Development and Evaluation of an Integrated Chassis

Development and Evaluation of an Integrated Chassis
Development and Evaluation of an Integrated Chassis
Control System
Youseok Kou1
5
Huei Peng2
DoHyun Jung3
1
Graduate
Student,
Dept.
of
Mechanical
Engineering,
10 U n i v e r s i t y o f M i c h i g a n , A n n A r b o r , M I 4 8 1 0 9 U S A
2Professor, Dept. of Mechanical Engineering, University of
Michigan, Ann Arbor, MI 48109 USA
3Senior Researcher, Body & Chassis Engineering Center,
Korea Automotive Technology Institute, South Korea
15
Abstract
The
development
and
worst-case
evaluation
of
an
Integrated Chassis Control (ICC) system is reported in this
paper. The ICC control system was
designed based on a
20 l a t e r a l - y a w - r o l l v e h i c l e m o d e l w i t h n o n l i n e a r t i r e s .
The
ICC controller was developed based on balanced objectives
in
controlling
vehicle
motions,
with
carefully
selected
thresholds and targets. The sliding mode control technique
is used to design the brake torque servo loop to achieve the
25 d e s i r e d o u t p u t s .
Vehicle response under the ICC control
1
is evaluated using the CarSim software. The effectiveness
of the ICC system was examined by applying the worst-case
dynamic evaluation (WCDE) procedure, which identifies the
worst-possible
excitation
(e.g.,
steering)
to
the
vehicle
5 with ICC and thus represents a procedure suitable for the
evaluation of active safety systems.
1 . INTORDUCTION
The
general
public
and
government
agencies
have
10 d e m o n s t r a t e d s u s t a i n e d i n t e r e s t i n a c t i v e s a f e t y t e c h n o l o g y
for
ground
vehicles.
Many
chassis
control
devices
that
manipulate braking, steering and suspension systems were
developed
and
applied
to
improve
vehicle
safety,
conveniences and comfort. As these devices become more
15 m a t u r e , t h e y n e e d t o s h a r e i n f o r m a t i o n w i t h e a c h o t h e r f o r
better
cost-leveraging
performance.
The
functions
loosely
Control
is
systems,
and
improved
integration
and
referred
has
of
to
been
reliability
these
as
chassis
Integrated
an
area
of
and
control
Chassis
intensive
20 d e v e l o p m e n t b y m a n y c o m p a n i e s i n r e c e n t y e a r s ( 1 ) . M a j o r
automotive
chassis
companies
control
have
functions,
developed
many
of
a
wide
which
are
array
of
already
commercialized (2).
A critical issue of these active safety systems is to
25 e n s u r e
their
functionality
under
2
extreme
circumstances.
Typically, large-scale test matrices were defined and the
active
safety
systems
were
evaluated
using
these
test
matrices iteratively. To avoid time-consuming field testing,
computer simulations can be used to systematically search
5 for worst-cases situations, i.e., potential cases when the
active safety systems might fail to perform satisfactorily.
The worst-case dynamic evaluation (WCDE) methodology is
an emerging field which has the potential to accelerate the
development
10 r e p l a c i n g
of
vehicle
lengthy
active
field
safety
tests
systems
and
(3),
calibration
by
with
elaborative numerical simulations.
Vehicle
evaluation
models
must
be
suitable
for
accurate
ICC
enough
design
under
and
extreme
maneuvers and in the meantime easy to be integrated with
15 I C C
controller
Because
conditions,
ICC
the
and
possibly
systems
accuracy
other
operate
of
the
software
under
model
wrappers.
near-incident
under
severe
maneuvers is crucial.
The vehicle model developed in this paper is a 3 DOF
20 ( y a w , r o l l , l a t e r a l ) v e h i c l e d y n a m i c m o d e l w i t h a n o n l i n e a r
tire sub-model. The model is verified against the CarSim
software, which has 16 DOF and comprehensive nonlinear
tire and suspension modules. It is assumed that the Carsim
model output represents the true vehicle response up to
25 w h e e l l i f t - o f f a n d w i l l b e u s e d t o a s s e s s t h e a c c u r a c y o f t h e
3
3DOF model.
In the ICC design, we focus on the integration of a
differential braking function (Electric Stability Program,
ESC)
and
a
suspension
5 Control, CDC).
function
(Continuous
Damping
This relatively simple ICC configuration
makes it easier to study the integration and interaction of
the
vehicle
control
functions.
The
functional
characteristics of the sub-systems are categorized by ride
comfort,
lateral
stability,
side-slip
control,
yaw
control,
10 r o l l o v e r p r e v e n t i o n a n d w h e e l s l i p c o n t r o l . T h e I C C c o n t r o l
was
designed
desired
at
two
suspension
calculated
based
levels.
At
damping
and
on
yaw,
side
the
upper
brake
slip,
level,
torques
roll
and
the
are
ride
considerations. The servo control for the braking control is
15 r e a l i z e d b a s e d o n a s l i d i n g m o d e c o n t r o l t e c h n o l o g y , w h i c h
is modified slightly to avoid the complex nonlinear form(4).
The braking forces are obtained by using the tire ellipse
concept (5). This ICC system is intended to emulate the
typical functions of a production ICC, and is designed to be
20 m o d u l a r s o t h a t a d d i t i o n a l c o n t r o l s y s t e m s c a n b e a d d e d .
This model will be used in our simulation based worst-case
study and could be integrated in HILS system with the ICC
part
implemented
in
hardware(6).
The
worst-case
evaluations, HIL test, and road test are future tasks of our
25 r e s e a r c h t h a t a r e n o t r e p o r t e d i n t h i s p a p e r .
4
The
remainder
of
this
paper
is
as
follows.
In
Section 2, a lateral yaw roll model is developed, which is
critical for the ICC control development.
In Section 3,
the ICC system design is described. In Section 4, standard
5 tests and WCDE procedure for vehicle rollover is discussed.
In Section 5, the performance of ICC rollover prevention is
evaluated via simulations based on both standard tests and
WCDE. A conclusion section is included at Section 6.
10 2 . V E H I C L E M O D E L
A
vehicle
simple
vehicle
handling
and
model
roll
is
developed
behavior,
which
to
includes
lateral, roll and yaw motions as shown in Eq.(1)
15
Fig. 1 Vehicle model
5
describe
the
2
4
i =1
i =3
mh1v + I xx p + mh1u x r = Lφφ + L p p + hcf ∑ Fyi + hcr ∑ Fyi
2
4
i =1
i =3
I zz r = a ∑ Fyi − b∑ Fyi − t f Fx1 − tr Fx 3 + t f Fx 2 + tr Fx 4
2
4
i =1
i =3
mv + mh1 p + mu x r = h f ∑ Fyi + hr ∑ Fyi
where
Eq.(1)
p = φ , Lφ = mgh − K R , L p = −CR , i = 1, 2,3, 4 .
stiffness and
The
is
KR
the
roll
the
SAE
CR i s t h e r o l l d a m p i n g c o e f f i c i e n t .
variables
and
parameters
5 standard as shown in Fig. 1.
all
follow
Eq.(1) can be written in the
state space form. For this 3DOF system, 4 state variables
are needed.
