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