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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 3, 2012
Minimum Fuel Control Strategy in Automated
Car-Following Scenarios
Shengbo Eben Li, Huei Peng, Keqiang Li, and Jianqiang Wang
Abstract—Fuel consumption of traditional ground vehicles is
significantly affected by how the vehicles are driven. This paper
focuses on the servo-loop control design of a Pulse-and-Gliding
(PnG) strategy to minimize fuel consumption in automated car
following. A switching-based framework is proposed for real-time
implementation. The corresponding controller was synthesized for
ideal conditions and subsequently enhanced to compensate for
practical factors such as powertrain dynamics, speed variations,
and plant uncertainties. Simulations in both uniform and naturalistic traffic flows demonstrate that, compared with a linear
quadratic (LQ)-based benchmark controller, the PnG controller
improves fuel economy up to 20%. The significant fuel saving
is achieved while maintaining precise range bounds so that the
negative impact on safety/traffic flow is contained. The developed
algorithm can potentially be embedded in adaptive cruise control
systems to achieve fuel-saving function.
Index Terms—Adaptive cruise control, fuel economy, longitudinal automation, optimal driving.
I. I NTRODUCTION
R
OAD vehicles account for more than three quarters of
total energy use in the transportation sector, and around
96% of transportation energy comes from petroleum-based
fuels [1]. Fuel consumption of road vehicles, particularly nonhybrid vehicles, is affected by not only powertrain efficiency
and vehicle weight but how they are driven as well. The
relationship between fuel economy and driving style has been
widely studied over the past few decades [2]–[4]. However,
application of “fuel-efficient driving” received relatively less
attention compared to “mainstream” techniques such as hybrid powertrain, low-drag styling, and lightweight designs [5].
Recent progress and increased availability in driver-assistance
systems present a large opportunity to bridge this gap.
A recent hot topic, in particular in Europe and Japan, is
eco-driving education [6], [7], which focuses on education to
This research work was supported in part by IAT (P. R. China) Autotomotive
Technology Co., Ltd. for designing advanced adaptive cruise control systems
and in part by the National Natural Science Foundation of China under Grant
51205228.The review of this paper was coordinated by Dr. W. Zhuang.
S. E. Li was with the University of Michigan, Ann Arbor, MI 48109 USA. He
is currently with the State Key Laboratory of Automotive Safety and Energy,
Department of Automotive Engineering, Tsinghua University, Beijing 10084,
China (e-mail: [email protected]).
H. Peng is with the Department of Mechanical Engineering, University of
Michigan, Ann Arbor, MI 48109 USA (e-mail: [email protected]).
K. Li and J. Wang is with the State Key Laboratory of Automotive Safety
and Energy, Tsinghua University, Beijing 100084, China.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2012.2183401
improve driver behavior. In theory, it is possible to save fuel
through driver education, but the improvement was found to
be temporary because of human complacency and behavioral
regression. To achieve long-term improvement, fuel-saving tips
can be implemented in control algorithms, e.g., optimal shiftcontrol of transmission [8], smooth longitudinal acceleration
[9], [10], and predicting traffic flow/road slope [11], [12]. Most
of these tips are not universal—they may be derived for one
type of situation and work well but not under other conditions.
Moreover, some of the rules are qualitative (e.g., accelerate
smoothly) and do not ensure optimality in any sense.
The Pulse-and-Gliding (PnG) strategy has been known to be
effective in reducing fuel [13]. The PnG uses a periodic operation, which first runs the engine at high power to accelerate
and then coasts down to a lower speed. Lee and Nelson tested
several qualitatively designed PnG strategies [13] and found
that, when compared with constant speed (CS) cruising, a fuel
reduction of 33%–77% was observed (with the engine off while
coasting). The qualitative PnG operation is suitable for driver
education but not quantitative enough for automated driving
[13]. To address this issue, we have quantitatively identified the
fuel-optimal driving operations in the car-following scenario
[15]. When the transient fuel consumption is ignored, an openloop PnG strategy (called full PnG) was found to be optimal,
and its control signals can be explicated solved, even when a
range constraint is imposed.
The purpose of this paper is to extend the open-loop PnG
maneuver so that it can be implemented in a servo-loop controller. The remainder of this paper is organized as follows:
Section II introduces the car-following model. Section III reviews the properties of the full-PnG maneuver and introduces a
framework for its real-time implementation. The design of the
switching controller under the simplified case is discussed in
Section IV, followed by its enhancement for practical factors in
Section V. Finally, simulations in both uniform and naturalistic
traffic flow are performed in Section VI.
