Modelling in vehicle dynamics of automobiles

A general problem formulation and the resulting scheme of modelling dynamical system behaviour is introduced before a specification with respect to automobiles is done. An essential component for the vehicle behaviour is the tyre. Models of different complexity with respect to its mathematical‐mechanical formulation are presented. Simple models of the automobile itself allow a separation of longitudinal, lateral, and vertical dynamics and a partially analytical derivation of corresponding equations of motion. These models are usually also the approximations used for the design of a state observer and controller to influence the vehicle behaviour. For a more detailed representation of the vehicle 3D‐models are assembled by their individual components, e.g. suspensions, drive train, and steering system. In this way a good agreement between measurements and simulation results can be realized up to the nonlinear range of vehicle behaviour. Nowadays MBS‐models, established with professional software packages, are applied. They integrate all essential components, taking into account different linkages, e.g. bushings and joints. For component strength design, a rough road surface description can be implemented additionally. To improve by simulation the active safety or handling of the vehicle, these models represent the controlled complex vehicle in the global control loop whereas linearized models as mentioned above are applied for the controller design. As an example the design of an extended ESP‐controller and its consequences for severe braking conditions during cornering are discussed showing the necessary steps in modelling and their mathematical formulation.