The central issue of this contribution is the discussion of the differential flatness of the planar holonomic bicycle model. The components of a flat output are given as the lateral and the longitudinal velocity component of a distinguished point located on the longitudinal axis of the vehicle. This property is shown for the front-, rear-and all-wheel driven vehicle, without referring to particular representatives of the functions modelling the lateral tire forces. The clear physical meaning of the flat output is regarded as particularly useful for the control design task. The vehicle dynamics control design is accomplished following the flatness based control theory.

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This contribution is primarily concerned with the system analysis of the bicycle dynamics, revealing the differential flatness property as a main result. A physically relevant representative for the flat output is introduced, with its components given as the lateral and the longitudinal velocity of a distinguished point

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In tandem hot strip rolling mills, different friction between the rolls and the strip material on the upper and lower strip surface can occur due to asymmetric surface temperatures or different conditions of oil lubrication. To capture these effects, this paper presents a hydrodynamic roll gap model with asymmetric friction. Based on similarities between the rolled material and viscous fluids, fluid mechanics theory is used to derive this model. Due to the nature of this model, the influence of the rolling speed is inherently taken into account, which allows an accurate prediction of the rolling force and the forward slip. As an analytic solution for the hydrodynamic roll gap model is available, it is well suited for online applications in rolling plants. For validation of the proposed model, an experiment with asymmetric work roll roughness was performed. A specimen of steel strip with copper pins inserted was repeatedly rolled to visualize the material flow inside the roll gap for multiple passes. The resulting deformed copper pins were cut out of the strip and show good agreement with the deformation profiles calculated by the developed model.