II. DYNAMIC C AR -F OLLOWING M ODEL FOR C ONTROL
This paper considers the design of fuel-efficient control
for an automated vehicle. We only consider two consecutive
vehicles, i.e., a preceding vehicle (PV) is the tracking target and
a following vehicle (FV) that is being controlled. The simple
governing equation is
0018-9545/$31.00 © 2012 IEEE
Δv̇ = ap − a
ΔṘ = Δv − Ṙdes
(1)
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where Δv is the relative speed, ΔR is the range error, v is
the FV speed, a is the FV acceleration, and ap is the PV
acceleration. Rdes is the desired range, which follows a constant
headway policy, and Rdes = τh • vp + d0 [14]. Due to safety
concerns, a constraint on the range error is imposed as [15]:
ΔRmin ≤ ΔR ≤ ΔRmax
(2)
where ΔRmin and ΔRmax are the range bounds, which can be
selected by the human driver. The FV is equipped with an internal combustion engine and a continuous variable transmission
(CVT) or a transmission with a large number of gears. Its main
longitudinal dynamics are captured by
1
Pecom
τe s + 1
Pe
M a = − CA v 2 + M gf + ηT
v
Pe =
(3)
Fig. 1. Open-loop full-PnG maneuver.
where Pecom is the commanded engine power, Pe is the actual
engine power, τe is the time constant of the powertrain dynamics, CA is the coefficient of aerodynamic drag, M is the vehicle
mass, g is the gravity coefficient, f is the coefficient of rolling
resistance, and ηT is the mechanical efficiency of the driveline.
For CVT, its speed ratio is assumed to be manipulated, so that
the engine operates on (close to) the optimal Brake Specific
Fuel Consumption (BSFC) [17].
In applications such as hybrid vehicle designs, static fuel
maps are commonly used to predict engine fuel consumption
[18]. However, significant error may arise due to transient operations due to the engine power switching. Hence, a correction
term for transient fuel consumption is added by
2
dTe
(4)
Qs = qBSFC (Te , ωe ) · Pe + ke ·
dt
fluctuate in a periodic manner (shown in Fig. 1), and its key
properties are summarized here.
Property 1: The engine switches between its minimum
BSFC point and the idling point, periodically undergoing two
phases, i.e., pulse and gliding.
Property 2: The range oscillates between its upper and lower
bounds, and the average FV speed is equal to the PV speed.
Property 3: The range reaches its bounds when PV and FV
have identical speeds. The state pair (Δv, Δd) at this moment is
defined as equal speed (ES) point, as highlighted by rectangles
in Fig. 1.
As stated in [15], Property 1 is the reason PnG saves
fuel, whereas Properties 2 and 3 ensure periodic car-following
operation. Even though PnG is quantitatively elaborated, its
servo-loop implementation is still quite challenging for three
reasons.
where Qs is the total fueling rate; qBSFC represents the static
fuel rate, which is a function of two variables Te (engine
torque) and ωe (engine speed); and ke is the coefficient for
transient fuel. Note that ke is calculated by assuming that
engine transient operation increases static fuel consumption
by around 4% under the U.S. Federal Test Procedure Cycle
(FTP-72) [16].
1) The optimization neglects the powertrain dynamics [15],
which delays the switching and will cause overshoot in
range.
2) The open-loop PnG maneuver is identified when PV
maintains a CS [15]. In reality, the PV speed fluctuates.
3) Existence of other plant uncertainties and exogenous
inputs.
III. M INIMUM F UEL C ONTROL S TRATEGY
A. Properties of the Open-Loop PnG Maneuver
To identify the optimal driving strategy in car-following
scenarios, an optimization problem was formulated and solved
using the Gauss pseudospectral optimization method [15].
The identified optimal maneuvers were found to fall into
three types: partial-PnG, full-PnG, and CS. The nonlinear engine static fuel consumption dominates the strategy decision.
As speed increases from zero, the optimal maneuver changes
from partial-PnG to full-PnG and, finally, to CS. The full-PnG
maneuver is of most importance becomes it covers the speed of
highway traffic flow for the engine that we studied. In full-PnG
operation, engine torque, vehicle speed, and intervehicle range
B. Configuration of the Servo-Loop Controller
The servo-loop controller, shown in Fig. 2(a), contains three
components, i.e., a finite-state machine, a switching logic, and
a range bound feedback regulator.
