNu ,,,
/
θ
∗
,
( )
catdemGear
TPVu ,,,
θ
∗
, and
( )
catdemiPSR
TTNu ,,,
θ
∗
.
h) Repeat b) through g) for all time steps k.
i) Repeat a) through h) for all other Tcat.
C. Extracted Results
1) Hot DP results (Tcat > 700K): Although two sets of
optimal control strategies (hot and cold) are extracted, only
cold strategy is presented in this paper due to limited space.
Readers are referred to the previous paper for hot strategy [3].
2) Cold DP results (Tcat < 700K): Four sets of the optimal
control strategies under
[ ]
97.06.035.002.0=
θ
at Tcat =
420K are selected and plotted in Figs. 7-9. In general, the
cold-start strategy of the PHEV is found to be similar to that of
the conventional HEV [4]. In fact, low-EDR results are almost
identical to those of conventional HEVs because low-EDR
solution is an optimal charge sustaining strategy, but the
transition of hot-to-cold strategy takes place gradually and
starts at a higher temperature than the catalyst light-off
temperature. With increasing
θ
, more interesting results are
observed as follows.
Figure 7 shows that the engine on/off should be triggered by
both the transmission input speed and driver power demand
when the catalyst cools down. While the transmission input
speed threshold stays constant throughout the range of
θ
, the
power threshold increases with increasing
θ
. Figure 8
indicates that late-shift strategy is desired for higher exhaust
gas temperature and fast catalyst warm-up during cold-starts.
Readers are referred to the previous paper by the authors for
engine maps [4]. Again, the low
θ
results are identical to
those of conventional HEVs, and this late-shift strategy does
not significantly change with increasing
θ
except for the
increased engine on/off threshold. For the cold-start
power-split strategy, Fig. 9 shows that another PSR line
should be used to reproduce optimal power-split strategy
during cold-starts for higher exhaust gas temperature, which
promotes faster catalyst warm-up.
V. OPTIMAL SUPERVISORY CONTROL VIA DP
Assuming that the remaining distance information is
available, the design and evaluation of the cold-start SPC for
the PHEV are carried out as follows. Two cold SPCs
(Map-based and DP-based) are developed for catalyst
temperature management. These cold SPCs are compared
with DP results under various EDR conditions.
A. Hot SPC Algorithm: Adaptive DP-based SPC
Based on the extracted hot results, the logic of the adaptive
Fig. 6. State space of the optimal control policy (uk*) showing the
two-dimensional comprehensive extraction algorithm with θ and Tcat
sweeps.
2735

01000 2000 3000 4000 5000
0
50
100
150
200
250
300
Transmission input speed [rpm ]
Torque demand at t he transm iss ion input [ Nm]
engine-on
engine-off
02.0=
θ
01000 2000 3000 4000 5000
0
50
100
150
200
250
300
Transmission input speed [rpm]
Torque demand at t he transm iss ion input [ Nm]
8kw
13kw
19kw
25kw
33kw
35.0=
θ
(a)
02.0=
θ
(b)
35.0=
θ
01000 2000 3000 4000 5000
0
50
100
150
200
250
300
Transmiss ion input speed [rpm]
Torque demand at t he transm iss ion input [ Nm
8kw
13kw
19kw
25kw
33kw
60.0=
θ
01000 2000 3000 4000 5000
0
50
100
150
200
250
300
Transmiss ion input speed [rpm]
Torque demand at t he transm iss ion input [ Nm
8kw
13kw
19kw
25kw
33kw
97.0=
θ
(c)
60.0=
θ
(d)
97.0=
θ
Fig. 7. Extracted cold-catalyst engine on/off strategies at four sample
θ
values.
Hot SPC algorithm is proposed as follows.
If Pdem<Pon/off
)(
θ
,
Turn off the engine and select the gear using the Electric
Vehicle (EV) shift-map.
/m g dem
PP=
If V<60mph, then disengage the clutch for engine
disconnect
Else, engage the clutch.
Else,
Turn on the engine
Select the gear using the engine-on mode shift-map and
find Tdem and Ni
Find PSR using Tdem and Ni and compute
demeng
PPSRP ⋅=
Compute M/G power:
/m g dem eng
P PP= −
End
The flow chart of the above DP-based SPC algorithm is
illustrated in Fig. 10 to help visualize the logic. Note that Pon/off
threshold and shift-map are functions of
θ
, and they can be
found from the previous paper [3]. Other non-adaptive design
parameters, PSR map and EV shift-map, are also used. In this
algorithm, the engine on/off power, gear shifting map, and
PSR commands are sequentially determined because the PSR
decision requires Tdem and Ni, which can only be determined
after gear selection is made, and the shift-map selection
depends on the engine on/off decision. Embedding DP
information in this rule-based control structure provides
decoupled control logics of three sub-control modules: engine
on/off, shift, and PSR, and is expected to perform near
optimally.
B. Cold SPC Algorithm
1) Map-based Cold SPC: The Map-based Cold SPC is an
instantaneous optimization method, previously developed by
the authors for the fast catalyst warm-up of conventional
HEVs [4]. Since tail-pipe emissions are primarily determined
by the catalyst light-off, the idea of the Map-based Cold SPC
is to find the optimal throttle and shift strategy that minimizes
engine-out HC but maximizes the exhaust gas temperature for
fast catalyst warm-up using transient (corrected) engine maps.
Again, due to limited space readers are referred to the
P
dem
>0?
Regenerative
Braking mode
No
Driving mode
Yes
Engine
Drag
Electric mode
(Engine-off)
Engine-on
P
dem
>P
on/off
(θ)?
No
Yes
Engine
Disconnect
V<60mph?
