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

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aCbCmV

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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.

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ssG

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1

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)()(

)(1

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)(

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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

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• 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

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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

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Vehicle on ground

test_12_3_b0_j0

frictiondfeedforwarfeedbackM

(Same controller as before)

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• 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

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z

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rf

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1ˆff CC

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Experimental testing at Moffett Field

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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

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mV

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r

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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