Four Wheel Steering Control System

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Advances in Control Systems

Four Wheel Steering Control System
2009.6.10 (Wed)

Pongsathorn Raksincharoensak, TUAT

Four Wheel Steering Control System

1

Vehicle Dynamics Control

Tokyo Univ. of Agriculture & Technology Mech. Sys. Eng. Nagai Laboratory

Enhancing vehicle dynamics performances by Active Chassis Control Technologies
Traction (driving)

Roles of Chassis Control
Respect to the driver intention

Cornering

Cornering

Reduce the driver workload Enhance its limit performance avoiding side-slip, spin,etc during emergency maneuver

Braking

Pongsathorn Raksincharoensak, TUAT

Four Wheel Steering Control System

2

Active Safety Technology

Tokyo Univ. of Agriculture & Technology Mech. Sys. Eng. Nagai Laboratory

Active Safety Technology is realized by active chassis control systems for enhancing Vehicle Dynamic Performance, as follows; ・ABS : Anti-skid Brake System ・TCS : Traction Control System ・4WS : Four-Wheel-Steering, (Active Rear Steer) ・AFS : Active Front Steer, (Steer-by-Wire, EPS) ・DYC : Direct Yaw-moment Control, (VSC, ESP)

Pongsathorn Raksincharoensak, TUAT

Four Wheel Steering Control System

3

Driver-vehicle system
Road

DRIVER
Recognition Decision Operation

Input

VEHICLE

Output

The relationship of input-output in the driver-vehicle-controller system
CONTROLLER

Road

DRIVER

VEHICLE

Pongsathorn Raksincharoensak, TUAT

Four Wheel Steering Control System

4

Vehicle Chassis Control
(1) Active Rear Steer
sideslip motion control

Tokyo Univ. of Agriculture & Technology Dept. of Mech. Sys. Eng. NAGAI Lab.

Active Chassis Control (Planar motion) ・Yaw motion ・Sideslip motion

(2) Direct Yaw Control

(3) Active Front Steer

Pongsathorn Raksincharoensak, TUAT

sideslip motion control(emergency) System Four Wheel Steering Control

yaw rate control

5

Four-Wheel-Steering System (4WS) Active Rear Steer System (ARS)
y
γ
V

β

x

Lr
Pongsathorn Raksincharoensak, TUAT Four Wheel Steering Control System

Lf
6

Equivalent Bicycle Model (Vehicle-Fixed Coordinate)
y

Fyr
lr

Fyf
lf V

2Cr

δr

β
2C f

δf

x

βr

γ&

βf

β : Side slip angle γ : Yaw rate

Pongsathorn Raksincharoensak, TUAT

Four Wheel Steering Control System

7

Bicycle Model

Four-Wheel-Steering & Side slip motion : mV ( β + γ ) = 2 Fyf + 2 Fyr
Yaw motion :

I γ& = 2l f Fyf − 2lr Fyr

lf ⎛ ⎞ Front tire lateral force : Fyf = C f ⎜ δ f − γ − β ⎟ V ⎝ ⎠ lr ⎛ ⎞ Rear tire lateral force : Fyr = Cr ⎜ δ r + γ − β ⎟ V ⎝ ⎠

Equations of Motions
& mV ( β + γ ) = 2C f (δ f − lf

lr γ − β ) + 2Cr (δ r + γ − β ) V V lf lr I γ& = 2l f C f (δ f − γ − β ) − 2lr Cr (δ r + γ − β ) V V
Four Wheel Steering Control System

Pongsathorn Raksincharoensak, TUAT

8

Bicycle Model

Plant = a Four-Wheel-Steering vehicle

4WS design employs two approaches. (1)
β= γ =

Transfer Function
b1 f s + ( −b1 f a22 + b2 f a12 )
2 s 2 + 2ζω n s + ω n

b1r s + ( −b1r a22 + b2 r a12 ) δf + δr 2 2 s + 2ζω n s + ω n

b2 f s + ( −b2 f a11 + b1 f a21 ) s 2 + 2ζω n s + ω n
2

b2 r s + ( −b2 r a11 + b1r a21 ) δf + δr 2 2 s + 2ζω n s + ω n

(2)

State Space Equation

& ⎡ β ⎤ ⎡ a11 a12 ⎤ ⎡ β ⎤ ⎡ b1 f ⎢ ⎥=⎢ ⎥ ⎢ γ ⎥ + ⎢b ⎣ γ& ⎦ ⎣a21 a22 ⎦ ⎣ ⎦ ⎣ 2 f
Pongsathorn Raksincharoensak, TUAT Four Wheel Steering Control System

b1r ⎤ ⎡δ f ⎤ b2 r ⎥ ⎢ δ r ⎥ ⎦⎣ ⎦
9

Control system design of 4WS
• Feedforward rear-wheel steering control
(1) Rear wheel steering angle is proportional to the front steering angle

δ r = kδ f
(2) Rear wheel steering angle is proportional to the front steering angle with dynamics.

τ 1s + 1 δr = k δf τ 2 +1
Pongsathorn Raksincharoensak, TUAT Four Wheel Steering Control System

10

Effect of 4WS on vehicle dynamics
Steer in-phase Steer out-of-phase

- Reduce yaw rate gain - Improve stability at high speed - Reduce side slip angle when cornering

- Increase yaw rate gain - Improve agility - Improve maneuverability at low speed

Pongsathorn Raksincharoensak, TUAT

Four Wheel Steering Control System

11

“Sideslip angle of 2WS” = Vehicle attitude (車体姿勢)
Slip Angle[rad]

V

0.04 0.02 0 -0.02

β

β

Heading outside

-0.04 0

Heading inside
50 100 Car Velocity[km/h] 150

To suppress the sideslip angle for making the vehicle easier to drive, we can add the rear wheel steering angle to control the vehicle attitude.
0.5

Low speed

β

V

δr δf

Ratio[-]

0 -0.5 -1 -1.5 0

Opposite direction

Same direction
150

50 100 Car Velocity[km/h]

High speed
12

Pongsathorn Raksincharoensak, TUAT

“Zero-side-slip 4WS” Steering Control System dependent 4WS = Speed Four Wheel

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