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Steer-by-Wire: Implications for Vehicle Handling and Safety
Paul Yih
May 27, 2004
What is by-wire?
• Replace mechanical and hydraulic control mechanisms with an electronic system.
• Technology first appeared in aviation: NASA’s digital fly-by-wire aircraft (1972).
• Today many civil and most military aircraft rely on fly-by-wire.• Revolutionized aircraft design due to improved performance and
safety over conventional flight control systems.
Source: NASASource: NASA
Source: BoeingSource: USAF
• By-wire technology later adapted to automobiles: throttle-by-wire and brake-by-wire.
• Steer-by-wire poses a more significant leap from conventional automotive systems and is still several years away.
• Just as fly-by-wire did to aircraft, steer-by-wire promises to significantly improve vehicle handling and driving safety.
Automotive applications for by-wire
Source: Motorola
• Introduction– Car as a dynamic system– Tire properties– Basic handling characteristics and stability
• Vehicle control• Estimation• Conclusion and future work
Outline
introduction steering system vehicle control estimation conclusion
• 42% of fatal crashes result from loss of control (European Accident Causation Survey, 2001).
• In most conditions, a vehicle under proper control is very safe.
• However, every vehicle has thresholds beyond which control becomes extremely difficult.
Why do accidents occur?
introduction steering system vehicle control estimation conclusion
• Assume constant longitudinal speed, V, so only lateral forces.
• Yaw rate, r, and sideslip angle, , completely describe vehicle motion in plane.
• Force and mass balance:
The car as a dynamic system
introduction steering system vehicle control estimation conclusion
ryfyz
ryfyy
FbFarI
FFam
,,
,,
cos
cos
• Lateral forces are generated by tire “slip.”
• C is called tire cornering stiffness.
• At large slip angles, lateral force approaches friction limits.
• Relation to slip angle becomes nonlinear near this limit.
Linear and nonlinear tire characteristics
CFy
introduction steering system vehicle control estimation conclusion
• Equations of motion:
• Valid even when tires operating in nonlinear region by approximating nonlinear effects of the tire curve.
Linearized vehicle model
introduction steering system vehicle control estimation conclusion
z
f
f
z
rf
z
fr
frrf
I
aCmV
C
VI
bCaC
I
aCbCmV
aCbC
mV
CC
rr ,
,
2,
2,,,
2
,,, 1
• Define understeer gradient:
• A car can have one of three characteristics:
Handling characteristics determined by physical properties
r
r
f
fus C
W
C
WK
,,
introduction steering system vehicle control estimation conclusion
Kus
less responsive more responsive
-+understeering oversteeringneutral steering
• Negative real roots at low speed.
• As speed increases, poles move off real axis.
• Understeering vehicle is always stable, but yaw becomes oscillatory at higher speed.
Understeering
introduction steering system vehicle control estimation conclusion
• Negative real roots at low speed.
• As speed increases, one pole moves into right half plane.
• At higher speed, oversteering vehicle becomes unstable!
• Analogy to unstable aircraft: the more oversteering a vehicle is, the more responsive it will be.
Oversteering
introduction steering system vehicle control estimation conclusion
• Single negative real root due to pole zero cancellation.
• Always stable with first order response.
• This is the ideal handling case.
• Not practical to design this way: small changes in operating conditions (passengers or cargo, tire wear) can make it oversteering.
Neutral steering
introduction steering system vehicle control estimation conclusion
• Full load of passengers shifts weight distribution rearward.• Vehicle becomes oversteering, unstable while still in linear handling
region.• Full load also raised center of gravity height, contributing to rollover.
Real world example: 15 passenger van rollovers
introduction steering system vehicle control estimation conclusion
• Most vehicles designed to be understeering (by tire selection, weight distribution, suspension kinematics).– Provides safety margin.– Compromises responsiveness.
• What if we could arbitrarily change handling characteristics?– Don’t need such a wide safety margin.– Can make vehicle responsive without crossing over to
instability.
• Can in fact do this with combination of steer-by-wire and state feedback!