The finite-state machine contains two dependent modes, i.e.,
pulse (P) and gliding (G). In the pulse mode, the engine runs
at the minimum BSFC point. In the gliding mode, the engine is
idled. Mathematically, the engine command input is
PeBSFC , Pulse mode
(5)
Pecom =
0,
Gliding mode
where PeBSFC denotes the engine power at the minimum
BSFC point. The switching logic contains a switching map, a
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Fig. 2. (a) Configuration of the servo-loop controller. (b) Pulse and gliding trajectories in the Δv−ΔR phase plot. (Thick solid line—pulse and gliding switch
line; thin solid line—arbitrary state trajectories.)
compensator, and a predictor. It generates a switching signal
SPnG to drive the finite-state machine, i.e.,
Pulse,
if SPnG = 1
(6)
Mode =
Gliding, if SPnG = −1.
conditions hold: 1) The powertrain dynamics are neglected.
2) FV speed is constant. 3) PV speed is also constant. The
idealized condition is used throughout Section IV.
The switching map is designed based on Properties 2 and 3.
The compensator and predictor improve the map by considering
three practical factors. The last component, i.e., range bound
feedback regulator, improves robustness. It continuously corrects driver desired range bound to enable an accurate following
distance tracking to deal with model uncertainties.
In the finite-state machine, the engine power command
Pecom is either PeBSFC or zero. Therefore, all pulse (or gliding)
trajectories are exclusively determined by their initial states.
Plugging (5) into (3), the FV acceleration is
IV. C ONTROLLER S YNTHESIS BASED ON
THE S WITCHING L OGIC
The controller design is centered on the switching map,
which contains two critical state trajectories, pulse and gliding
switch lines. The relative position of state (Δv, Δd) to the
two lines determines how to generate SPnG . For simplicity, we
define an idealized condition by assuming that the following
A. Analysis of Pulse and Gliding Switch Lines
ηT PeBSFC
1 CA vp2 +M gf +
M
M vp
1 CA vp2 +M gf
āgld = −
M
āpls = −
if SPnG = 1
if SPnG = −1.
(7)
Plugging (7) into (1), the pulse and gliding trajectories are
calculated, as illustrated in Fig. 2(a).
In Fig. 2(b), two state trajectories are unique and are highlighted by thick solid lines. They cross the upper and lower ES
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1001
are accessible, and either of them can deliver state to expected
boundary. Formalizing this concept naturally leads to a regionbased switching logic
SPnG (n)
⎧
⎨ 1,
= SPnG (n − 1),
⎩
−1,
if [Δv, ΔR] ∈ Pulse region
if [Δv, ΔR] ∈ Hold region
if [Δv, ΔR] ∈ Gliding region.
(10)
Such a switching logic eventually forms a steady PnG operation under idealized conditions, driving state to counterclockwise follow the acorn-shaped loop.
Fig. 3.
V. C ORRECTION OF S WITCHING L OGIC
FOR P RACTICAL FACTORS
Regional division of the simplified switching map.
points, respectively. They are called pulse and gliding switch
lines and are expressed as
Δv = − āpls · t
,
1
ΔR = ΔRmax − āpls · t2
2
Δv = − āgld · t
,
1
ΔR = ΔRmin − āgld · t2
2
t ∈ (−∞, +∞)
(8)
t ∈ (−∞, +∞).
(9)
Any trajectory started from these two lines passes through
some ES point (i.e., Property 3 holds). Furthermore, the two
switching lines enclose an acorn-shaped area symmetric to
the vertical line Δv = 0 (i.e., Property 2 holds). Therefore,
a simplified switching logic is to switch whenever the state
crosses the pulse or gliding switch lines. Note that the gliding
trajectory crossing the upper ES point is defined as the upper
gliding line, and the pulse trajectory crossing the lower ES point
is defined as the lower pulse line. They are used as auxiliary
lines when dividing regions in Section IV-B.
B. Simplified Switching Logic Based on Regional Division
In theory, a switch happens when the state pair (Δv, Δd)
crosses a switch line. However, in practice, this cannot be precisely executed because of measurement noise, time discretization, and variable quantization. A more practical approach is
to implement switching based on regions, as shown in Fig. 3.
The phase plot is divided into three regions: pulse region, hold
region, and gliding region. They are separated by two parts of
the switch lines (i.e., solid lines) and two auxiliary lines (i.e.,
dashed lines in Fig. 3, which are called the upper and lower
pulse lines).
The switching logic is designed according to the following
straightforward observation: State delivery onto the centrally
localized acorn-shaped boundary is critical to formalize a periodic PnG operation. In the gliding region, any pulse operation
eventually moves a state far away from center, which is no
way to start a PnG operation; however, a gliding operation in
this region always shifts the state into the hold region, finally
reaching the right-top quarter of the acorn-shaped loop. On
the contrary, only a pulse operation can be fulfilled similarly
to, but opposite in direction from, state delivery in the pulse
region. In the hold region, both pulse and gliding operations
The simple switching logic in (11) only works well under
idealized condition. In reality, the fluctuating FV speed increases aerodynamic drag, and the powertrain dynamics introduce time delay on driving operations. In addition, in real traffic
flow, the PV speed also varies. These factors may cause violation of range constraint, thus affecting safety and smoothness
of traffic flow. A compensator and a predictor are introduced
to correct both pulse and gliding switch lines, yielding more
accurate PnG operations.