The state space model is
M 1 X = M 2 m X + M y Fy + M x Fx
Eq.(2)
where
X = [r v φ
10
p]
T
Eq.(3)
Fy = ⎡⎣ Fy1
Fy 2
Fy 3
Fy 4 ⎤⎦
Fx = [ Fx1
Fx 2
Fx 3
Fx 4 ]
0
0
0
0
tf
0
−tr
0
Eq.(4)
T
⎡ 0 m 0 mh1 ⎤
⎡ −mu x
⎢ 0 mh 0 I ⎥
⎢ −mh u
xx ⎥
1
1 x
⎢
M1 =
, M 2m = ⎢
⎢ I zz 0 0 ε I zz ⎥
⎢ 0
⎢
⎥
⎢
⎣0 0 1 0 ⎦
⎣ 0
⎡ 0
⎢ 0
Mx = ⎢
⎢ −t f
⎢
⎣ 0
T
0⎤
⎡ 1
⎥
⎢h
0⎥
,My = ⎢ f
⎢ a
tr ⎥
⎥
⎢
0⎦
⎣ 0
0 0
0 Lφ
0
0
0
0
0⎤
L p ⎥⎥
0⎥
⎥
1⎦
1 1 1⎤
h f hr hr ⎥⎥
a −b −b ⎥
⎥
0 0 0⎦
Eq.(5)
Eq.(6)
The tire forces shown in Fig.2 are calculated from
15 t h e t i r e f o r c e e q u a t i o n s :
J wω j = −Tb + rw Fxj
6
Eq.(7)
λj =
The
wheel
λi
slip,
u x − rwω j
ux
in
, j = 1, 2,3, 4
Eq.(8)
Eq.(8)
determines
the
tire
longitudinal force and is used for wheel slip control.
our
tire
model,
tire
longitudinal
forces
and
the
In
lateral
5 force are calculated via the tire ellipse concept:
⎛ F
Fyj = Fy max (α , Fzj ) 1 − ⎜ xj
⎜ μ Fzj
⎝
where
Tb
is
the
braking
torque,
moment inertia of the wheel,
road friction coefficient, and
⎞
⎟⎟
⎠
α
2
Eq.(9)
is
Jw
the
angular
is the slip angle,
μ
is
rw i s t h e w h e e l r a d i u s .
10
Fig. 2
For
the
above
Wheel model & Ellipse of tire
equations,
the
inputs
for
the
body
motion are the tire forces and those for the wheel motions
are
the
braking
15 l o n g i t u d i n a l
ellipse
tire
Eq.(9).
torques.
force
The
are
tire
Lateral
related
model
7
tire
through
consists
forces
the
of
and
friction
3
major
components,
which
calculate
tire
vertical
forces,
slip
angles, and the tire relaxation length. In this paper, we
use look-up tables identical to those used in the CarSim
software.
5
The vehicle model is written in MATLAB based on Eq.
(1)-(9).
It
has
four
lateral/yaw/roll
major
dynamics,
sub-systems
longitudinal
for
vehicle
velocity,
wheel
dynamics, and tire force computations. In the vehicle state
space block, the vehicle model is processed linearly using
10 t h e
tire
forces
addition
to
and
the
4
the
vehicle
state
longitudinal
variables
shown
velocity.
in
In
Eq.(3),
longitudinal velocity is another important variable, which
is assumed to be slow-varying in the linear lateral/yaw/roll
model computation. The longitudinal velocity and the wheel
15 s p e e d s a r e c a l c u l a t e d s e p a r a t e l y b a s e d o n t i r e f o r c e s a n d
wheel rotational dynamics. Since these dynamic variables
are
included,
the
performance
of
brake
control
systems
such as ABS and ESC can be included and evaluated.
It should be noted that even though we refer to the
20 m o d e l p r e s e n t e d a b o v e a s a 3 D O F m o d e l , w h i c h r e f l e c t s t h e
major dynamic captured, it is somewhat misleading.
reality,
we
also
simulate
vehicle
forward
speed
and
In
the
wheel speeds, and thus the overall DOF is 8, instead of 3.
The
developed
model
is
verified
by
comparing
its
25 s i m u l a t i o n r e s u l t s a g a i n s t t h o s e o f t h e C a r S i m s o f t w a r e .
8
We performed a large number of simulations, with frequent
rollover, spin out and plow out.
The target vehicle in this paper is an SUV, which
has a higher center of gravity (C.G). To match the response
5 from the two models, we need to carefully adjust the tire
cornering
stiffness,
sprung
mass
height
h f , hr
and
suspension roll stiffness and damping rate.
Fig. 3 shows the difference between the responses from
the two models, measured in infinity-norm. The difference
10 i n
the
vehicle
lateral
speed
is
as
large
as
20%.
This
difference may cause some discrepancies in the ICC system
response when the vehicle side slip angle is used in the
control decision.
15 Fig. 3
e ∞ , difference between CarSim and the 3DOF model under step steer of 100
degrees.
3. ICC SYSTEM DESIGN
The ICC system studied in this paper consists of a
Continuous
Damping
Control
(CDC)
9
system,
and
an
Electronic Stability Control (ESC) system. The CDC system
manipulates
suspension
considerations:
damping
lateral
motion
based
control
on
and
two
vertical
vibration suppression. The ESC system adjusts hydraulic
5 pressure at the brake cylinder of four wheels independently
to assist vehicle lateral, yaw and roll motion. These two
control
functions
will
be
explained
in
the
following
sections.
3.1 CDC System
10
The Continuous Damping Control system controls the
sprung mass motion by changing the setting of the variable
damper using a solenoid valve. The control algorithm uses
information such as vertical acceleration and velocity, and
steering input to manifest the behavior of the vehicle and
15 t h e i n t e n t i o n o f t h e d r i v e r .
Ride
control
is
based
on
Skyhook
damping
concept,
which uses a desired damping force that is proportional to
the
vertical
velocity
of
the
sprung
mass
(39).
Kinetic
energy of the sprung mass is dissipated by the imagined
20 s k y - h o o k
and
thus
sky-hook
damper
which
improved
ride
damper
is
ensures
decaying
quality
realized
for
the
through
energy
content
occupants.
the
The
variable
suspension dampers of CDC system.
The sprung mass vertical velocities at the four corners
25 n e c e s s a r y f o r r e a l i z i n g t h e s k y h o o k d a m p i n g s t r a t e g y a r e
10
calculated
band-pass
from
the
filtered
corner
acceleration
integrators.
Ride
sensors
through
control
of
the
developed CDC is based on damping of vehicle motions in
three
directions:
heave,
pitch
and
roll,
which
are
5 calculated from
4
2
4
4
i =1
i =1
i =3
i =1
zheave = ∑ zi , zptch = ∑ zi −∑ zi , zroll = ∑ ( −1) zi
i
Eq.(10)
for each control mode
heave
pitch
roll
T h e c o n t r o l g a i n s , K ride
, K ride
, K ride
are adaptively calibrated according to vehicle speed and
then
10 m o d e
the
desired
damping
are
calculated
forces
corresponding
to
l
a s Fl CDC = K ride
⋅ zl , where l = heave,pitch,roll .
each
The
averaged desired damping forces are finally distributed to
each axles in accordance with the ride control gain of each
i
c o r n e r , K ride
w h e r e i =1~ 4 .