How are vehicles designed?
introduction steering system estimationvehicle control conclusion
• Active steering has been demonstrated using yaw rate and lateral acceleration feedback (Ackermann et al. 1999, Segawa et al. 2000).
• Yaw rate alone not always enough (vehicle can have safe yaw rate but be skidding sideways).
• Many have proposed sideslip feedback for active steering in theory (Higuchi et al. 1992, Nagai et al. 1996, Lee 1997, Ono et al. 1998).
• Electronic stability control uses sideslip rate feedback to intervene with braking when vehicle near the limits (van Zanten 2002).
• No published results for smooth, continuous handling control during normal driving.
Prior art
introduction steering system vehicle control estimation conclusion
• An approach for precise by-wire steering control taking into account steering system dynamics and tire forces.– Techniques apply to steer-by-wire design in general.
• The application of active steering capability and full state feedback to virtually and fundamentally modify a vehicle’s handling characteristics.– Never done before due to difficulty in obtaining accurate sideslip
measurement, and– There just aren’t that many steer-by-wire cars around.
• The development and implementation of a vehicle sideslip observer based on steering forces.– Two-observer structure combines steering system and vehicle dynamics
the way they are naturally linked.– Solve the problem of sideslip estimation.
Research contributions
introduction steering system vehicle control estimation conclusion
• Steering system: precise steering control– Conversion to steer-by-wire– System identification– Steering control design
• Vehicle control• Estimation• Conclusion and future work
Outline
introduction steering system estimationvehicle control conclusion
Conventional steering system
introduction steering system estimationvehicle control conclusion
Conversion to steer-by-wire
introduction steering system estimationvehicle control conclusion
Steer-by-wire actuator
introduction steering system estimationvehicle control conclusion
Steer-by-wire sensors
introduction steering system estimationvehicle control conclusion
Force feedback system
introduction steering system estimationvehicle control conclusion
System identification
• Open loop transfer function.
• Closed loop transfer function.
sbsJs
ssG
ssM
2
1
)(
)()(
)(1
)(
)(
)(
sKG
sKG
s
s
d
introduction steering system estimationvehicle control conclusion
Closed loop experimental response
test_11_13_pb
introduction steering system estimationvehicle control conclusion
Bode plot fitted to ETFE
test_11_13_pb
introduction steering system estimationvehicle control conclusion
• Bode plot confirms system to be second order.• Obtain natural frequency and damping ratio from Bode plot.• Solve for moment of inertia and damping constant.
• Adjust for Coulomb friction.
System identification
22
2
2 2)(
)(
nn
n
ssd ssKsbsJ
K
s
s
Msss FbJ sgn
introduction steering system estimationvehicle control conclusion
Identified response with friction
test_11_13_pb
• Not perfect, but we have feedback.
introduction steering system estimationvehicle control conclusion
What do you need in a controller?
• Actual steer angle should track commanded angle with minimal error.
• Initially consider no tire-to-ground contact.
M actuator torque
commanded angle (at handwheel)
actual angle (at pinion)
effective moment of inertia
effective damping
d
sJ
sb
introduction steering system estimationvehicle control conclusion
Feedback control only
dddpfeedback KK
feedbackM
test_12_3_b0_j0
introduction steering system estimationvehicle control conclusion
Feedback with feedforward compensation
test_12_3_b0_j0
dddfeedforwar bJ
dfeedforwarfeedbackM
introduction steering system estimationvehicle control conclusion
Feedforward and friction compensation
test_12_3_b0_j0
dcfriction F sgn
frictiondfeedforwarfeedbackM
introduction steering system estimationvehicle control conclusion
Vehicle on ground
test_12_3_b0_j0
frictiondfeedforwarfeedbackM
(Same controller as before)
introduction steering system estimationvehicle control conclusion
• Part of aligning moment from the wheel caster angle. • Offset between intersection of steering axis with ground and
center of tire contact patch.• Lateral force acting on contact patch generates moment about
steer axis (against direction of steering).
