Brake systems have become increasingly complex. They must not only slow down or stop a vehicle under extreme conditions within short distances, but also reduce the effort exerted by the driver. This phenomenon is difficult to approach because it depends on the vehicle's architecture. This is why, in this paper, the first part will give the basis for modelling of the complete vehicle including the frame and the tires, in a 3D format. A 2D control law model will be synthesized to obtain the best performances for road behaviour. This control law is based on the theory of Linear Quadratic control (LQ). It is also extended to cover the 3D vehicle model. The last part gives the numerical simulation results which demonstrate the effectiveness of this law for vehicle performances.
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