Approximations for Nonlinear Differential Algebraic Equations to Increase Real-time Simulation Efficiency

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Virginia Tech

Full-motion driving simulators require efficient real-time high fidelity vehicle models in order to provide a more realistic vehicle response. Typically, multi-body models are used to represent the vehicle dynamics, but these have the unfortunate drawback of requiring the solution of a set of coupled differential algebraic equations (DAE). DAE's are not conducive to real-time implementation such as in a driving simulator, without a very expensive processing capability. The primary objective of this thesis is to show that multi-body models constructed from DAE's can be reasonably approximated with linear models using suspension elements that have nonlinear constitutive relationships.

Three models were compared in this research, an experimental quarter-car test rig, a multi-body dynamics differential algebraic equation model, and a linear model with nonlinear suspension elements. Models constructed from differential algebraic equations are computationally expensive to compute and are difficult to realize for real-time simulations. Instead, a linear model with nonlinear elements was proposed for a more computationally efficient solution that would retain the nonlinearities of the suspension. Simplifications were made to the linear model with nonlinear elements to further reduce computation time for real-time simulation.

The development process of each model is fully described in this thesis. Each model was excited with the same input and their outputs were compared. It was found that the linear model with nonlinear elements provides a reasonably good approximation of actual model with the differential algebraic equations.

Suspension Modeling, Real Time Modeling, Driving Simulator