4569846498
Modelling and assembly of the full vehicle 393 ψ (deg/s) α (deg) β (deg) a y (m/s 2 ) δ (deg) 10 5 0 5 10 0 2 1 0 1 2 0 1 0.5 0 0.5 1 0 5 0 5 0 2 1 0 1 2 Fig. 6.63 response 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1.5 1.5 1.5 1.5 1.5 2 2 2 2 2 2.5 2.5 2.5 2.5 2.5 front Time (s) 3 3 3 3 3 3.5 rear 3.5 3.5 3.5 3.5 4 4 4 4 4 Simulink ADAMS Comparison of Simulink and MSC.ADAMS predictions of vehicle 4.5 4.5 4.5 4.5 4.5 5 5 5 5 5 stiffness model, for example, does not include heave and pitch degrees of freedom relative to the front and rear axles. During the simulation, however, the degrees of freedom exist for the body to heave and pitch relative to the ground inertial frame. These degrees of freedom must still be solved and in this case are damped only by the inclusion of the tyre model. In the 3 degrees of freedom model these motions are ignored and solution is only performed on the degrees of freedom that have been modelled. While the main theme in this book is to demonstrate the use of multibody systems analysis the Matlab/Simulink model is useful here in providing the basis for additional modelling and simulation of the modern control systems involved in enhancing the stability and dynamics of the vehicle. The effort invested in this modelling approach also provides educational benefits reinforcing fundamental vehicle dynamics theory. 6.15 Summary Many different possibilities exist for modelling the behaviour of the vehicle driver. That none has reached prominence suggests that none is correct for
394 Multibody Systems Approach to Vehicle Dynamics every occasion. In general, the road car vehicle dynamics task is about delivering faithful behaviour during accident evasion manoeuvres – where most drivers rarely venture. Positioning the vehicle in the linear region is relatively trivial and need not exercise most organizations unduly, but delivering a good response, maintaining yaw damping and keeping the demands on the driver low are of prime importance in the non-linear accident evasion regime. For this reason, controllers that take time to ‘learn’ the behaviour of the vehicle are inappropriate – road drivers do not get second attempts. For road vehicles, the closed loop controller based on front axle lateral acceleration gives good results and helps the analyst understand whether or not the vehicle is actually ‘better’ in the sense of giving an average driver the ability to complete a manoeuvre. In motorsport applications, however, drivers are skilled and practised and so controllers with some feed-forward capability (to reflect ‘learned’ responses), plus closed loop control of body slip angle are appropriate to reflect the high skill level of the driver. Whether or not advanced gain scheduling models, such as the Model Reference Adaptive Scheme or Self- Tuning Regulator, are in use depends very much on whether or not data exists to support the verification of such a model. The authors preference is that ‘it is better to be simple and wrong than complicated and wrong’ – in other words, all other things being equal, the simplest model is the most useful since its shortcomings are more easily understood and judgements based on the results may be tempered accordingly. With elaborate schemes, particularly self-tuning ones, there is a strong desire to believe the complexity is in and of itself a guarantee of success. In truth if a relatively simple and robust model cannot be made to give useful results it is more likely to show a lack of clarity in forming the question than a justification for further complexity.
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Modelling and assembly of the full vehicle 393<br />
ψ (deg/s)<br />
α (deg)<br />
β (deg)<br />
a y (m/s 2 )<br />
δ (deg)<br />
10<br />
5<br />
0<br />
5<br />
10<br />
0<br />
2<br />
1<br />
0<br />
1<br />
2<br />
0<br />
1<br />
0.5<br />
0<br />
0.5<br />
1<br />
0<br />
5<br />
0<br />
5<br />
0<br />
2<br />
1<br />
0<br />
1<br />
2<br />
Fig. 6.63<br />
response<br />
0.5<br />
0.5<br />
0.5<br />
0.5<br />
0.5<br />
1<br />
1<br />
1<br />
1<br />
1<br />
1.5<br />
1.5<br />
1.5<br />
1.5<br />
1.5<br />
2<br />
2<br />
2<br />
2<br />
2<br />
2.5<br />
2.5<br />
2.5<br />
2.5<br />
2.5<br />
front<br />
Time (s)<br />
3<br />
3<br />
3<br />
3<br />
3<br />
3.5<br />
rear<br />
3.5<br />
3.5<br />
3.5<br />
3.5<br />
4<br />
4<br />
4<br />
4<br />
4<br />
Simulink<br />
ADAMS<br />
Comparison of Simulink and MSC.ADAMS predictions of vehicle<br />
4.5<br />
4.5<br />
4.5<br />
4.5<br />
4.5<br />
5<br />
5<br />
5<br />
5<br />
5<br />
stiffness model, for example, does not include heave and pitch degrees of<br />
freedom relative to the front and rear axles. During the simulation, however,<br />
the degrees of freedom exist for the body to heave and pitch relative<br />
to the ground inertial frame. These degrees of freedom must still be solved<br />
and in this case are damped only by the inclusion of the tyre model. In the<br />
3 degrees of freedom model these motions are ignored and solution is only<br />
performed on the degrees of freedom that have been modelled. While the<br />
main theme in this book is to demonstrate the use of multibody systems<br />
analysis the Matlab/Simulink model is useful here in providing the basis<br />
for additional modelling and simulation of the modern control systems<br />
involved in enhancing the stability and dynamics of the vehicle. The effort<br />
invested in this modelling approach also provides educational benefits<br />
reinforcing fundamental vehicle dynamics theory.<br />
6.15 Summary<br />
Many different possibilities exist for modelling the behaviour of the vehicle<br />
driver. That none has reached prominence suggests that none is correct for