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Modelling and assembly of the full vehicle 361
The purpose of the STEP FUNCTION is to define a change of state in the
expression that is continuous.
The step function can be used to factor a force function by ramping it on
over a set time period. In this case the driving torque is being switched on
between time 0 and time 1 second. This is important because it is necessary
to perform an initial static analysis of the vehicle at time 0 when
Va 0 and the torque must not act.
As can be seen a ‘reference’ (desired) state is needed, an error term is
defined by the difference between the current state and the reference state
and finally, responses to that in terms of throttle or brake application to
adjust the speed back towards the reference value. There are two possible
approaches; the simplest provides a speed ‘map’ for the track, similar to the
curvature map description of it. More elaborately, it is possible to examine
the path curvature map locally and decide (through a knowledge of the ultimate
capabilities of the vehicle, perhaps) whether or not the current speed
is excessive, appropriate or insufficient for the local curvature and use
brakes or engine appropriately. For the development of vehicles, open loop
throttle or brake inputs may be preferable and are sometimes mandated in
defined test manoeuvres, rendering the whole issue of speed control moot.
In many ways the skill of the competition driver lies entirely in this ability
to judge speed and adjust it appropriately. It is also a key skill to cultivate
for limit handling development and arguably for road driving too, so as not
to arrive at hazards too rapidly to maintain control of the vehicle. For this
functionality, some form of preview is essential. It is both plausible and
reasonable to run a ‘here and now at the front axle’ model for the path follower
and a ‘previewing’ speed controller within the same model, described
in subsequent sections.
6.12 The steering system
6.12.1 Modelling the steering mechanism
There are a number of steering system configurations available for cars and
trucks based on linkages and steering gearboxes. The treatment in the following
sections is limited to a traditional rack and pinion system. Space
does not permit discussion of the modelling of power steering or steer-bywire
here.
For the simple full vehicle models discussed earlier, such as that modelled
with lumped mass suspensions, there are problems when trying to incorporate
the steering system. Consider first the arrangement of the steering system
on the actual vehicle and the way this can be modelled on the detailed
linkage model as shown in Figure 6.36. In this case only the suspension on
the right-hand side is shown for clarity.
The steering column is represented as a part connected to the vehicle body
by a revolute joint with its axis aligned along the line of the column. The
steering inputs required to manoeuvre the vehicle are applied as motion or
torque inputs at this joint. The steering rack part is connected to the vehicle
body by a translational joint and connected to the tie rod by a universal