Lateral
stability
control
of
CDC
aims
to
stabilize
15 v e h i c l e m o t i o n r e s u l t e d f r o m d r i v e r ’ s s t e e r i n g d u r i n g h i g h
speed cornering. The activation of lateral stability control
is decided based on vehicle lateral acceleration, estimated
from the bicycle model:
(
aˆ y = δ ⋅ u x2 ⋅ 1 + ( u x / uch )
20
)
2 −1
1
L
Eq.(11)
This estimated acceleration is a better signal to use
than that from an accelerometer because of its predictive
nature and because it is less vulnerable to road grade and
cross-talk
disturbances.
The
quality
11
of
the
estimation
provided
by
estimate
of
Eq.(11)
depends
characteristic
on
speed,
the
accuracy
of
our
which
depends
on
tire
cornering stiffness. The gain scheduling process for lateral
stability control follows a similar process executed in the
5 ride
control.
Lateral
stability
control
gains,
is
K lat
adaptively calibrated according to vehicle speed and then
the
desired
damping
torque
which
is
calculated
as
TlatCDC = K lat ⋅ aˆ y a r e d i s t r i b u t e d t h r o u g h f i n a l g a i n s a l l o c a t i o n .
The
overall
procedure
of
the
10 d e s c r i b e d i n t h e f l o w c h a r t i n F i g . 5 .
CDC
algorithm
is
A desired force is
calculated from both the lateral stability and ride control
parts.
The
lateral
stability
takes
priority
over
ride
control when the estimated lateral acceleration is higher
than a speed-dependent safety threshold value.
12
Lateral stability control
Lateral Acc. estimation
Severity check
aˆ y = f (δ , u x )
aˆy > a
δ
Desired Damping torque
for lateral stability
K lat
TlatCDC
K lat = gl (u x )
ux
thr
y
K lati
Adaptive gain based on speed
Desired damping force
for lateral stability
Ride control
Rejection of DC offset & integration
zs1
Heave mode
s
a z1
s 2 + 2ζω s + ω 2
az 2
Front Right
az 3
Rear Left
az 3
Rear Right
K
zpitch
CDC
ptch
ptch
ride
F
Pitch mode
(F
CDC
heave
F
CDC
CDC
+ Fptch
+ Froll
Yes
)
No
i
Fride
i
lat
F
Desired damping force
for ride control
Damping Control
roll
K ride
zroll
Lateral stability
Control ?
i
ride
4
CDC
roll
Roll mode
K ride = g r (u x )
ux
K
heave
K ride
zheave
zs 2
i
Fride
CDC
Fheave
Flati
Adaptive gain based on
speed
azi : i = 1, 2,3, 4
4 Vertical Acc.
Fig. 4 Flow chart of the CDC algorithm
3.2 ESC System
5
The ESC system controls the braking forces of the
four
tires
Based
on
states.
used
target
stabilize
Eq.(1)-(9),
we
vehicle
roll
obtain
a
and
vehicle
yaw
motions.
model
of
four
Adding the wheel speeds, an eight-state model is
for
10 d e f i n e
to
our
the
control synthesis.
major
state
functions
values.
The
of
In
the
general
the
following
we
will
system
and
the
ESC
ESC
system
(which
includes the ABS functions) includes four control objectives.
In the order of descending priority, these four functions
are:
wheel
15 c o n t r o l
and
slip
side
control,
slip
rollover
control.
prevention
The
wheel
control,
slip
yaw
control
is
imposed to limit magnitude of the wheel slip to be below
13
0.1.
The other three control functions are active when
threshold values are exceeded (roll and side slip) or when
the error is large (yaw).
A desired yaw rate is calculated
first from linear vehicle steady-state cornering:
rd =
5
This
value
is
then
δ ⋅ ux
1 + ( u x / uch )
saturated
2
⋅
1
L
based
Eq.(12)
on
a
nominal
road
friction value and vehicle forward speed
rd ≤ rlim =
μ⋅g
ux
=
ay
ux
Eq.(13)
The obtained desired yaw rate is used to calculate a yaw
10 e r r o r , Δr = rd − rm w h e r e rm
measured yaw rate, based on which
a yaw control command will be calculated.
T h e l i m i t f o r t h e s i d e s l i p a n g l e , λthresh
5 degrees.
is chosen to be
When this threshold value is exceeded, yaw
moment will be requested to reduce the magnitude of the
15 s i d e s l i p a n g l e t o m a i n t a i n d r i v e r ’ s c o n t r o l a u t h o r i t y .
Fig. 5 Analysis of rollover dynamics
Fig. 5 shows the change of geometry characteristics
14
based on Center of Gravity (C.G) point during a rollover of
ground
total
vehicle.
amount
The
of
rollover
energy
threat
stored
in
is
measured
the
the
vehicle—including
both potential energy and kinetic energy.
5 Ks
by
Assuming that
φc i s t h e r o l l a n g l e ,
is the suspension roll stiffness and
the vehicle critical roll rate, beyond which enough kinetic
energy exists to roll over the vehicle, can be calculated
from
φc =
10
mg
(
4h 2 + T 2 − 2h
) = 2mg (h − h ) + K φ
c
I xx
0
2
Eq.(14)
s c
I xx
I xx
To improve the responsiveness of the control system,
predicted vehicle roll rate, instead of measured vehicle roll
rate, is used.
The predicted roll rate is calculated from
φ p (t ) = φ (t + τ ) = φ (t ) + φ ⋅τ
⎛ k ⋅ φ (t ) + bφ ⋅ φ (t ) mhRc
⎞
= φ (t ) + ⎜ − φ
+
⋅ a y ⎟ ⋅τ
⎜
⎟
I xx
I xx
⎝
⎠
where
τ
t is the present time and
Eq.(15)
is the prediction time.
15 T h e r o l l r a t e i s p r e d i c t e d b a s e d o n r o l l r a t e a t t h e p r e s e n t
time
and
the
roll
acceleration.
The
roll
acceleration
information is estimated from a simple roll dynamic model.
The
ESC
control
logic
is
shown
in
Figure
6.
The
desirable yaw rate is first inferred from steering input and
20 f o r w a r d s p e e d , w h i c h i s s a t u r a t e d a c c o r d i n g t o
parallel, the side slip
roll
rate
of
the
Eq.(13). In
threshold, 5[deg] and the critical
vehicle
are
derived.