A. Compensator for Speed Fluctuation and
Powertrain Dynamics
The effects of increased aerodynamic drag and delayed operations are assumed to be independent, i.e.,
Δvc = Δv + εvSF + εvPD
ΔRc = ΔR + εRSF + εRPD
(11)
where Δvc , Δdc represent corrected states, εvSF εdSF are for
FV speed fluctuation, and εvPD εdPD are for powertrain dynamics. When the FV speed varies, it first slightly increases aerodynamic drag and consequently affects the state trajectories. Its
correction terms are
εvSF =
K(v − vp ) 2
,
2ā
εRSF =
K(v − vp ) 3
6ā2
(12)
where ā is the FV acceleration under the idealized condition,
and parameter K is defined as
2C v
A p
+ ηMT PeBSFC
, if SPnG (k) = 1
vp2
K = 2CMv
(13)
A p
if SPnG (k) = −1.
M ,
The effectiveness of correction is shown in Fig. 4. Both
PtoG and GtoP switching are found to be delayed, compared
with the original switching logic. Moreover, it is observed that
the corrected switching lines are very close to the actual state
trajectories.
The key in compensating for the powertrain dynamics
is to cancel its introduced lag. The correction terms are
mathematically derived by comparing simplified and real
switching points, i.e.,
εvPD = SPnG (k) · (āpls − āgld )τe
(14)
εRPD = −SPnG (k) · (āpls − āgld )τe2 .
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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 3, 2012
Fig. 4. Effects of speed fluctuation on switching lines. (Thin solid line)
Simplified switch lines. (Thick dashed line) Corrected switch lines. (+) Actual
state trajectories.
Fig. 5. Effect of powertrain dynamics on switch lines. (Thin solid line)
Simplified switch lines. (Thick solid line) Corrected switch lines. (Thick dashed
line) Actual trajectory considering powertrain dynamics.
Fig. 6. State trajectory in a PnG period without correction for PV acceleration
(ap = 0.2 m/s2 ).
Fig. 7. Comparison of the predicted and simplified switch lines considering
PV acceleration. (Thin lines) Simplified. (Thick lines) Predicted.
Fig. 5 demonstrates how the powertrain dynamics affect
the switching timing. It is found that both PtoG and GtoP
switches start earlier (at points highlighted by “+” markers). It
is observed that the starting points of all state trajectories (“+”
markers) coincide with the corrected switching lines.
B. Predictor for Naturalistic Traffic Flow
Another issue associated with the simplified switching logic
is the range overshoot in naturalistic traffic flow, due to varying
PV speed. Fig. 6 shows a segment of the state trajectory when
the PV accelerates (where Points A, B, D, and D in the state
trajectory correspond to Points A , B , C , and D in the
PV speed line). When the PV accelerates, range overshoot is
observed in both pulse and gliding modes. Note that −Tlast is
the past time that a PtoG switch occurred, and Tp is the future
time when a GtoP switch will occur. Their appearance here will
help readers to understand how to derive the predictor used to
compensate for speed-varying traffic flow.
One way to address this issue is to predict PV acceleration
and adjust the switching logic to shrink the acorn-shaped state
trajectory inside the range constraint. Obviously, the modified
trajectory must be tangent to both upper and lower bounds.
Suppose that the state is in the gliding mode now. The
latest PtoG switch was done at t = −Tlast (Point B, known),
Fig. 8.
Effect of model uncertainties on state trajectory.
the current time is at t = 0, and the upcoming GtoP switch
(Point C, unknown) will happen at a future time t = Tp . Then,
Tlast + Tp is the time length of the gliding mode. In a smooth
traffic flow (which is proper for ACC), it is reasonable to
assume that PV holds constant acceleration from t = 0 to Tp .
Therefore, the PV speed at Tp is predicted to be
vp (Tp ) = vp (0) + āp · Tp
TPnG (1 − λPnG ) − Tlast , if SPnG = 1
(15)
Tp =
if SPnG = −1
TPnG λPnG − Tlast ,
where TPnG is the PnG period, λPnG is the duty cycle of the
PnG period, and āp is the PV acceleration in [0, Tp ], which is
assumed to be constant, i.e.,
āp = âp (0).
(16)
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Fig. 9. Effectiveness of the simple switching logic controller. (a) Range performance under nominal conditions. (b) Range performance with decelerating PV.
