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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.

2737

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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