Vehicle Dynamic System
In control system design the modeling of a dynamic system is important as it represents the behaviour and characteristics of the system being controlled. In vehicle dynamic studies, the mathematical modeling of vehicle dynamic motion is done based on physical laws that describe the forces and moment acting on the vehicle body and tyres. The vehicle mode with steering system is drawn in Fig. 1. The equations of Vehicle dynamics are as follows: m( ˙vy + vxγ) = (Fx 1 + Fx 2)sinδf + Fy 3 + Fy 4
+(Fy 1 + Fy 2)cosδf (1)
Iz
γ˙ = (Fy 1cosδf + Fy 2cosδf + Fx 1sinδf + Fx 2sinδf)lf
−(Fy 3 + Fy 4)lr + Mc
(2)
Mc
=
t w2 (Fx 1cosδf − Fx 2cosδf − Fy 1sinδf + Fy 2sinδf
+Fx 3 − Fx 4)
(3)
The front wheel steer angle used in these equations is δf and is given by
δ
…show more content…
Furthermore, the longitudinal and lateral forces of tyre are Fxi, Fyi where as F w is the crosswind and lf, lr are the distances between the wheel center of mass and front and rear axes and t w the track width of wheels on an axle. Moreover, lw is the distance between the position of the crosswind and vehicle center of mass. Furthermore, m, vx, vy are the vehicle mass, longitudinal velocity and lateral velocity. Moreover, αi is the side slip angle of tyre. The vehicle side slip angle and yaw rate are represented by β, γ. Iz is the moment of inertia and
Mc
is the DYC controller generated yaw moment about the vertical axis.
For small tyre side slip angle, the equation (1) and (2)
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