(c) Range performance under plant uncertainty.
Note that the prediction of vp at t = Tp is critical for the
switching logic. Its accuracy directly affects the calculation
of FV acceleration at t = Tp , and, subsequently, that of the
pulse/gliding switching lines. The FV acceleration is estimated
to be (when SPnG = −1)
apls (Tp ) = −
ηT PeBSFC
1 CA vp2 (Tp ) + M gf +
. (17)
M
M vp (Tp )
Plugging (15) into (1) and also considering aforementioned
tangent condition, a predicted pulse switch line is derived by
celeration. The horizontal shift and shape deformation together
have a relatively complex influence on the switching logic.
Whether to postpone or advance the switching timing depends
on their common interaction.
VI. R ANGE B OUND F EEDBACK R EGULATOR
Uncertainties exist in real vehicle operations, e.g., unknown
vehicle mass, varying road slopes, etc. In such cases, the
range constraint may be violated. The violation may deteriorate
smoothness and safety and must be mitigated.
Δv = (āp − apls (Tp )) t
ΔR = ΔRmax +
− τh āp t +
(τh āp )2
2 (āp − apls (Tp ))
1
(āp − apls (Tp )) t2 .
2
A. Design of the Range Bound Feedback Regulator
(18)
In (18), the tangent point happens at
Δv = τh āp .
(19)
which means that Property 3 does not hold when PV accelerates
or decelerates. The predicted gliding switch line can be derived
in a similar fashion. Combining two predicted switching lines, a
new regional division is obtained, followed by its corresponding
switching logic.
Fig. 7 compares the original and modified switching lines.
The switching lines were found to horizontally shift, no longer
symmetric to Δv = 0. Their shapes also deform; the tendency
and amount of shape deformation is dependent of the PV ac-
To handle uncertainties, the bounds used in the calculations
of pulse and gliding should be modified, so that the bounds
specified by the driver is achieved. A proportional-gain feedback regulator was found to work well. The following content
only introduces the regulator for upper bound. The same is
to that for lower bound. In the kth step, the bound error is
defined as
emax (k) = ξmax (k) − ΔRmax
(20)
where ΔRmax is the desired upper bound initialized by drivers,
ξmax is the maximum range error, and n represents kth PnG
operation. The virtual bound command for next-step PnG operation is
ΔR̄max (k + 1) = ΔR̄max (k) − λ · emax (k),
0<λ<1
(21)
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Fig. 10. Performance under PnG and LQ controllers in a uniform traffic flow. (a) Engine torque and engine speed. (b) Relative speed and range error.
(c) Accumulated average fuel. (d) Fuel saving of PnG at different speeds.
where ΔR̄max is the virtual bound command. Its initial value is
equal to the driver-specified upper bound.
B. Stability Analysis
For simplicity, the stability proof is only conducted for the
idealized condition. First, lump the effects of model uncertainties and described them in the form of an error in longitudinal
acceleration
ãpls = āpls + ςa
|ςa − ς a | ≤ Δυ.
(22)
where āpls represents the pulse acceleration in the nominal case,
ãpls denotes the pulse acceleration in the mismatch case, and
ςa is the acceleration error due to uncertainties. Note that ςa is
centered on ς a , and the residue is bounded by Δυ.
Fig. 8 shows two pulse trajectories after identical GtoP
switch (one is for the nominal case, and the other is for the
mismatch case). In the nominal case, the range constraint is
observed. For the case with uncertainties, the maximum range
exceeds the specified bound and reaches ξmax .
Using (8) in two cases and eliminating ΔR and t, we get
ΔR̄max (k) = ξmax (k) +
ãpls − āpls
Δv 2 .
2āpls ãpls
(23)
Combining (22) and (23), an inequality is derived as
C
C (ς a − Δς) ≤ ΔR̄max (k) − ξmax (k) ≤ (ςa + Δς)
2
2
Fig. 11. Speed profiles obtained from naturalistic traffic flow and used as PV
speed in simulations.
C=
Δv 2
.
(apls + ς a )apls
(24)
Equation (24) reflects the relationship between the virtual
bound command and the actual range extrema. Plugging (21)
into the aforementioned equation, an inequality on emax (k) is
obtained, followed by its convergence property:
− CΔυ ≤ emax (k + 1) − (1 − λ)emax (k) ≤ CΔυ.
lim |emax (k)| ≤
k→+∞
Δυ
Δv 2
.
λ (apls + ς a ) apls
(25)
(26)
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Fig. 12. Simulation of PnG and LQ in naturalistic traffic flow. (a) Engine torque and engine speed. (b) Vehicle speed of FV and PV. (c) Range between two
vehicles. (d) Accumulated average fuel.
