Vehicle handling modification via steer-by-wire
Paul Yih Jihan Ryu J. Christian Gerdes
Dynamic Design LabStanford University
June 5, 2003
Outline
• Concept of handling modification• Techniques for steer-by-wire control• GPS-based state estimation• A physically intuitive handling modification• Experimental results
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 2
How do you make a Cavalier handle like a Corvette?
• Goal: tune handling behavior to driver preference or variations in operating conditions.
• Approach: artificially adjust tire characteristics with modified steering inputs.
• Implementation: precise active steering control and accurate vehicle state feedback.
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 3
Conventional steering system
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 4
pinion
rotary spool valve
intermediate shaft
steering column
handwheel
universal joints
steering rack
Steer-by-wire system
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 5
pinion angle sensor
steering actuatorhandwheel angle sensor
belt drive handwheel feedback motor
• Actual steer angle should track commanded angle with minimal error.
• Initially consider no tire to ground contact.
Steer-by-wire controller
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 6
τ actuator torque
commanded angle (at handwheel)
actual angle (at pinion)
effective moment of inertia
effective damping
dθθJb
θ
θd
τ
J, b
6 8 10 12 14 16 18 20 22 24-10
-5
0
5
10
time (s)
stee
ring
angl
e (d
eg) actual
commanded
6 8 10 12 14 16 18 20 22 24-0.5
0
0.5
time (s)
stee
ring
angl
e er
ror (
deg)
Feedback control only
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 7
test_12_3_b0_j0
( ) ( )θθθθτ && −+−= dddpfeedback KKfeedbackττ =
6 8 10 12 14 16 18 20 22 24-10
-5
0
5
10
time (s)
stee
ring
angl
e (d
eg) actual
commanded
6 8 10 12 14 16 18 20 22 24-0.5
0
0.5
time (s)
stee
ring
angl
e er
ror (
deg)
Feedback with feedforward compensation
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 8
test_12_3_b0091_j0036
dddfeedforwar bJ θθτ &&& +=
dfeedforwarfeedback τττ +=
6 8 10 12 14 16 18 20 22 24-10
-5
0
5
10
time (s)
stee
ring
angl
e (d
eg) actual
commanded
6 8 10 12 14 16 18 20 22 24-0.5
0
0.5
time (s)
stee
ring
angl
e er
ror (
deg)
Feedforward and friction compensation
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 9
test_12_3_b0091_j0036_f7
( )dcfriction F θτ &sgn=
frictiondfeedforwarfeedback ττττ ++=
• Reintroduce tire to ground contact (vehicle moving at normal driving speeds).
• In a conventional steering system, self-centering tendency isdue to aligning moment.
• Aligning moment acts as a (known) disturbance on steer-by-wire system.
Effects of tire self-aligning moment
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 10
τa
θ
θd
τ
τa
10 15 20 25 30 35 40 45 50 55-20
-10
0
10
20
time (s)
stee
ring
angl
e (d
eg) actual
commanded
10 15 20 25 30 35 40 45 50 55-1
-0.5
0
0.5
1
time (s)
stee
ring
angl
e er
ror (
deg)
Error due to aligning moment disturbance
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 11
test_1_7_a0
frictiondfeedforwarfeedback ττττ ++=
(Same controller as before)
10 15 20 25 30 35 40 45 50 55-20
-10
0
10
20
time (s)
stee
ring
angl
e (d
eg) actual
commanded
10 15 20 25 30 35 40 45 50 55-1
-0.5
0
0.5
1
time (s)
stee
ring
angl
e er
ror (
deg)
Controller with aligning moment correction
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 12
test_1_13_a8_c
aligningfrictiondfeedforwarfeedback τττττ +++=
aaaligning K ττ ˆ=
Linear vehicle model
• Force and moment equations
• Side forces (linear tire model)
• Steering angle
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 13
ryfyz
ryfyy
FbFarIFFam
,,
,,
cos
cos
⋅−⋅⋅=⋅
+⋅=⋅
δ
δ&
rrryfffy CFCF αα −=−= ,, ,
θδsteeringr1
=
Vehicle sideslip
• Angle between vehicle heading and direction of velocity at CG
• Sideslip angle (β) at CG and yaw rate (r) as state variables
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 14
x
y
x
y
uu
uu
≈
=−= −1tanψγβ
( )δ
ββα
α
αααα
αααα
+
+−=
−−−
−−−
z
f
f
z
rf
z
fr
frrf
IaC
mVC
CG
VIbCaC
IaCbC
mV
aCbCmVCC
CG
rr22
21&
&
Physically motivated handling modification
• Steer angle is linear combination of states and driver command angle
• Define new cornering stiffness as• Choose gains such that state space equation is
exactly the same as before with new cornering stiffness
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 15
ddr KKrK δβδ β ++=
( )ηαα += 1ˆff CC
( )d
IaC
mVC
CG
VIbCaC
IaCbC
mVaCbC
mVCC
CG
z
f
f
z
rf
z
fr
frrf
rrδ
ββα
α
αααα
αααα
+
+−=
−−−
−−−
ˆ
ˆ
ˆˆ
ˆˆ
22
21&
&
)1( ηηηβ +=−=−= dr KVaKK
GPS-based state estimation• Accurate estimates of sideslip angle and yaw rate are
available from combined Global Positioning System (GPS) and inertial navigation sensor (INS) measurements.
• Multiple-antenna GPS receivers provide absolute velocity and heading information.
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 16
Validation of state estimation: experiment vs. model
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 17
0 50 100 150 200-15
-10
-5
0
5
10
15
time (s)
side
slip
ang
le (d
eg)
0 50 100 150 200-60
-40
-20
0
20
40
60
time (s)
yaw
rate
(deg
/s)
Handling modification tests at Moffett Federal Airfield
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 18
5 10 15 20 25-40
-30
-20
-10
0
10
20
30
40
time (s)
yaw
rate
(deg
/s)
simulationexperiment
Model: normal front cornering stiffness
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 19
mo_1_3_eta0_d
5 10 15 20 25-40
-30
-20
-10
0
10
20
30
40
time (s)
yaw
rate
(deg
/s)
normalreduced
Experiment: effectively reduced front cornering stiffness
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 20
mo_1_3_a05u_b
5 10 15 20 25-40
-30
-20
-10
0
10
20
30
40
time (s)
yaw
rate
(deg
/s)
simulationexperiment
Model: effectively reduced front cornering stiffness
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 21
mo_1_3_a05u_b
5 10 15 20 25-40
-30
-20
-10
0
10
20
30
40
time (s)
yaw
rate
(deg
/s)
normalincreased
Experiment: effectively increased front cornering stiffness
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 22
mo_1_3_a05o_b
5 10 15 20 25-40
-30
-20
-10
0
10
20
30
40
time (s)
yaw
rate
(deg
/s)
simulationexperiment
Model: effectively increased front cornering stiffness
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 23
mo_1_3_a05o_b
Conclusion
• The combination of steer-by-wire and full state feedback provides a way to modify vehicle handling characteristics for improved driving feel and safety.
• By effectively changing front cornering stiffness, the same vehicle can be made to handle differently.
• Therefore, it is possible to maintain consistent handling characteristics under variable operating conditions.
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 24
Future work
• What happens outside the linear region of operation and when tires reach the limits of adhesion?
• In some situations, active steering intervention is an effective means of stability control.
• What are the limitations of active steering intervention and how can it be combined with other control inputs such as differential braking?
Dynamic Design Lab Vehicle handling modification via steer-by-wire Slide 25