Aligning moment due to mechanical trail
introduction steering system estimationvehicle control conclusion
• Other part from tire deformation during cornering. • Point of application of resultant force occurs behind center of
contact patch.• Pneumatic trail also contributes to moment about steer axis
(usually against direction of steering).
Aligning moment due to pneumatic trail
introduction steering system estimationvehicle control conclusion
Controller with aligning moment correction
test_12_3_b0_j0
aligningfrictiondfeedforwarfeedbackM
aaaligning K ˆ
introduction steering system estimationvehicle control conclusion
• Disturbance force acting on steering system causes tracking error.
• Simply increasing feedback gains may result in instability.• Since we have an idea where the disturbance comes from, we
can cancel it out.
• We now have precise active steering control via steer-by-wire system…what can we do with it?
From steering to vehicle control
introduction steering system estimationvehicle control conclusion
• Steering system: precise steering control– Conversion to steer-by-wire– System identification– Steering control design
• Vehicle control: infinitely variable handling characteristics– Handling modification– Experimental results
• Estimation• Conclusion and future work
Outline
introduction steering system estimationvehicle control conclusion
• One of the main benefits of steer-by-wire over conventional steering mechanisms is active steering capability.
• For a conventional steering system, road wheel angle has a direct correspondence to driver command at the steering wheel.
driverconventional
steering system vehicleenvironment
steer angle
vehicle states
command angle
Active steering concept
introduction steering system estimationvehicle control conclusion
• For an active steering system, actual steer angle can be different from driver command angle to either alter driver’s perception of vehicle handling or to maintain control during extreme maneuvers.
Active steering concept
driver vehicleenvironment
command angle
vehicle states
controlleractive
system
steer angle
introduction steering system estimationvehicle control conclusion
• Automotive racing example: driver makes pit stop to change tires.
• Virtual tire change: effectively alter front cornering stiffness through feedback.
• Full state feedback control law: steer angle is linear combination of states and driver command angle.
• Obtain sideslip from GPS/INS system (Ryu’s PhD work).
Physically motivated handling modification
ddr KKrK
introduction steering system estimationvehicle control conclusion
• Define new cornering stiffness as:
• Choose feedback gains as:
• Vehicle state equation is now:
Physically motivated handling modification
)1( dr KV
aKK
d
I
aCmV
CCG
VI
bCaC
I
aCbCmV
aCbC
mV
CC
CG
z
f
f
z
rf
z
fr
frrf
rr
ˆ
ˆ
ˆˆ
ˆˆ
22
21
1ˆff CC
introduction steering system estimationvehicle control conclusion
Experimental testing at Moffett Field
introduction steering system estimationvehicle control conclusion
Unmodified handling: model vs. experiment
introduction steering system estimationvehicle control conclusion
• Confirms model parameters match vehicle parameters.
mo_1_3_eta0_d
Experiment: normal vs. reduced front cornering stiffness
introduction steering system estimationvehicle control conclusion
• Difference between normal and reduced cornering stiffness.
mo_1_3_a05u_b
Reduced front cornering stiffness: model vs. experiment
introduction steering system estimationvehicle control conclusion
• Understeer characteristic in yaw exactly as predicted.
mo_1_3_a05u_b
introduction steering system estimationvehicle control conclusion
• Verifies sideslip estimation is working.
mo_1_3_eta0_d
Unmodified handling: model vs. experiment
introduction steering system estimationvehicle control conclusion
• Understeer characteristic in sideslip as predicted.
mo_1_3_a05u_b
Reduced front cornering stiffness: model vs. experiment
• Reducing front cornering stiffness returns vehicle to unloaded characteristic.
Modified handling: unloaded vs. rear weight bias
mo_2_3_eta02u_w_b
introduction steering system estimationvehicle control conclusion
• We need accurate, clean feedback of sideslip angle to smoothly modify a vehicle’s handling characteristics.
• Can we do this without GPS?
