1. Okwuchi Emereole and Malcolm Good, University of Melbourne
The Effect of Tyre Dynamics on Wheel Slip Control Using Electromechanical Brakes
Okwuchi Emereole and Malcolm Good, University of Melbourne

2. Motivation
Antilock braking systems (ABS) for Electro-Mechanical Brakes (EMB)
ABS controllers maintain wheel slip in a target region by manipulating braking torque
Need a fundamental analysis of torque  slip dynamics, accounting for tyre and EMB dynamics
Use understanding gained to guide design of a simple ABS control strategy

3. Wheel slip control model
The model consists of:
Electromechanical brake (EMB) actuator
Plant – model of slip response to brake torque perturbations
Controller – acts on combined effect of the actuator and the plant

4. EMB actuator model
Nonlinear EMB model has force, velocity and current controller loops and implements integral anti-windup.
The nonlinear model was represented using an equivalent transfer function (identified at 30kN) for controller design purposes:
 The EMB model was developed by Chris Line, a Ph.D candidate at the University of Melbourne

5. Linearised plant model — no tyre dynamics
Key equations
Trim
Perturbed
1/4-car vehicle dynamics

6. Linearised plant model with 1st-order tyre dynamics
s = relaxation length

7. Dynamic tyre model: effect of trim slip for different trim speeds
-4500
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
500
1000
1500
2000
0.4
0.72
0.99
0.91
0.58
0.2
0.96
0.83
Dynamic tyre model: effect of trim slip for different trim speeds
Root Locus
Real Axis
Imaginary Axis 80
120
160
increasing l0
For low trim slips, damping increases with speed, but wn approximately constant with speed 80
120
160

8. Comparison of static and dynamic tyre models
At higher trim slips, dominant dynamics similar to static tyre model
static
160
dynamic
120 80
Dry concrete surface
13%

9. Effect of road surface: static model
Dry ice
Dry concrete

10. Brake torque-to-slip frequency response (plant)
Within BW of EMB, gain insensitive to surface and trim slip, and scales with trim speed
___ Dry ice …… Dry concrete

11. Controller design
Integral control introduced for disturbance rejection; eliminate steady-state error
Consider plant frequency response with actuator dynamics and integral action included …

12. Plant with integral action:
Extend -20 dB/dec slope for crossover
Boost phase for stability
PI control required to stabilize and achieve gain crossover at high frequency

13. OLTF with PI control ___ Dry ice …… Dry concrete
Crossover insensitive to surface and trim slip PM
Could increase gain margin with PID control

14. OLTF with PID control ___ Dry ice …… Dry concrete
Crossover insensitive to surface and trim slip PM
More robust against increased
open-loop gain

15. Closed-loop PID slip control
___ Dry ice …… Dry concrete
Bandwidth  80 rad/s (13 Hz).
Still within EMB bandwidth

16. Evaluation of controller performance
Half-car vehicle model
Nonlinear EMB model
Nonlinear tyre model with relaxation length
Antilock Performance Index (API)

17. Some results – 10% target slip

18. Some results – 10% target slip

19. Conclusions
Linearizing vehicle/wheel dynamics about 'trim' braking condition yields insights into 'plant' dynamics
Tyre dynamics (relaxation length) unimportant at high slip states
High-gain slip control loop reduces sensitivity to road surface condition and slip state
PID control with gains proportional to vehicle speed yields robust closed-loop dynamics
PID control formulated with simple 1/4-car model and linearized dynamics works well in nonlinear 1/2-car simulation with nonlinear EMB dynamics