MANUELE BERTOLUZZO, GIUSEPPE BUJA, and ROBERTO MENIS
S
Overview
TEER-BY-WIRE (SbW)
systems are candidates to
replace the conventional
steering equipment in the
new generation of vehicles.
The task of an SbW system
is two-fold: turning the
steered wheels by tracking the hand-
wheel rotation and providing the driver
with a feeling of the steering effort. In
this article, the issues of designing and
testing the control scheme for an SbW
system are discussed. Two schemes
are considered: the first one is derived
from the model of the conventional
steering equipment, while the second
one exploits the capabilities of an SbW
system to cope with the interaction of
the steered wheels to the road surface.
Implementation of the schemes on a
test vehicle is described and experi-
mental results are reported to show the
features of the schemes.
During the last decades, use of embed-
ded electronic circuits and power
devices has deeply innovat-
ed the vehicular tech-
nology, producing a
tremendous impact on
engine efficiency with the man-
agement of the combustion process, on
vehicle stability with the control of the
longitudinal and lateral behaviors, and
on driver assistance and comfort with
the introduction of plenty of systems
easing the driving maneuvers and mak-
ing the cruise more pleasant [1]. More
recently, interest has grown on the
replacement of the conventional appa-
ratus utilized to drive the vehicles with
all-electric systems such as throttle-,
brake-, and SbW systems [2]. Throttle-
by-wire systems have been installed for
a few years now and have greatly con-
tributed to both increased fuel econo-
my and reduced gas emissions.
Brake-by-wire systems are soon to be
installed, propelled on one hand by the
improvement in the vehicle control
achievable with individual wheel brak-
ing and on the other hand by the multi-
redundant setup that does not suffer
from a fault in one wheel unit. SbW sys-
tems constitute the most advanced
challenge in the assembly of an all by-
wire vehicle because of the critical role
played by the steering maneuver and
the consequent very stringent require-
ments posed on their
dependability.
In today’s vehicles, the hand-
wheel is connected to the steered
wheels by a link that can be mechani-
cal, hydraulic, or a combination of
both. The introduction of SbW systems
would eliminate such a link while carry-
ing out the peculiar tasks of steering
equipment, namely turning of the
steered wheels by tracking the hand-
wheel rotation and providing the driver
with a reaction torque representative of
the steering effort. To this aim, the
steering command is converted into an
electronic form by a sensor located on
the handwheel, is executed by an actu-
ator made up of an electric drive cou-
pled directly or through mechanical
limbs to the steered wheels, and is
transmitted from the sensor to the
actuator by a communication network;
another electric drive is coupled to the
handwheel and applies the reaction
torque to the driver.
The vehicles will benefit noticeably
by the adoption of SbW systems in
terms of active and passive driving
safety, driving ergonomics, and envi-
ronment safeguards. Active driving
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safety is achieved thanks to the avail-
ability of the steering command in elec-
tronic form that enables its conditioning
in accordance with the driving maneu-
vers, the environment conditions, and
the vehicle status. Passive driving safe-
ty is increased because of the removal
of the steering column, which is a
potentially unsafe element in case
of an accident. Driving
ergonomics is enhanced on account of
the larger spaces within the driver com-
partment and the possibility of shaping
the handwheel more conveniently. Envi-
ronmental safeguards are achieved in
vehicles, such as in many industrial
trucks, currently steered by means of a
hydraulic apparatus by eliminating this
apparatus as well as the relevant, highly
polluting fluids. These and other advan-
tages of an SbW system are extensively
discussed in [3].