From control to estimation
introduction steering system estimationvehicle control conclusion
• Steering system: precise steering control– Conversion to steer-by-wire– System identification– Steering control design
• Vehicle control: infinitely variable handling characteristics– Handling modification– Experimental results
• Estimation: steer-by-wire as an observer– Steering disturbance observer– Vehicle state observer
• Conclusion and future work
Outline
introduction steering system estimationvehicle control conclusion
• Yaw rate easily measured, but sideslip angle much more difficult to measure directly.
• Current approaches:– GPS: loses signal under adverse conditions– optical ground sensor: very expensive
• Steer-by-wire approach:– Aligning moment transmits information about the vehicle’s
motion—we canceled it out, remember?– Can be determined from current applied to the steer-by-wire
actuator.
Sideslip estimation
introduction steering system estimationvehicle control conclusion
Steering system dynamics
w
w
w
a
M
M
M
J
b
F
k
i
road wheel angle
moment of inertia
damping constant
Coulomb friction
aligning moment
motor torque
motor constant
motor current
w w w a s M
M M M
J b F r
k i
introduction steering system estimationvehicle control conclusion
Steering system as a disturbance observer
• Express in state space form. Choose steering angle as output (measured state). Motor current is input. Aligning moment is disturbance to be estimated.
0 1 0 0
10
0 0 0 0
1 0 0
w s MM
w w wa a
a
b r ki
J J J
introduction steering system estimationvehicle control conclusion
Link between aligning moment and sideslip angle
• Aligning moment can be expressed as function of the vehicle states, and r, and the input, .
fympa Ftt ,
fmpfmp
fmp
fmp
ffmp
CttrV
CttaCtt
V
arCtt
Ctt
introduction steering system estimationvehicle control conclusion
Vehicle state observer
• Express in state space form. Steering angle is input. Yaw rate and aligning moment (from the disturbance observer) are outputs (measurements).
fmp
CG
V
Ctta
fmpa
I
aCmV
CCG
VI
bCaC
I
aCbCmV
aCbC
mV
CC
CG
CttrCtt
r
rr
fmp
z
f
f
z
rf
z
fr
frrf
010
122
2
introduction steering system estimationvehicle control conclusion
Aligning moment and state estimation
• Choose disturbance observer gain T so that A-TC is stable and xerr=x-xest approaches zero.
estestest yyTBuAxx
errerr xTCAx
TyBuxTCA est
introduction steering system estimationvehicle control conclusion
• Not exact, but doesn’t need to be.
Estimated aligning moment
data_012504b
introduction steering system estimationvehicle control conclusion
• Sideslip estimate from observer is comparable to estimate from GPS.
Estimated sideslip and yaw rate
data_012504b
introduction steering system estimationvehicle control conclusion
• State feedback from observer: yaw results comparable to using GPS.
Experiment: normal vs. reduced front cornering stiffness
mo_041104_stetam3_a
introduction steering system estimationvehicle control conclusion
Experiment: normal vs. reduced front cornering stiffness
mo_041104_stetam3_a
introduction steering system estimationvehicle control conclusion
• Sideslip results also comparable to using GPS.
• Driving safety depends on a vehicle’s underlying handling characteristics.
• Can make handling characteristics anything we want provided we have:– Precise active steering capability– Full knowledge of vehicle states
• Precise steering control requires understanding of interaction between tire and road.– Treated as disturbance to be canceled out.
• Vehicle state estimation uses interaction between tire and road as source of information.– Seen by observer as force that govern vehicle’s motion.
Conclusion
introduction steering system estimationvehicle control conclusion
• Adaptive modeling to accommodate nonlinear handling characteristics.
• Apply knowledge of tire forces to determine where the limits are and stay below them.
• Bounding uncertainty in observer-based sideslip estimation.• Apply control and estimation techniques to a dedicated by-wire
vehicle (Nissan project).
Future work
introduction steering system estimationvehicle control conclusion
• Advisor, Chris Gerdes• Committee members: Prof. Rock, Prof. Waldron, Prof.
Niemeyer, Chair Enge• Fellow members of the DDL!• Stanford Graduate Fellowship• Staff at Moffett Airfield• General Motors Corp.• Nissan Motor Co.
Acknowledgements
introduction steering system estimationvehicle control conclusion