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Modelling and assembly of the full vehicle 373
equally it can obscure performance changes and so adaptive modelling of
driver behaviour is not preferred except for circuit driving. Several techniques
come under the headline of adaptive control; the simplest is to
change the control parameters in a predetermined fashion according to the
operating regime, an operation referred to as ‘gain scheduling’. Gain is the
term used for any treatment given to an error state before it is fed to an
input – thus the PID controller described above has a P-gain, an I-gain and
a D-gain. It might be, for example, that under conditions of opposite lock
the P-gain is increased since the driver needs to work quickly to retain control,
or under conditions of increasing speed the P-gain is reduced since
slower inputs are good for stability at higher speeds. A more complex
method is to carry a model of the plant on board in the controller and to use
it to better inform some form of gain scheduling, perhaps using information
that cannot readily be discerned from on-board instrumentation – such
as body slip angle. This is referred to as a Model Reference Adaptive
Scheme (MRAS). A further variation on the theme is to use the controller
to calculate model parameters using system or parameter identification
methods (described above). The control system parameters can be modified
based on this information – in effect there is an ongoing redesign of the
control system using a classical deterministic method, based on the reference
state and the plant characteristics according to the latest estimate. This
is referred to as a ‘self-tuning-regulator’ and is useful for unpredictably
varying systems. Finally, a method known as ‘dual control’ intentionally
disturbs the system in order to learn its characteristics, while simultaneously
controlling it towards a reference state. In many ways this is similar
to a top level rally driver stabbing the brakes in order to assess friction levels
while disturbing the overall speed of the vehicle as little as possible; the
knowledge gained allows the driver to tune their braking behaviour according
to recently learned characteristics. Such behaviour is in marked contrast
to circuit drivers, who concentrate on learned braking points and
sometimes have difficulty adapting to changing weather conditions. With
the exception of the simplest gain scheduling methods, in general adaptive
control techniques are unsuitable for the modelling of driver behaviour as
part of any practicable process. Once again the variation in simulation output
cannot readily be traced to any particular aspect of the system and
hence the success or otherwise of an intended modification is difficult to
interpret.
In the light of the preceding description, the authors believe a PID controller,
with some form of simple gain scheduling, is most appropriate for
the modelling of driver behaviour in a multibody system context. The art of
implementing a successful model is in selecting the state variables within
the model to use with the controller.
6.13.2 A path following controller model
The first hurdle to be crossed is the availability of suitable state variables
and the use of gain terms to apply to them. Typically in a multibody system
model, many more variables are available than in a real vehicle. Within the
model, these variables can be the subject of differential equations in order
to have available integral and differential terms. Table 6.4 shows a portion