The development of SbW systems
opens new research topics on the sys-
tem components (sensors, actuators,
communication network, electronic
units) that must be tailored to the auto-
motive context for size, reliability,
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21
the shaft, the pinion, the rack, the tie
and costs; the system hardware and
rods, the arms, and the steered wheels,
software that must tolerate a fault
as illustrated in Figure 1.
according to the dependability require-
A workable model of the equipment
ments; and the system control that
is shown in Figure 2 [10]. In the model
must reproduce or even outperform the
the elements of the kinematic chain are
behavior of conventional steering
grouped into two rigid bodies with an
equipment [4].
in-between elastic element constituted
The control topic has received con-
by the shaft. The elements on the hand-
siderable attention in the literature. The
wheel side and those on the steered-
majority of the papers have faced the
wheel side are represented by their
problem of avoiding an abnormal
total moments of inertia (designated
behavior of the SbW systems that could
with
J
h
and
J
s
, respectively) and vis-
result from the elimination of the
mechanical link. A key point is
the synthesis of an appropri-
ate reaction torque. In [5] it is
Handwheel
obtained by matching the SbW
system with a suitable model
Column
of the steering equipment. In
[6] two sensors, one of torque
located on the handwheel and
Shaft
the other one of force located
on the rack, determine the
Tie Rod
Pinion
reaction torque. In [7] an
Rack
extensive vehicle model is
used to estimate the lateral
forces acting on the tires and
Arm
to reconstruct from them the
reaction torque. Other papers
Steered Wheel
have focused on algorithms
intended to alter the steering
command with the aim of
FIGURE 1 — Conventional steering equipment.
improving either the maneu-
verability of a vehicle [8] or its
Steered-Wheel Side
lateral stability [9].
τ
e
1
1
Despite the numerous
s
−
B
s
+
sJ
s
papers, the arrangement of
+
τ
s
simple but effective control
schemes for the SbW systems
ε
ϑ
is still open. Furthermore,
K
f
+
sC
f
there is a lack of experimen-
1
1
tal analysis of the various
N
τh
N
ϑh
Shaft
proposals since nearly all of
them report simulations or
τ
r
−
hardware-in-the-loop up-
τ
d
1
1
shots. In an attempt to con-
s
+
B
h
+
sJ
h
tribute to the matter, this
Handwheel Side
article discusses the designs
and experiments of two con-
FIGURE 2 — Conventional steering system model.
trol schemes that accomplish
in a simple way the tasks required by
cous friction coefficients (designated
the steering maneuver.
with
B
h
and
B
s
, respectively). The shaft
is represented by its torsional stiffness
K
f
and damping coefficient
C
f
, while
Conventional Steering Equipment
the interaction of the steered wheels to
Conventional steering equipment is a
the road surface is represented by the
kinematic chain composed by several
torque
τ
e
, commonly termed environ-
elements: the handwheel, the column,
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ment torque. Other quantities in Figure
2 are the driver torque
τ
d
, which is the
torque exerted by the driver on the
handwheel; the steering torque
τ
s
,
which is the torque exerted by the shaft
on the steered-wheel side elements; the
reaction torque
τ
r
, which is the torque
exerted by the shaft on the handwheel
side elements; the steering and hand-
wheel angles
θ
s
and
θ
h
, which are
respectively the direction of the steered
wheels and the rotation of the hand-
wheel; the torque ratio 1/N
τh
, which is
the ratio between
τ
r
and
τ
s
;
and the angle ratio 1/N
θh
,
which is the ratio between
θ
s
and
θ
h
. Of course, the two
ratios 1/N
τh
and 1/N
θh
have
an equal value, determined by
the rack-and-pinion coupling
and the tie rod and arm lever-
age. Due to the structure of the
kinematic chain, the ratios are
a nonlinear function of the
steered-wheel direction. The
nonlinearity is inherent to the
structure of the steering equip-
ment and is compensated for
by the driver that adjusts the
handwheel position to give the
vehicle the desired trajectory.
Regarding
τ
e
, two situations
can be envisaged. When the
vehicle is stationary and the
driver starts rotating the hand-
ϑ
s
wheel, the contact patches of
the tires do not turn because
the stiction torque opposes the
steering torque; now
τ
e
is equal
−
to the stiction torque and is
+
transferred to the steered-
wheel side elements through
the elastic twisting of the tires.