15
The
differences
between
yaw
rate,
side
slip
and
roll
rate
and
their
threshold values are then calculated. If the difference is
l a r g e r t h a n a t h r e s h o l d g a p , Δβ thr , Δrthr , Δφthr , t h e c o r r e s p o n d i n g
control module is turned on. Based on the priorities of the
5 four control objectives, the corresponding servo controllers
in Section 3.3 are checked to see whether they should be
activated.
servo
The
desirable
controller
is
brake
passed
force
onto
the
obtained
brake
from
system.
the
The
controller detects the vehicle turning direction based on
10 t h e
direction
of
the
lateral
acceleration
to
select
the
wheels to be braked. The brake force is finally regulated by
wheel slip control to prevent wheel lock-up, which is based
on ABS system.
ux
β=
v
v
ux
φ
δ
Δβ = β − βthr
rd =
Δr = r − rd
Δβ > Δβthr
15
φ p = fφ (φ , φ , a y )
rd = G (δ , u x )
rd ≤ a y / u x
φ ay
ay
r ⋅ ωi
λj =
ux
u x − rwω j
ux
Δφ = φ − φc
ux
Δr > Δrthr _ o
Δφ p > Δφc
λ j → λd
Fig. 6 Flow chart of the ESC control algorithm
Before the CDC and ESC control command can be sent to
16
the servo loop, an ICC master needs to determine the final
control
command
based
on
prioritized
control
objectives.
The ESC control command will take priority over that of
CDC and the respective control system is operated in its
5 priority sequence as explained above. Network between ride
control
of
CDC
and
rollover
prevention
control
of
ESC
enables two modules to share the information about vehicle
roll
motion.
Networks
of
various
control
information
for
performance improvement and fault tolerance system are
10 a l s o p o s s i b l e .
Integration strategy in this paper is based
on organizing the control elements in priority sequence as
shown in Fig. 8.
ICC Master
CDC control
Ride control
Lateral stability control
ESC control
Side slip Control
Yaw stability Control
Rollover prevention Control
Wheel slip control
Priority sequence based on
safety first
Networking
for sharing sensor
information
Fig. 7 ICC master strategy
15
3.3 Sliding Mode Control (SMC) Strategy
17
In the previous two sections, we presented the CDC
and
ESC
sliding
algorithms.
mode
In
control
this
section,
algorithm,
we
will
which
present
calculates
a
the
braking torque to achieve the desired slip ratios and other
5 desired vehicle state. The CDC control is achieved through
servo
valves
and
algorithms.
additional
control
does
However
not
need
the
ESC
servo-control
to
overcome
additional
controller
algorithm
the
servo-control
such
parametric
needs
as
the
the
robust
uncertainties
and
10 u n - m o d e l e d d y n a m i c s .
In
this
paper
we
use
SMC
as
the
servo-control
because of its robustness. Chattering, which is sometimes a
concern
for
practical
implementations,
uncommon for brake control.
15 w e
first
re-compose
b r a k i n g f o r c e Fx
the
is
nothing
To apply the SMC algorithm,
linear
vehicle
model
where
the
is defined as the control input. This linear
model enables us to avoid complexity and difficulty found
in
the
nonlinear
tire
model-based
SMC
design,
where
nonlinear observer-based design such as extended Kalman
20 f i l t e r s a n d s l i d i n g o b s e r v e r s m a y b e n e c e s s a r y . U s i n g t h i s
linear
model,
the
nonlinearities
such
as
tire
friction
ellipse will be lumped to the uncertainty term, which will
be addressed by the high-gain switching.
The simple vehicle model derived earlier in Eq.(2)
25 w i l l
now
be
rewritten
with
steering
18
angle
as
the
disturbance input.
X = M 1−1M 2 X + M 1−1M 3δ = AX + Bδ δ
where
and
δ
Eq.(16)
is tire steering angle,
M2 a n d
is given in Eq. (3),
M1
M3 a r e d e f i n e d a s f o l l o w s
M2 =
⎡ − aCα f + bCar
− mu x
⎢
u
x
⎢
⎢
− mR h1u x
⎢
2
a Cα f + b 2Cα r
⎢
−
⎢
ux
⎢
⎢⎣
0
5
−
factor,
ux
− Lφ + mgh1
−aCα f + bCα r
roll
CnR &Cφ
ux
0
0
0 ⎤⎦
0 aCα f
Cα f , Cα r : C o r n e r i n g s t i f f n e s s ,
Lφ , L p :
stiffness
⎤
0 ⎥
⎥
− Lp ⎥
⎥
⎥
0 ⎥
⎥
1 ⎥⎦
CyR &Cφ
0
M 3 = ⎡⎣Cα f
where
Cα f + Cα r
T
Eq.(17)
Eq.(18)
CyR&Cφ , CnR &Cφ : R o l l s t e e r
and
damping
coefficient.
Eq.(16) is idealized without any plant uncertainties and no
10 c o n t r o l i n p u t .
It can be rewritten as
M 1 X = M 2 X + M 3δ
where
Fy0
is
the
pure-slip
lateral
Eq.(19)
tire
force.
With
Fx
input, Eq.(19) becomes
X = AX + Bδ δ + BFx + F
15 w h e r e
the
model
uncertainty, F and
Eq.(20)
the
matrix
B
are
derived in the following.
The overall tire input
U
is defined as
U = M x Fx + M y Fy
Eq.(21)
The truncated Taylor’s series at the operating point
20 i s
19
∂F
⎛
⎞
M x Fx + M y Fy = M x Fx + M y ⎜ Fy 0 + y ( Fx − Fx 0 ) ⎟
∂Fx
⎝
⎠
Eq.(22)
∂F ⎞
⎛ ∂F
⎞ ⎛
U + M y ⎜ y ⋅ Fx 0 − Fy 0 ⎟ ≈ ⎜ M x + M y y ⎟ Fx
∂Fx ⎠
⎝ ∂Fx
⎠ ⎝
∂F ⎞
⎛
B = M 1−1 ⎜ M x + M y y ⎟
∂Fx ⎠
⎝
Eq.(23)
w h e r e Fx 0, Fy 0 : T h e t i r e f o r c e s o f t h e o p e r a t i n g p o i n t , w h e r e
braking force is generated
⎡cl1L
∂Fy 0 ⎢ 0
=⎢
∂Fx ⎢ 0
⎢
⎣ 0
5
And
then
0
0
cl1R
0
0
cl 2 L
0
0
the
The lateral force
Fy
0 ⎤
− Fxi 0 Fy max (α1 , Fzi )
0 ⎥⎥
, cli =
2
0 ⎥
μ Fzi ( μ Fzi ) − Fxi 0 2
⎥
cl 2 R ⎦
linearized
tire
model
using
can be estimated from
∂Fy
∂Fy
⎛
⎞
M y Fy ≈ M y ⎜ Fy 0 −
Fx 0 ⎟ + M y
Fx
∂Fx
∂Fx
⎝
⎠
If we eliminate the effect of
10 s i d e o f
Eq.(22).
