*Traction Control block diagram*

*Traction Control Setup on Input Figure*

__Role of subsystem in vehicle__

The traction control block ensures that the tractive force and linear speed required at the tire patch are consistent with the traction limit of the tires. That is, no more force, either positive (accelerating) or negative, will be requested than can be provided by the tire without its ‘peeling out’ or skidding. Also, no greater change in speed, either positive or negative, will be requested than can be caused by the limited force requirement.

__Relationship to other component/subsystem models__

The traction control block interacts only with the ‘wheel and axle’ block and other control blocks that operate on the ‘wheel and axle.’

__Description of modeling approach__

The maximum attainable speed is computed by solving SF=ma for max. speed, by discretizing a in terms of speeds at the beginning and end of the time step, and accounting for the fact that the maximum force at the tire patch is a function of weight on the axle, which is turn a function of acceleration. The minimum speed is likewise computed, with a sign reversal or two. The maximum force is then computed by using the limited requested speed to compute the requested acceleration, going on to compute the weight on the front (drive) axle

__Equations used in model__

(max. speed at end of time step) = [ max(**wh_slip_force_coeff) * veh_mass * veh_gravity * veh_front_wt_frac - veh_mass * veh_gravity * (wh_1st_rrc** + sin(atan(**cyc_grade**))) - 1/2 ***veh_mass * veh_gravity *wh_2nd_rrc** * (speed at beginning of time step) - 1/8 * **veh_air_density * veh_CD * veh_FA** * (speed at beginning of time step)^2 + max(**wh_slip_force_coeff) * veh_mass * veh_cg_height / veh_wheelbase** * (speed at beginning of time step) / (time step duration) + **veh_mass** * (speed at beginning of time step) / (time step duration) ] / [ 3/8 * **veh_air_density * veh_CD * veh_FA** * (speed at beginning of time step) + ½ * **veh_mass * veh_gravity * wh_2nd_rrc + veh_mass** / (time step duration) + max(**wh_slip_force_coeff) * veh_mass * veh_cg_height / veh_wheelbase** ]

(speed at beginning of time step) = (speed at end of previous time step)

The (min. speed at end of time step) is computed using an equation similar to the above, with some sign changes, and is applicable in braking situations.

(maximum force) = max(**wh_slip_force_coeff) * [ veh_mass * veh_gravity * veh_front_wt_frac - veh_mass * veh_cg_height / veh_wheelbase** * 2 * ( (requested average vehicle speed) – (speed at beginning of time step) ) / (time step duration) ]

In braking situations, the maximum force computed above is negative and is the most negative value that the tractive force can take.

__Variables used in subsystem__

See Appendix A.2: Input Variables

Beginning with the ADVISOR 2003 model there is now the availability to run front, rear or both axles for traction. The new variables in the wheel data files are in the code as follows:

% front or rear or both axles driving?

wh_front_active_bool=1; % 0==> inactive; 1==> active

wh_rear_active_bool=0; % 0==> inactive; 1==> active