As the driver continues rotat-
ing the handwheel, the steering
ϑ
h
torque exceeds the stiction
torque and the steered wheels
begin to turn through a stick-
slip motion, if any; subsequent-
ly,
τ
e
settles down to the dry
friction torque. When the vehicle is
moving, another component of
τ
e
arises,
given by a self-aligning moment that
thrusts the steered wheels toward the
center position. This moment depends
on the steering geometry (i.e., caster
angle) and increases with the vehicle
speed and the steering angle, roughly
resembling an elastic torque.
Despite the elasticity of the tires
and shaft, the conventional steering
equipment shows a smoothed behav-
ior because of the damping inherent in
the shaft and of the friction in the cou-
plings between elements and with the
vehicle chassis.
Figure 2 points out that the shaft acts
as a proportional derivative (PD) regula-
tor that closes two position
loops, one on the steered-
wheel side and the other one
τ
e
on the handwheel side. The
−
output position of one loop
+
τ
s
enters as the reference input
for the other loop, and this
forces the handwheel and the
steered wheels to assume an
identical angular position.
The gains of the PD regulator
are given by the mechanical
parameters of the shaft so
τ
r
−
τ
d
that the responsiveness of
+
conventional steering equip-
ment is not modifiable.
SbW System
Control Schemes
In an SbW system the shaft
of the conventional steering
equipment is substituted by
two electric drives. One of
the drives, termed the steer-
ing drive, is coupled to the
rack and exerts the steering
torque, while the other one,
termed the reaction drive, is
coupled to the handwheel
and exerts the reaction
torque. This section pres-
ents two control schemes
for an SbW system. The first
scheme, designated with
the torque scheme, is derived from the
model of the conventional steering
equipment, while the second one, des-
ignated with the speed scheme, copes
with the interaction of the steered
wheels to the road surface.
Speed Scheme
The torque
τ
e
disturbs the control of
the steered wheel. At low cruising
speeds,
τ
e
has a value comparable with
the steering torque and hence its effect
on the scheme performance is appre-
ciable. For instance, when the vehicle
is stationary, the difference
ε
θ
between the position of the
Steered-Wheel Side
handwheel and that of the
ϑ
s
steered wheels can be conspic-
1
1
s
B
s
+
sJ
s
uous before they begin to turn.
To overcome this inconven-
τ
s,ref
ience, a closed loop of speed is
DR
s
PR
s
built up inner to the position
ε
ϑ
−
loop on the steered-wheel side
τ
r,ref
+
1
DR
r
PR
r
as outlined in Figure 4. The
N
τh
resultant control scheme is
1
N
ϑh
termed the speed scheme
SbW System
because PR
s
delivers the
ϑ
h
speed reference
ω
s,ref
to the
1
1
s
B
h
+
sJ
h
steering drive.
The speed loop is con-
Handwheel Side
trolled by a proportional-inte-
gral (PI) regulator (denoted
FIGURE 3 — Torque scheme.
with SR in Figure 4) that com-
pensates for
τ
e
, thus relieving
the position loop from this
Steered-Wheel Side
τ
e
ϑ
s
ω
s
task and making it capable of
1
1
−
B
s
+
sJ
s
s
+
tracking the handwheel posi-
τ
s
tion closely. A similar result
−
τ
s,ref
ω
s,ref
DR
s
PR
s
could have been obtained
SR
+
ε
ϑ
−
with the torque scheme by
τ
r,ref
1
+
PR
r
DR
r
including an integral action in
N
τh
1
the regulator PR
s
, but at the
SbW System
N
ϑh
expenses of a potential insta-
τ
r
bility of the SbW system due
−
ω
h
τ
d
ϑ
h
1
1
to the presence of two inte-
B
h
+
sJ
h
Handwheel Side
+
s
grators and one real pole in
the same loop.
FIGURE 4 — Speed scheme.
the only constraints being for the con-
trol scheme to meet the specifications.