Eq.(24)
Fx f r o m t h e r i g h t - h a n d
Eq.(24), the estimated free rolling vehicle model is
M 2 m X + M y Fy0
≈ M 2 m X + M y Fy − M y
∂Fy
∂F
⎛
⎞
Fx = M 2 m X + M y ⎜ Fy 0 − y Fx 0 ⎟
∂Fx
∂Fx
⎝
⎠
which can be written using
Eq.(19)
as
∂Fy
⎛
⎞
M 2 X + M 3δ ≈ M 2 m X + M y ⎜ Fy 0 −
Fx 0 ⎟
∂Fx
⎝
⎠
If we insert
Eq.(26)
Eq.(25)
Eq.(26)
to the linearized vehicle form
15 E q . ( 2 7 ) .
20
∂F
∂F
⎛
⎞
M 1 X ≈ M 2 m X + M y ⎜ Fy 0 − y Fx 0 ⎟ + M y y Fx + M x Fx
∂Fx
∂Fx
⎝
⎠
Eq.(27)
We can then get the final vehicle model
M 1 X = M 2 X + M 3δ + M y
∂Fy
∂Fx
Fx + M x Fx
Eq.(28)
(∵ M 2 m X + M y Fy + M x Fx )
The nominal linear vehicle model is then
X = AX + Bδ δ + BFx ≡ f ( X , t ) + BFx
5
where
is
f ( X , t)
nominal value
unknown
can
be
approximated
by
a
fˆ , t h e e s t i m a t i o n e r r o r i s a s s u m e d t o b e
f ( X , t ) − fˆ ≤ F .
F , i.e.,
bounded by
but
Eq.(29)
To achieve the control target respect to the desired
10 y a w , s i d e - s l i p , r o l l r a t e a n d w h e e l s l i p r a t i o , t h e b r a k e
torque at each wheel is designed from the SMC strategy.
For
sliding
mode
controls,
we
first
define
a
switching
surface:
S = X = X − Xd
15 w h e r e
Xd
denotes the desired value of the state vector.
X d = ⎡⎣ rd
The
sliding
Eq.(30)
sliding
surface
surface
vector
si
vd
φd ⎤⎦
T
defined
Eq.(31)
the
element
S . S u p e r s c r i p t , i = N ,Y , L
of
the
represents
the three control modules shown in Fig.7 ( N : Yaw motion,
20 Y : S i d e s l i p m o t i o n ,
L : roll motion).
The sliding mode
control gain is assumed to be bounded by
bci min ≤ bci ≤ bci max
21
Eq.(32)
where
bci i s t h e c o l u m n v e c t o r o f t h e c o n t r o l g a i n v e c t o r B .
The parameters for control gain
β
i −1
≤
βi , bci c a n b e w r i t t e n a s
bˆci
bci max
i
i
i
i
≤
β
=
β
=
,
,
b
b
b
i
c
c min c max
bci
bci min
Eq.(33)
The dynamics while in the sliding mode can be written as
S = AX + Bδ δ + bc u − X d = 0
5
To
satisfy
Eq.(34),
the
Eq.(34)
equivalent
control
input
without model error needs to satisfy
bc ueq = − AX − Bδ δ + X d
The equivalent control input
10 e l e m e n t
of
ueq
.The
equivalent
Eq.(35)
ueqi a r e d e f i n e d a s t h e
control
input
of
yaw/lateral/roll motion are taken as
aNr r + aNv v + aNφφ + bNδ δ = −bcN ueqN + rd
Y
aYr r + aYv v + aYφφ + aYφφ + bY δ δ = −bcY ueq
+ vd
Eq.(36)
aLr r + aLv v + aLφφ + aLφφ + bLδ δ = −bcLueqL + φd
The
coefficients
of
Eq.(36)
following.
22
are
given
in
the
aNr = −
aYr =
a 2Caf + b 2Car
I zz u x
, aNv =
(− aCα f + bCα r )
I zz u x
CNRCφ
, aNφ =
I zz
I (C + Cα r )
⎞ h12 mu x
I xx ⎛ (− aCα f + bCα r )
mu
, aYv = − xx α f
,
−
⎜
x ⎟−
m⋅D ⎝
ux
D
mu x D
⎠
aYφ = −
I xx C yrφ
aLφ = −
h1C yrφ
h ( − K f − K r − mgh1 )
+
, aYφ =
h1 ( − B f − Br )
m⋅D
D
D
h (C + Cα r )
⎞ hmu x
h ⎛ (− aCα f + bCα r )
aLr = 1 ⎜
, aLv = − 1 α f
,
− mu x ⎟ −
m⋅D ⎝
ux
D
ux D
⎠
bNδ
−
h ( − K f − K r − mgh1 )
, aLφ = −
( −B
− Br )
f
m⋅D
D
D
aC
I C
hC
= α f , bY δ = − xx af , bLδ = − 1 af , D = mh12 − I xx
I zz
m⋅ D
D
The
final
control
law
which
satisfies
the
sliding
condition is (9):
u i = ueqi − k i / bci ⋅ isat ( s i )
with k i ≥ β i ( F i + η i ) + ( β i − 1) u i eq
Eq.(37)
if s ≥ 1
⎧1
⎪
where isat ( s ) = ⎨ s if − 1 < s < 1
⎪−1 if s ≤ −1
⎩
H e r e , isat ( s )
5
order
to
avoid
is
used
instead
chattering
of
problem
a
sign
due
to
function
a
in
switching
control.
The final wheel slip control regulates the braking
force,
to
10 ( 0 . 1 ~ 0 . 1 5 )
realize
the
maintain
of
the
maximizing
wheel
slip
longitudinal
the
braking
control,
we
slip
force.
define
a
ratio
In
zone
order
new
to
sliding
surface as
s λ = λ − λd
Eq.(38)
And the wheel dynamics along the sliding surface is
23
λ − λd = −
ux
r
(λ − 1) − w ( rw Fx − Tb ) − λd
ux
J wu x
Eq.(39)
The corresponding equivalent brake torque as
ueqλ = rw Fx +
J wu x
(λ − 1)
rw
T h e w h e e l s l i p c o n t r o l i n p u t , uλ
Eq.(40)
can be obtained in
5 the same way in shown as Eq.(34)~Eq.(36) and it is used as
t h e b r a k i n g f o r c e b a s e d o n Tb ∝ Fb ⋅ rw .
The
final
control
inputs
forms
including
the
body
motion and the wheel motion are taken as
ur = ueqN − bcN −1k N ⋅ isat (r − rd )
Y
uv = ueq
− bcY −1k Y ⋅ isat (v − vd )
uRI = ueqL − bcL −1k L ⋅ isat (φ − φd )
Eq.(41)
uλ j = ueqλ − bcλ −1k λ ⋅ isat ( s λ )
j = 1, 2,3, 4
10 w h e r e
ur
: Y a w c o n t r o l i n p u t , uv : S i d e s l i p c o n t r o l i n p u t
uRI : R o l l o v e r p r e v e n t i o n c o n t r o l i n p u t ,
uλ j : L o n g i t u d i n a l
slip control input.
The
obtained
braking
control
inputs
are
applied
according to the priority sequences of the braking control
15 ( w h e e l s l i p c o n t r o l , r o l l o v e r p r e v e n t i o n , s i d e - s l i p c o n t r o l ,
yaw control), which is superior to CDC control application
focusing
on
providing
the
ride
comfort
and
the
stable
maneuver for the driver. Especially when we need the multi
wheel
20 c o n t r o l
braking,
the
(ex:
vehicle)
one
the
wheel
braking
necessary
24
is
not
braking
enough
forces
to
are
allocated at the additionally applied wheel.