In the PnG maneuver, the FV speed fluctuates, and Δv in
(26) is bounded. Therefore, emax (k) is bounded as k goes to
infinite. Larger λ helps to reduce the steady-state error. The
limiting case is the model uncertainty is fixed to an unknown but
constant value (which means that Δυ is zero). Then, sequence
emax (k) satisfies
emax (k + 1)
= 1 − λ,
emax (k)
if Δυ = 0.
(27)
Apparently, emax (k) converges when 0 < λ < 1. Equation
(27) defines the convergence speed of emax (k), which depends
on λ. Larger λ results in faster convergence.
Fig. 13. Fuel economy comparison of LQ and PnG controllers. (a) Engine
operating points.
VII. S IMULATIONS AND A NALYSES
The PnG-based controller is tested in two types of traffic
flow, i.e., uniform traffic flow, in which the PV speed is constant, and naturalistic traffic flow, in which the PV speed profiles are extracted from a set of driver experiment data. The PnG
controller has three design parameters, i.e., λ = 0.5 for bound
feedback regulator and ΔRmax = 3 m and ΔRmin = −3 m for
range bounds. A linear quadratic (LQ)-based controller is used
as the benchmark. Its weighting matrices are selected to achieve
a similar range error to that of the PnG controller. For details,
see [9].
The car-following model used for simulations is more complicated than the control model presented earlier. A major
difference is on CVT, in which a speed ratio controller and
state-dependent efficiency are considered [17]. All vehicle parameters are the same as those in [15].
A. Effectiveness of the Proposed Switching Logic
Observing the range constraint is critical for traffic flow
and safety. Fig. 9 shows a series of simulations demonstrating
the individual effect of (with and without) the compensator,
predictor, and bound feedback regulator. In Fig. 9(a) and (c),
the PV runs at a CS of 20 m/s. In Fig. 9(b), PV decelerates
at −0.3 m/s2 with an initial speed of 30 m/s. In addition, in
Fig. 9(c), the vehicle mass is 20% less than the nominal value.
In Fig. 9(a), the effect of compensating for the powertrain
dynamics and vehicle speed fluctuation is shown. In Fig. 9(b),
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Fig. 14. Performance comparison of PnG and LQ controllers in naturalistic driving. (a) Average fuel consumption. (b) Maximum range error.
the effectiveness for the predictor is shown. In Fig. 9(c), acceleration is underestimated in the controller due to the reduced
vehicle weight, and the range bound error is reduced after a few
cycles of compensations.
In addition, the compensator, predictor, and bound feedback
regulator can be separately deployed. In some applications,
e.g., adaptive cruise control in light traffic flow with long time
headway, accurate space tracking may not be critical. In such
cases, a subset of these three components may be adequate.
B. Performance Verification in Uniform Traffic Flow
In this section, vp is fixed at a given speed. Simulation
results for vp = 21 m/s are shown in Fig. 10. The engine torque
switches between Te = 150 N · m (minimum BSFC point) and
Te = 0 N · m (idling). The range oscillates between its upper
and lower bounds. Under the LQ controller, the engine torque
gradually converges to a steady state; both speed and range
become constant. Compared with LQ, the fuel consumption
using the PnG control is significantly lower after a few cycles.
The fuel saving of PnG at different PV speeds is shown in
Fig. 10(d). The fuel benefit reaches its peak at 15 m/s and
then decreases to zero. (At which point the PnG algorithm is
no longer used, see [15].) Compared with LQ, the maximum
saving is almost 20%.
C. Performance Verification Naturalistic Traffic Flow
The naturalistic driving data come from experiments in real
traffic flow [19]. The speed profiles are extracted from the database using the following query conditions: 1) Speed is between
15 and 40 m/s, 2) acceleration is between −0.4−0.3 m/s2 ,
and 3) duration of car following > 80 s. There are a total of
56 extracted segments, some of which are shown in Fig. 11.
Figs. 12 and 13 show the simulation results on one segment
of naturalistic speed profiles. It is found that the PnG controller
maintains a switching driving behavior, with uneven periods.
The FV speed fluctuates up and down around the PV speed and
the range bounds between its upper and lower bounds. There
is a slight discrepancy in bound tracking, but the error is very
small—assuming all measurement is noise-free.
In PnG, the engine works at either the minimum BSFC points
or the idling point, as shown in Fig. 13. The PnG controller
consumes less fuel compared with LQ.
The total fuel consumption and maximum range error in
all naturalistic simulations are shown in Fig. 14. As shown in
Fig. 14(a), test results following naturalistic PV are scattered
but centered around the uniform traffic flow results. This means
the fuel benefit of PnG in uniform traffic flow can be used to
estimate fuel saving under naturalistic driving. Fig. 14(b) shows
that the average range error of LQ and that of PnG controller are
similar. The later, however, has a little less scatter while uses
less fuel.