The ratios 1/N
τh
and 1/N
θh
are
also by-choice parameters and can be
adapted dynamically to the driving
conditions of the vehicle; as an exam-
ple, 1/N
θh
can be decreased at low
speeds to ease the steering maneuver
in narrow spaces; 1/N
τh
, in turn, can
be set at a value lower than 1/N
θh
to
assist the driver in the same way as a
power steering system does; moreover,
with DR
s
and DR
r
, receive the torque
references
τ
r,ref
and
τ
s,ref
by individual
PD position regulators, denoted with
PR
s
and PR
r
. The resultant control
scheme is termed the torque scheme
because PR
s
delivers the torque refer-
ence to the steering drive. In contrast
to the conventional steering equip-
ment, here the position loops are inde-
pendent and the gains of the PD
regulators can be freely chosen, with
its value can be suitably adjusted to
adapt the torque reaction level to the
driver demands.
Experimental Setup
A photo of the test vehicle used in
this article is shown in Figure 5(a). It
is a lift truck produced by Cesab Com-
pany and arranged to accommodate
an SbW system. The truck comes with
a hydraulic steering apparatus that
turns the rear wheels and consists of
1) a distribution valve activated by
the handwheel, 2) a hydraulic jack fed
by the distribution valve and connect-
ed to the rear wheels, playing the
Torque Scheme
If a shaft-like operation is maintained
for the SbW system, the control scheme
becomes one as in Figure 3, where the
steering and reaction drives, denoted
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IEEE INDUSTRIAL ELECTRONICS MAGAZINE
23
same function as the rack in the con-
ventional steering equipment, and 3)
a pump that pressurizes the hydraulic
fluid. The rear-axle geometry of the
lift truck is such that there is no self-
aligning component of
τ
e
.
Installation of the SbW system
has required the removal of the dis-
tribution valve and the hydraulic
jack. On the steered-wheel side, a
ball screw has been mounted in
place of the hydraulic jack and an ac
brushless drive has been fitted, with
the motor coupled to the ball screw
through a gear; on the handwheel
side, another ac brushless drive has
been fitted, with the motor directly
coupled to the handwheel axle. Each
motor is endowed with a 12-b
encoder, the output of which is
employed both to control the drive
and to close the position loops of the
SbW system. The SbW arrangement
for the steering axle and the hand-
wheel of the lift truck are shown in
Figure 5(b) and (c).
The control scheme implemented
in the SbW system has the general
structure of Figure 6. It differs from the
conceptual schemes of Figures 3 and 4
in the following points:
■
the steering drive is not directly
coupled to the steered wheels; thus
a torque ratio 1/N
τ
s
exists between
τ
s
and the torque
τ
m
developed by
the steering drive, and, conse-
quently, an angle ratio 1/N
θ
s
(equal
to 1/N
τ
s
) exists between the angu-
lar position
θ
m
of the steering drive
and
θ
s
■
the angular position sensed on the
steered-wheel side is
θ
m
instead of
θ
s
■
in the speed scheme the angular
speed
ω
m
of the steering drive is
used as feedback instead of that of
the steered wheels (ω
s
).
The angular range of the steered
wheels is of 180
◦
. In the control algo-
rithm the angle ratio 1/N
θh
has been
set at 1/4; then, two rotations of the
handwheel turn the steered wheels
fully. To cover the angular range of
the steered wheels, the steering drive
does 32 revolutions. Then the angle
ratio 1/N
θ
s
has an average value of
64, with its actual value a function of
θ
s
. The steering angle
θ
s
utilized in
the implemented scheme is calculat-
ed by multiplying
θ
m
by the constant
quantity
N
θ
s
, fixed at 1/64; this entails
that the variation of 1/N
θ
s
does not
affect the control. The correction of
the difference between the actual
steered-wheel direction
θ
s
and
θ
s
is
left to the driver as with the conven-
tional steering equipment. Moreover,
some backlash exists in the elements
linking the steering drive with the
steered wheels; however, it does not
influence the position loop in the
implemented scheme since the loop
is closed around
θ
m
and the backlash
is external to it.
The gains of the position regulators
are chosen in order to fulfill the
requirements of an average driver.
They are to direct the steered wheels
from an end position to the other one
Handwheel
Column
(a)
Motor
Kingpin
Motor
Tie Rod
Ball Screw
(c)
(b)
FIGURE 5 — (a) Test vehicle, (b) steering axle top view, and (c) handwheel front view of the test vehicle with an SbW system.
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