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

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

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

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

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

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

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

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%

Effect of road surface: static model Dry ice Dry concrete

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

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

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

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

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

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

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

Some results – 10% target slip

Some results – 10% target slip

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