PSR
Map
Assist mode
Recharge
mode
Yes
No
T
dem
N
i
PSR>1
PSR<1
Engine-only
mode
Gear
(V,P
dem
,θ)
Gear
EV
θ
Fig. 10. Flowchart of the adaptive DP-based SPC.
2736

010 20 30 40 50 60 70
0
10
20
30
40
50
60
Vehic le speed [mph]
Power demand [k w]
1st
2nd
3rd
4th
02.0=
θ
010 20 30 40 50 60 70
0
10
20
30
40
50
60
Vehic le speed [mph]
Power demand [k w]
1st
2nd
3rd
4th
35.0=
θ
(a)
02.0=
θ
(b)
35.0=
θ
010 20 30 40 50 60 70
0
10
20
30
40
50
60
Vehic le speed [mph]
Power demand [k w]
1st
2nd
3rd
4th
60.0=
θ
010 20 30 40 50 60 70
0
10
20
30
40
50
60
Vehic le speed [mph]
Power demand [k w]
1st
2nd
3rd
4th
P
on/off
97.0=
θ
(c)
60.0=
θ
(d)
97.0=
θ
Fig. 8. Extracted cold-catalyst shift strategies at four sample
θ
values.
050 100 150 200 250 300
0
0.5
1
1.5
2
2.5
3
3.5
4
Torque demand at the transmis sion input [Nm]
Power Spli t Ratio
02.0=
θ
050 100 150 200 250 300
0
0.5
1
1.5
2
2.5
3
3.5
4
Torque demand at the transmis sion input [Nm]
Power Spli t Ratio
35.0=
θ
Cold PSR
Hot PSR
(a)
02.0=
θ
(b)
35.0=
θ
050 100 150 200 250 300
0
0.5
1
1.5
2
2.5
3
3.5
4
Torque demand at the transmis sion input [Nm]
Power Spli t Ratio
60.0=
θ
050 100 150 200 250 300
0
0.5
1
1.5
2
2.5
3
3.5
4
Torque demand at the transmis sion input [Nm]
Power Spli t Ratio
97.0=
θ
(c)
60.0=
θ
(d)
97.0=
θ
Fig. 9. Extracted cold-catalyst power-split strategies at four sample
θ
values.
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cold-start HEV study for the optimization algorithm [4].
2) DP-based Cold SPC: The DP-based Cold SPC is simply
using a set of cold maps in the proposed DP-based Hot SPC
algorithm (Fig. 10) except for the engine on/off algorithm.
The engine on/off logic of the Cold SPC is triggered by both
the transmission input speed (Ni) and power demand (Pdem),
where the power threshold is adjusted based on
θ
.
C. Results and Discussion (Cold SPC algorithms)
For a fair comparison of the DP-based vs. Map-based Cold
SPC, both controllers share the adaptive DP-based Hot SPC
so that the control strategy is different only during the cold
transient. Also, the cost function of the DP problem is used to
evaluate combined fuel economy and emissions performance.
First, the DP-based Cold SPC is implemented, and its
simulation responses are compared with DP solution. Figure
11 indicates that cold DP results are successfully extracted
and the control signals and vehicle states of the DP-based SPC
are very similar to those of DP. For cold-start performance
evaluation, Fig. 12 shows that the DP-based SPC outperforms
the Map-based SPC under various
θ
conditions. The main
reason for the inferior performance of the Map-based SPC is
its engine on/off strategy because the Map-based optimization
method is unable to determine when the engine should be
turned on/off during a cold-start, and thus the engine on/off
algorithm of the DP-based Hot SPC is used for the Map-based
Cold SPC.
VI. CONCLUSION
This paper studies the simultaneous optimization of fuel
economy and emissions for Plug-in HEVs under various travel
distance and SOC conditions. In order to quantify the level of
SOC with respect to the remaining distance, the variable
Energy to Distance Ratio (EDR), θ, is introduced and used to
extract key control strategies from the DP solutions. The
extracted results indicate that the supervisory controller must
be properly adjusted depending on EDR and the catalyst
temperature. In particular, for the pre-transmission parallel
configuration, engine on/off and gear-shift strategies play key
roles in the adaptive optimal charge management by
controlling the engine speed and consequently the electric
energy flow, while the power-split strategy mainly focuses on
optimizing the engine efficiency for the given engine speed.
ACKNOWLEDGMENT
The authors would like to thank General Motors R&D’s
Propulsion Systems Research Lab for supporting this project.
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cold-start, θ_bar =0.667
0.95
1
1.05
1.1
1.15
Normalized Cos t
DP
DP-based SP C
Map-based SP C
cold-start, θ_bar =0.381
0.95
1
1.05
1.1
1.15
Normaliz ed Cost
DP
DP-based S PC
Map-based S PC
Fig. 12. FC and HC combined performance comparison of DP, Map-based
SPC, and DP-based SPC for various
θ
on the cold-start LA92 cycle.
*Cost function:
)(500)( gHCgFCJ⋅+=
0200 400 600 800 1000
0
2
4
Gear
Throttl e (0~1)
SPC
DP
0200 400 600 800 1000
-40
-20
0
20
40
Power [k W]
engine (SPC)
motor (S PC)
engine (DP)
motor (DP )
0200 400 600 800 1000
0
0.5
1
1.5
PSR
SPC
DP
0200 400 600 800 1000
500
1000
T
cat
[K]
SPC
DP
0200 400 600 800 1000
0
5
10
time [ sec]
wtd. Tai lpipe HC
[mg/ mile]
SPC
DP
Fig. 11. Simulation response comparison of DP vs. DP-based SPC for
381.0=
θ
on the cold-start LA92 cycle.
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