VIII. C ONCLUDING R EMARKS
A servo-loop implement of a PnG strategy has been introduced. The controller is based on the switching logic, which
has been designed using simple vehicle models and then enhanced by three elements, i.e., a compensator, a predictor, and
a bound feedback regulator to deal with common uncertainties.
Its performance has been validated under both uniform and
naturalistic driving conditions. Compared to a benchmark LQbased controller, the PnG controller reduces fuel consumption
by up to 20% while maintains a more precise range with the PV.
A possible concern of the PnG control is the switching
nature of its operation, which might be objectionable due to
NVH and comfort considerations. It is possible that heavy-duty
trucks might be a better application than passenger cars. This is
because fuel expense is high and important for truck operations.
In addition, the relatively low power/mass ratio means that the
switching operations might be less perceptible. We do not think
direct implementation of the switching algorithm is the best
way forward. Rather, striking a balance between fuel saving and
NVH/comfortable is important.
R EFERENCES
[1] S. Kobayashi, S. Plotkin, and S. Ribeiro, “Energy efficiency technologies for road vehicles,” Energy Efficiency, vol. 2, no. 2, pp. 125–137,
May 2009.
[2] M. Ross, “Automobile fuel consumption and emissions: Effects of
vehicle and driving characteristics,” Annu. Rev. Energy Environ., vol. 19,
pp. 75–112, Nov. 1994.
LI et al.: MINIMUM FUEL CONTROL STRATEGY IN AUTOMATED CAR-FOLLOWING SCENARIOS
1007
[3] L. Evans, “Driver behavior effects on fuel consumption in urban driving,”
Human Factors, J. Human Factors Ergonom. Soc., vol. 21, no. 4, pp. 389–
398, Aug. 1979.
[4] J. Mierlo, J. G. Maggetto, E. van de Burgwal, and R. Gense, “Driving
style and traffic measures-influence on vehicle emissions and fuel consumption,” Proc. Inst. Mech. Eng. D, J. Automobile Eng., vol. 218, no. 1,
pp. 43–50, Jan. 2004.
[5] J. Barkenbus, “Eco-driving: An overlooked climate change initiative,”
Energy Policy, vol. 38, no. 2, pp. 762–769, Feb. 2010.
[6] B. Beusen, S. Broekx, T. Denys, C. Beckx, B. Degraeuwe, M. Gijsbers,
K. Scheepers, L. Govaerts, R. Torfs, and L. Int Panis, “Using on-board
logging devices to study the longer-term impact of an eco-driving course,”
Transp. Res. D, Transp. Environ., vol. 14, no. 7, pp. 514–520, Oct. 2009.
[7] M. Zarkadoula, G. Zoidis, and E. Tritopoulou, “Training urban bus drivers
to promote smart driving: A note on a Greek eco-driving pilot program,”
Transp. Res. D, Transp. Environ., vol. 12, no. 6, pp. 449–451, Aug. 2007.
[8] J. Ino, T. Ishizu, and H. Sudou, “Adaptive cruise control system using
CVT gear ratio control,” in Proc. Autom. Transp. Technol. Congr. Expo.,
Barcelona, Spain, 2001.
[9] S. E. Li, K. Li, R. Rajamani, and J. Wang, “Model predictive multiobjective vehicular adaptive cruise control,” IEEE Trans. Control Syst.
Technol., vol. 19, no. 3, pp. 556–566, May 2011.
[10] J. Zhang and P. Ioannou, “Longitudinal control of heavy trucks: Environmental and fuel economy considerations,” IEEE Trans. Intell. Transp.
Syst., vol. 7, no. 1, pp. 92–104, Mar. 2006.
[11] C. Manzie, H. Watson, and S. Halgamuge, “Fuel economy improvements
for urban driving: Hybrid vs. intelligent vehicles,” Transp. Res. C, Emerg.
Technol, vol. 15, no. 1, pp. 1–16, Feb. 2007.
[12] E. Hellstrom, M. Ivarsson, J. Åslund, and L. Nielsen, “Look-ahead control
for heavy trucks to minimize trip time and fuel consumption,” Control
Eng. Pract., vol. 17, no. 2, pp. 245–254, Feb. 2009.
[13] J. Lee, D. Nelson, and H. Lohse-Busch, “Vehicle inertia impact on fuel
consumption of conventional and hybrid electric vehicles using acceleration and coast driving strategy,” presented at the Soc. Automotive Eng.
World Congr. Exh., Detroit, MI, 2009, Paper 2009-01-1322.