4.
STANDARD
TEST
AND
WORST-CASE
DYNAMIC
EVALUTION
5
4.1 Standard test procedure
The performance of vehicles is frequently assessed
by
government
tests.
Car
agencies
through
standard
The test results are then published through New
Assessment
10 f a c t o r
in
rollover
system,
Programs,
consumer
propensity
which
is
which
purchase
is
assessed
based
on
selected
by
become
through
static
National
has
decisions.
correction based on fishhook test.
is
well-defined
In
a
critical
the
a
5-star
stability
factor
US,
rating
plus
a
The fishhook maneuver
Highway
Transportation
15 A d m i n i s t r a t i o n ( N H T S A ) b a s e d o n o b j e c t i v i t y , r e p e a t a b i l i t y ,
performability and discriminatory capability (21). Starting
from
the
systems
late
1990’s,
quickly
electronic
penetrate
active safety device.
the
stability
market
as
control
an
(ESC)
important
Car companies soon realize ESC is a
20 r e l a t i v e l y c h e a p w a y t o i m p r o v e t h e r o l l o v e r s t a r - r a t i n g o f
a SUV or light trucks.
Instead of redesigning the vehicle
chassis or weight distributions, ESC can be calibrated to
affect
vehicle
handling
and
roll
behaviors
to
boost
the
vehicle star rating.
25
NHTSA now faces a new and difficult problem: design
25
a
simple,
repeatable
and
reliable
way
to
assess
the
performance of vehicles with smart chassis control systems.
The
problem
students.
5 announcing
is
analogous
to
assessing
the
learning
of
Traditional “standard test” procedure is akin to
the
exam
questions
ahead
of
time,
and
trying to assess learning by grading the exam papers.
then
Is
it possible some “students” may do a great job answering
the exam questions but otherwise learn very little about
the rest if the course material?
With “students” armed
10 w i t h a d v a n c e d c h a s s i s c o n t r o l s y s t e m s w h i c h c a n b e e a s i l y
tuned
for
any
pre-announced
standard
test,
the
teacher
(NHTSA) needs to find a revolution way to assess learning
(safety performance).
The new testing method, we believe, needs to have
15 t h r e e
major
characteristics:
one-size-fit-all.
Instead,
it
1)
The
test
needs
to
create
cannot
be
customized
test maneuvers for each vehicle; 2) The test needs to be
simulation based, instead of experiment-based; and 3) The
test
needs
20 m a n e u v e r s ;
maneuvers.
to
be
based
instead
These
of
on
comprehensive
relying
three
on
a
handful
characteristics
separately in the following.
26
and
are
rich
of
test
test
discussed
Fig. 8 NHTSA Fishhook tests for rollover
NHTSA
started
to
move
away
from
one-size-fit-all
toward customized tests in recent years. As an example,
5 Fig/8 shows the fishhook test maneuver defined by NHTSA
for
vehicle
rollover
propensity
test.
The
hand-wheel
steering magnitude ‘A’, and dwell time ‘T1’ are selected
based on vehicle response and thus are different for each
vehicle.
10 t e s t
is
This
customization
somewhat
is
normalized,
necessary
and
to
vehicles
ensure
the
with
low
steering ratio or high performance tires are not penalized
inadvertently.
We
believe
more
customization
is
necessary, to thoroughly assess the performance of smart
control systems.
15
The current standard test practice also faces another
major
hurdle:
experimental
evaluations
are,
by
nature,
expensive, time-consuming and low repeatability because of
the large number of uncontrolled variables and parameters
such as tire wear and road friction.
27
4.2 Worst-case dynamic evaluation (WCDE)
The worst-case dynamic evaluation (WCDE) process,
we
believe,
is
a
good
alternative
to
the
current
experiments-based evaluation process for future vehicles,
5 especially
when
devices.
The
they
are
WCDE
equipped
method
with
is
a
active
safety
simulation-based
evaluation process that identifies weaknesses of a vehicle
through extensive numerical search. The simulation-based
approach eliminates the effect of human uncertainties. In
10 a d d i t i o n , i t a l l o w s a w i d e v a r i e t y o f s c e n a r i o s , i n c l u d i n g
those that are not feasible or too costly in field testing.
Through extensive numerical search, WCDE challenges the
vehicle
with
a
large
set
of
severe
maneuvers
and
is
a
valuable asset in the development of active safety systems.
15
Mathematically,
trajectory
optimization
worst-possible
driver’s
WCDE
can
problem,
maneuvers
be
which
that
formulated
searches
as
a
for
the
a
cost
maximize
function, e.g., the 2-norm of vehicle roll angle through the
optimization horizon. WCDE for ground vehicles and their
20 c o n t r o l s y s t e m h a d b e e n a t t e m p t e d ( 3 6 ) ( 3 7 ) . T h e f o c u s o f
(36) was rollover and jackknifing of articulated vehicles
using
various
the
worst-case
evaluation
methodology.
optimization methods such as
In
direct method
(37),
and
indirect method were investigated and compared for WCDE
25 a p p l i c a t i o n s .
28
The
numerical
machine
of
WCDE
must
be
able
to
accommodate problems with one or more of three features:
(i) nonlinear problems with complex numerical subroutines
(e.g.,
CarSim,
Adams,
etc.);
(ii)
Problems
with
equality
5 and/or inequality constraints; and (iii) performance index
in non-accumulated form (e.g infinity norm). In addition,
based on our past experience, the Dynamic Programming
method, which ensures global optimality, is not practical
for
high-dimension
10 d i m e n s i o n a l i t y .
choose
the
dynamic
systems
due
to
the
curse
of
Based on all these considerations, we
Sequential
Quadratic
Programming
(SQP)
method which is a local search method but is very efficient
even
for
high-dimensional
problem
due
to
its
rich
development history.
15
The WCDE problem is set up as follows. The time
horizon is discretized into grid points
t0 = τ 1 < ... < τ N −1 < τ N = t f
where t0 : intial time t f : final time .
wheel
angle)
at
these
The
Eq.(42)
disturbance
discrete
time
grid
(e.g.,
steering
p o i n t s , w sw ,
are
20 d e s i g n v a r i a b l e s t o b e s o l v e d f o r t h e o p t i m i z a t i o n p r o b l e m
but
the
applied
input
is
smoothed
through
interpolation
(see Figure 9)
1
2
N −1
N
w sw = [ wsw
, wsw
,..., wsw
, wsw
]
29
Eq.(43)
Fig. 9 WCDE problem setup
After
surveying
various
methods,
two
numerical
methods based on Mesh Adaptive Direct Searching (MADS)
5 and Sequential Quadratic Programming (SQP) are selected
(26). The MADS algorithm is a generalization of the class
of
Generalized
derivative-free
Pattern
method
Search
(28).
The
(GPS)
SQP
algorithms,
method
has
a
been
widely applied to many optimization problems (26)(27) and
10 e f f i c i e n t s o f t w a r e s a r e a v a i l a b l e . H o w e v e r , b o t h m e t h o d s
are local search methods and thus global optimality cannot
be guaranteed.
set
of
initial
Therefore, it is critical to provide a rich
guess
of
disturbance
inputs,
and
both
numerical methods will be used to find local optimum.
