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Modelling and assembly of the full vehicle 367 As the simulation progresses the torque is constantly modi-fied based on the observed path of the vehicle and the desired trajectory. Such an input is referred to as closed loop since the response is observed and fed back to the input, thus closing the control loop. To return to the open-loop case, we can consider an example of an open loop manoeuvre for a steering input where we want to ramp a steering input of 90 degrees between 1 and 1.5 seconds of simulation time. Using an MSC.ADAMS solver statement the function applied to the steering motion would be: FUNCTION STEP(TIME, 1, 0, 1.5, 90D) In a similar manner if we wanted to apply a sinusoidal steering input with an amplitude of 30 degrees and a frequency of 0.5 Hz we could use: FUNCTION 30D * SIN(TIME*180D) For the lane change manoeuvre described earlier the measured steering wheel angles from a test vehicle can be extracted and input as a set of XY pairs, which can be interpolated using a cubic spline fit. A time history plot for the steering inputs is shown in Figure 6.42 for lane change manoeuvres at 70 and 100 km/h. By way of example the MSC.ADAMS statements which apply the steering motion to the steering column to body revolute joint and the spline data are shown in Table 6.3 for a 100 km/h lane change. The x values are points in time and the y values are the steering inputs in degrees. In the absence of measured data it is possible to construct an open loop single or double lane change manoeuvre using a combination of nested arithmetic IF functions with embedded step functions with some planning and care over syntax. Note that for a fixed steering input a change in vehicle configuration will produce a change in response so that the vehicle fails to follow a path. For a closed loop steering manoeuvre a torque is applied to the steering column, or a force to the steering rack if the column is not modelled, that will vary during the simulation so as to maintain the vehicle on a predefined 120.0 STEERING INPUT – LANE CHANGE MANOEUVRE Steering wheel angle (deg) 80.0 40.0 0.0 40.0 80.0 120.0 0.0 1.0 2.0 3.0 4.0 5.0 Time (s) Fig. 6.42 Steering input for the lane change manoeuvre at 70 km/h (dashed line) and 100 km/h (solid line)

368 Multibody Systems Approach to Vehicle Dynamics Table 6.3 MSC.ADAMS statements for lane change steering inputs MOTION/502,JOINT=502,ROT ,FUNC=(PI/180)*CUBSPL(TIME,0,1000) SPLINE/1000 ,X=0,1,2,3,4,5,6,7,8,9 ,9.1,9.2,9.3,9.4,9.5,9.6,9.7 ,9.8,9.9,10,10.1,10.2,10.3,10.4,10.5,10.6,10.7,10.8,10.9,11 ,11.1,11.2,11.25,11.3,11.4,11.5,11.6,11.7,11.8,11.9,12,12.1 ,12.2,12.3,12.4,12.5,12.6,12.7,12.8,12.9,13,13.1,13.2,13.3 ,13.4,13.5,13.6,13.7,13.75,13.8,13.9,14,14.1,14.2,14.3,14.4,14.5 ,14.6,14.7,14.8,14.9,15 ,Y 0,0,0,0,0,0,0,0,0,0 ,0,0,0,0,0,0,0 ,0,0,-5,-17,-40,-55,-57,-52,-43,-30,-5,15,35,55,72,75,70,65,45,10 ,-10,-17,-11,-7,15,50,75,67,66,60,50,35,0,-50,-95,-110,-100,-70,-35,0 ,20,20,35,55,20,-6,-3,-2,-1,0,0,0,0,0,0 Torque applied to handwheel Error T Fn (error) Fig. 6.43 Principle of a closed loop steering controller path. This requires a steering controller to process feedback of the observed deviation from the path (error) and to modify the torque accordingly as illustrated in Figure 6.43. 6.13 Driver behaviour It becomes inevitable with any form of vehicle dynamics modelling that the interaction of the operator with the vehicle is a source of both input and disturbance. In flight dynamics, the phenomenon of ‘PIO’ – pilot induced oscillation – is widely known. This occurs when inexperienced pilots, working purely visibly and suffering from some anxiety, find their inputs are somewhat excessive and cause the aircraft to, for example, pitch rhythmically instead of holding a constant altitude (Figure 6.44).

368 Multibody Systems Approach to Vehicle Dynamics<br />

Table 6.3<br />

MSC.ADAMS statements for lane change steering inputs<br />

MOTION/502,JOINT=502,ROT<br />

,FUNC=(PI/180)*CUBSPL(TIME,0,1000)<br />

SPLINE/1000<br />

,X=0,1,2,3,4,5,6,7,8,9<br />

,9.1,9.2,9.3,9.4,9.5,9.6,9.7<br />

,9.8,9.9,10,10.1,10.2,10.3,10.4,10.5,10.6,10.7,10.8,10.9,11<br />

,11.1,11.2,11.25,11.3,11.4,11.5,11.6,11.7,11.8,11.9,12,12.1<br />

,12.2,12.3,12.4,12.5,12.6,12.7,12.8,12.9,13,13.1,13.2,13.3<br />

,13.4,13.5,13.6,13.7,13.75,13.8,13.9,14,14.1,14.2,14.3,14.4,14.5<br />

,14.6,14.7,14.8,14.9,15<br />

,Y 0,0,0,0,0,0,0,0,0,0<br />

,0,0,0,0,0,0,0<br />

,0,0,-5,-17,-40,-55,-57,-52,-43,-30,-5,15,35,55,72,75,70,65,45,10<br />

,-10,-17,-11,-7,15,50,75,67,66,60,50,35,0,-50,-95,-110,-100,-70,-35,0<br />

,20,20,35,55,20,-6,-3,-2,-1,0,0,0,0,0,0<br />

Torque applied to<br />

handwheel<br />

Error<br />

T Fn (error)<br />

Fig. 6.43<br />

Principle of a closed loop steering controller<br />

path. This requires a steering controller to process feedback of the observed<br />

deviation from the path (error) and to modify the torque accordingly as<br />

illustrated in Figure 6.43.<br />

6.13 Driver behaviour<br />

It becomes inevitable with any form of vehicle dynamics modelling that the<br />

interaction of the operator with the vehicle is a source of both input and<br />

disturbance. In flight dynamics, the phenomenon of ‘PIO’ – pilot induced<br />

oscillation – is widely known. This occurs when inexperienced pilots,<br />

working purely visibly and suffering from some anxiety, find their inputs<br />

are somewhat excessive and cause the aircraft to, for example, pitch rhythmically<br />

instead of holding a constant altitude (Figure 6.44).

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