[14] P. Ioannou and C. Chien, “Autonomous intelligent cruise control,” IEEE
Trans. Veh. Technol., vol. 42, no. 4, pp. 657–672, Nov. 1993.
[15] S. E. Li and H. Peng, “Optimal driving strategies to minimize fuel consumption of passenger cars during car-following scenarios,” P. iMechE D,
J. Automobile Eng., 2011.
[16] S. Lee, Transient Dynamics and Control of Internal Combustion Engines.
Beijing, China: Peoples’ Transp., 2001.
[17] R. Pfiffner, L. Guzzella, and C. Onder, “Fuel-optimal control of CVT
power trains,” Control Eng. Prac., vol. 11, no. 3, pp. 329–336, Mar. 2003.
[18] C. Lin, H. Peng, J. Grizzle, and J.-M. Kang, “Power management strategy
for a parallel hybrid electric truck,” IEEE Trans. Control Syst. Technol.,
vol. 11, no. 6, pp. 839–849, Nov. 2003.
[19] H. Yang and H. Peng, “Development and evaluation of collision warning/
collision avoidance algorithms using an errable driver model,” Veh. Syst.
Dyn., vol. 48, no. Suppl. 1, pp. 525–535, 2010.
Huei Peng received the Ph.D. degree from the University of California, Berkeley, in 1992.
He is currently a Professor with the Department
of Mechanical Engineering, University of Michigan,
Ann Arbor. He served as an Associate Editor for the
ASME Journal of Dynamic Systems, Measurement
and Control from 2004 to 2009. His research interests include adaptive control and optimal control,
with emphasis on their applications to vehicular and
transportation systems. His current research interests
include design and control of hybrid electric vehicles
and vehicle active safety systems.
Dr. Peng is an active member of the Society of Automotive Engineers and
the ASME Dynamic System and Control Division (DSCD) and is an ASME
Fellow. He served as Chair of the ASME DSCD Transportation Panel from
1995 to 1997 and is a member of the Executive Committee of ASME DSCD.
He served as an Associate Editor for the IEEE/ASME T RANSACTIONS
ON M ECHATRONICS from 1998 to 2004. He received the National Science
Foundation Career Award in 1998.
Shengbo Eben Li received the B.Eng. degree from
the University of Science and Technology Beijing,
Beijing, China, in 2004 and the M.S. and Ph.D.
degrees from Tsinghua University, Beijing, in 2006
and 2009, respectively.
From 2010 to 2011, he was with the University
of Michigan, Ann Arbor, as a Research Fellow. He
is currently an Assistant Professor with the State
Key Laboratory of Automotive Safety and Energy,
Department of Automotive Engineering, Tsinghua
University. He has authored about 20 journal/
conference proceeding papers. He is the holder of seven patents in China. His
research interests include vehicle dynamics and control, driver behavior and
factor, and battery management systems.
Dr. Li has received the “Tsinghua Distinguished Doctoral Dissertation” in
2009 and the “Tsinghua Distinguished Ph.D. Graduates” in 2010.
Jianqiang Wang received the B.Tech. and M.S.
degrees from Jilin University of Technology,
Changchun, China, in 1994 and 1997, respectively, and the Ph.D. degree from Jilin University,
Changchun, in 2002.
He is currently an Associate Professor of automotive engineering with the State Key Laboratory of
Automotive Safety and Energy, Tsinghua University,
Beijing, China. He has been engaged in more than
ten projects such as the National Natural Science
Foundation of China and National High Technology
Research and Development Program of China. He has authored more than 40
journal papers. He is the holder of 20 patent applications. His research interests
include intelligent vehicles, driving-assistance systems, and driver behavior.
Dr. Wang received six awards, including the Jilin Province S&T Progress
Award and the Chinese Automotive Industry S&T Progress Award.
Keqiang Li received the B.Tech. degree from
Tsinghua University of China, Wuhan, China,
in 1985 and the M.S. and Ph.D. degrees from
Chongqing University of China, Chongqing, China,
in 1988 and 1995, respectively.
His is currently a Professor of automotive engineering with the State Key Laboratory of Automotive
Safety and Energy, Tsinghua University, Beijing,
China. He has authored more than 90 papers. He
is the holder of 12 patents in China and Japan.
His research interests include vehicle dynamics and
control for driver-assistance systems and hybrid electrical vehicles.
Dr. Li has served as Senior Member of the Society of Automotive Engineers
of China and on the Editorial Boards of the International Journal of ITS
Research and the International Journal of Vehicle Autonomous Systems. He
received the “Changjiang Scholar Program Professor” Award and several
awards from public agencies and academic institutions of China.