15
The
major
components
of
WCDE
program
are
a
constraint block and an initial point generation block. In
these blocks, constraints such as magnitude saturation and
rate limits are imposed.
The initial point generation is
30
the
most
critical
part
of
WCDE.
Since
both
numerical
methods only search locally, smart initial points that are
rich and “bad enough” are critical for reaching an array of
local
optimal
that
truly
reflect
the
safety
performance.
5 The generation of initial points is explained in details in
the next section.
4.3. Generation of initial points
A common practice in generating initial points for
10 l o c a l
search
methods
pseudo-random
such
points.
as
The
SQP
idea
is
is
to
to
start
cover
form
the
high
dimensionality of the disturbance inputs in a systematical
way.
level
The
of
generated
randomness
inputs,
for
however,
richness.
will
Some
have
of
the
certain
initial
15 p o i n t s u s e d i n o u r W C D E p r o g r a m w i l l b e g e n e r a t e d i n t h i s
pseudo-random fashion.
on
another
standard
Adoption
20 v e h i c l e
generation
test,
of
However, we put more emphasis
method—to
engineering
common
safety
practice
testing
research
leverage
and
controls
maneuvers
group
such
existing
as
theory.
developed
NHTSA
by
and
University of Michigan Transportation Research Institute
(UMTRI) are very appropriate. In addition, linear systems
analysis,
e.g.,
worst
allowable
persistent
bounded
disturbance (WAPBD) (25) also provides useful insight into
25 d i s t u r b a n c e
input
generation.
This
31
concept
generates
worst-case input based on impulse response of linear time
invariant (LTI) system.
10. First,
g (t ) , t h e i m p u l s e r e s p o n s e d u e t o s t e e r i n g i n p u t
is obtained.
5 error
and
persistent
from
The procedure is described in Fig.
The response is trimmed at 3% steady-state
the
time
span, T
disturbance,
value
i s δ max ,
determined.
w0 (t , T ) for t ∈ [0,T]
w0 (t , T ) = sign{g (T − t )} .
steering
is
Assuming
then
a
is
worst
then
obtained
the
maximum
that
good
The
initial
point
is
δ max ⋅ sign{g (T − t )} .
10
g (t )
⇒
w0 (t , T ) = g (T − t ) ⇒
δ max ⋅ sign{g (T − t )}
Fig. 10 The initial point obtained from the impulse-response based WAPBD approach.
In addition to the WAPBD method, initial guess is
also
generated
based
on
J-turn,
fish-hook,
15 f i s h - h o o k - w i t h - d w e l l , U M T R I d r a s t i c m a n e u v e r , s i n u s o i d a l
steering,
and
double
lane-change.
Search
for
local
optimal around these commonly used testing maneuvers, as
well as a set of pseudo-random initial conditions provide
rich
and
customized
search
needed
32
to
provide
rigorous
evaluations.
Despite
local-search
of
the
methods,
fact
if
both
large
SQP
and
number
of
MADS
are
iterations
is
allowed, both methods may find local optimum that is quite
5 different
from
the
initial
illustrated below.
guess.
One
such
example
is
In this example, the cost function to be
minimized is selected to be
J = 1000
φmax
2
.
From the initial
condition using WAPBD explained in the above, both MADS
and SQP methods are invoked. The maximum steering angle
10 a n d s t e e r i n g r a t e a r e l i m i t e d t o 2 9 0 [ d e g ] a n d 1 0 0 0 [ d e g / s ]
based on NHTSA Fishhook test standard in Fig. 11.
Fig. 12 MADS searching history J = 1000
The
searching
15 s h o w n i n F i g . 1 2 .
history
of
the
φ
2
MADS
method
is
It can be seen that the solution may be
stuck at a certain cost function value for extended number
of
iterations
better
before
optimum
it
point.
suddenly
This
is
33
break
loose
typical
of
and
local
find
a
search
methods,
which
demonstrates
the
need
to
allow
large
numbers of iterations.
Iteration
Number
74
349
SQP
MADS
Evaluation
Function
2019
729
Table 1.
Convergence
Tolerance
0.001
0.001
Final Cost
function
0.31
0.31
WCDE searching results
Both SQP and MADS methods were able to cause
5 rollover,
under
the
same
initial
condition.
Detailed
evaluation results are shown in Table 1. The performance
of the two solutions is the same (J=0.31) despite of the fact
the steering angle and vehicle roll motions are different
(see
Fig.
13).
This
indicates
that
they
converge
to
10 d i f f e r e n t l o c a l m i n i m u m , b o t h o f w h i c h m i g h t b e o f i n t e r e s t
in
understanding
the
performance
of
the
vehicle
ICC
Steering Angle[deg]
system.
400
Worst cae:SQP
Worst case: MADS
200
0
-200
-400
0
0.5
1
1.5
2
time[sec]
2.5
3
3.5
4
Roll angle[deg]
50
Worst case:SQP
Worst case: MADS
0
-50
-100
0
0.5
1
1.5
2
time[sec]
2.5
3
3.5
4
Fig. 13 Worst case maneuver result from SQP & MADS u x = 82[ kph], μ = 0.9
15
The
effectiveness
of
the
34
obtained
worst-case
maneuver
(from
SQP)
is
compared
against
a
standard
rollover test, the NHTSA Fishhook test. As shown in Fig.
14, It can be seen that the vehicle rolls over under the
WCDE steering but not under the standard fishhook test.
5 What is even more interesting is that we are able to repeat
the
same
initial
process
vehicle
and
speed
achieves
is
rollover
10kph
lower
even
than
when
that
of
the
the
10
Fig. 14
Fishhook
Worst case maneuver
400
20
Roll angle[deg]
200
0
-200
-400
0
1
2
time[sec]
3
4
100
-20
-40
-60
1
2
time[sec]
3
4
1
2
time[sec]
3
4
50
80
60
40
20
0
0
0
-80
0
Yaw rate[deg/sec]
Longitudinal speed[kph]
Steering Wheel Angle[deg]
fishhook test (see Fig. 14).
1
2
time[sec]
3
0
-50
-100
-150
0
4
Comparison simulation between standard Fishhook and the worst-case
maneuver for rollover
5. SIMULATION RESULTS
In
15 s u m m a r y
this
table
simulations
is
section,
are
to
two
sets
presented.
demonstrate
of
simulations
The
how
the
purpose
and
of
developed
one
these
WCDE
procedure can be used to assess the performance of the ICC
35
system developed in Section 3.
The simulations are all based on the CarSim SUV
vehicle model and the ICC system, if used, is calibrated
based on this target vehicle. The first simulation is based
5 on a double lane-change maneuver on low-µ surface, which
is a “closed-loop” test using the MacAdam preview driver
model.
The purpose of this simulation is to illustrate the
effect of ICC interacting with a human driver.
It can be seen from Fig. 14 that the driver’s steering
10 a c t i o n i s o f m u c h l o w e r m a g n i t u d e c o m p a r e d t o t h a t o f t h e
ICC-off case.
high
(85kph),
In fact, since the vehicle speed is relatively
the
ICC-off
case
hits
the
saturation bound and the vehicle spins out.
road
friction
The loss of
vehicle stability is evident from the steep drop of vehicle
15 s p e e d . T h e d r i v e r o f t h e I C C - o f f v e h i c l e t r i e s t o c o u n t e r
steer but fails to stabilize the vehicle.
36
200
0
-200
-400
0
5
10
time[sec]
15
40
20
0
-20
0
5
time[sec]
10
2
0
-2
-4
0
Braking Pressure[Mps]
60
Yaw rate[deg/sec]
4
ICC ON
ICC OFF
Roll angle[deg]
Steering Wheel Angle[deg]
400
15
5
time[sec]
10
15
10
15
20
15
10
5
0
0
5
time[sec]
Fig. 15 Simulation results, Double lane change at u x = 85[kph] , µ= 0.37
In
Fig.
15,
the
worst-case
maneuver
from
WAPBD-based initial point and SQP search in section 4.3
5 was simulated on a high-µ road surface. The ICC-off vehicle
rolls over while the ICC-on vehicle does not.
37
20
ICC ON
ICC OFF
200
Roll angle[deg]
Steering Wheel Angle[deg]
400
0
-200
-400
0
1
2
time[sec]
3
4
-40
-60
Braking Pressure[Mps]
Yaw rate[deg/sec]
-20
-80
0
50
0
-50
-100
0
Fig. 16
0
1
2
time[sec]
3
4
1
2
time[sec]
3
4
1
2
time[sec]
3
4
30
20
10
0
0
Simulation Results, WCDE @ u x = 85[ kph] , µ= 0.9
Table.2 Evaluation of ICC rollover prevention via standard test simulation and WCDE
μ = 0.9
5
Table.2
WCDE
is
an
evaluation
important
process.
result
The
cost
obtained
from
function
to
the
be
minimized is the same as the one used in Section 4, aiming
to generate large roll motions.
The results of WCDE are
10 o b t a i n e d b y 1 0 i n i t i a l p o i n t c a s e s i n c l u d i n g s t a n d a r d t e s t
maneuvers, the resonance characteristics analysis, WAPBD,
38
etc.
The SQP and MADS algorithms are then used to find
local optimum.
The result with the highest roll angle is
then reported in table 2.
simulation
results
from
For the “standard test” row,
the
NHTSA
fishhook
test
and
5 NHTSA sine-dwell test are obtained and the highest roll
angle is reported. When ICC is turned off, WCDE identified
steering
inputs
that
result
in
rollover
vehicle under all vehicle speeds.
for
the
target
For standard tests, the
vehicle might rollover or spin-out.
In other words, the
10 s t a n d a r d m a n e u v e r s a r e s e l e c t e d a p r i o r i , a n d m a y n o t b e
the
best
choice
performance.
in
terms
of
assessing
vehicle
rollover
The performance of the developed ICC is
able to achieve consistently lower roll angle, in comparison
with the ICC-off case.
The results confirm that the ICC is
15 t u n e d p r o p e r l y , f r o m t h e w o r s t - c a s e s e n s e .
If any of the
ICC-on case shows higher roll angle than ICC-off case, it
will indicate a serious problem—the control-on case should
never
be
worse-off
circumstances.
20 a s s e s s e d
through
than
This
the
the
no-control
required
WCDE
condition
process,
but
case
under
can
not
be
any
easily
traditional
standard test process.
6.CONCLUSION
The
development
of
a
vehicle
model
with
an
25 i n t e g r a t e d c h a s s i s c o n t r o l s y s t e m a n d t h e e v a l u a t i o n o f i t s
39
performance
based
on
a
worst-case
dynamic
evaluation
process are reported in this paper.
The developed simple vehicle model acaptures the
vehicle lateral-yaw-roll motions as well as the tire friction
5 ellipse behavior.
ICC
design
It was found to be accurate enough for
purposes.
The
Integrated
Chassis
Control
(ICC) system studied in this paper includes an electronic
stability Control sub-system and a semi-active suspension
sub-system.
10 c o n t r o l ,
The ICC system is designed considering ride
lateral
motion
control,
yaw
control,
side-slip
control, rollover prevention control and wheel slip control.
The
sliding
mode
control
technique
is
used
for
the
servo-loop design of ESC for guaranteed robustness.
The
simulation
based
Worst-Case
Dynamic
15 E v a l u a t i o n ( W C D E ) e v a l u a t i o n p r o c e d u r e i s a n o p t i m i z a t i o n
method which aims to find worst possible disturbance (e.g.,
driver’s
Because
methods,
steering
of
the
input)
high
Sequential
for
system
defined
dimension,
Quadratic
vehicle
two
local
Programming
motion.
search
(SQP)
20 M e s h A d a p t i v e D i r e c t S e a r c h i n g ( M A D S ) a r e u s e d .
and
Due to
the local-search nature of these two methods, it is critical
to provide good and rich starting points.
points,
compiled
automotive
field
from
testing,
common
plus
25 c o n t r o l t h e o r i e s a r e s u g g e s t e d .
practice
procedures
A set of initial
used
in
motivated
the
by
The worst-case evaluation
40
process
is
described
and
example
results
in
assessing
rollover performance of a vehicle with and without ICC are
used to demonstrate the design process.
5 6.CONCLUSION
The
development
of
a
vehicle
model
with
an
integrated chassis control system and the evaluation of its
performance
based
on
a
worst-case
dynamic
evaluation
process are reported in this paper.
10
The developed simple vehicle model is applied for
controller
design
and
evaluation
process
based
minimal complexity.
organizing
based
basic
on
system
its
analysis
modeling
including
accuracy
with
ICC controller model is composed by
on
safety
priorities
sequences
the
15 r e s p e c t i v e f u n c t i o n a l i t i e s m o d u l e s u c h r i d e c o n t r o l , l a t e r a l
motion
control,
prevention
yaw
control
control,
and
wheel
side-slip
slip
control,
control
that
rollover
stability
focusing chassis control systems, CDC and ESC include .
Sliding mode technique using 3 DOF vehicle model based on
20 l i n e a r i z e d t i r e e l l i p s e m o d e l a l l o w s a c o m p a c t a n d a d a p t i v e
servo-loop control design of ESC, which is based on the
vehicle parameters.
The novel simulation based evaluation procedure,
WCDE,
25 s y s t e m ,
which
the
is
designed
optimization
by
vehicle
method
41
model
and
an
with
initial
control
point
generation, provided a systematic approach to validate the
performance
of
the
developed
ICC
system.
From
the
worst-case study defined by rollover, feasibility of WCDE is
approved by finding the failure mode the vehicle standard
5 test can’t detect. And based on this approved procedure the
performance of the developed ICC model for SUV vehicle is
verified in the various speed zones.
In
an
era
when
active
control
system
for
ground-vehicle and complex evaluation process continues to
10 p r o l i f e r a t e , t h e w o r s t - c a s e d y n a m i c e v a l u a t i o n p r o c e d u r e i s
the
next
step
for
a
customized
evaluation
approach
via
computer simulation.
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