Analytical Aspects and Practical Pitfalls in Technical Applications of AD

Abstract

We apply AD to three technical problems from multibody dynamics, vehicle dynamics and finite element material modeling. The multibody dynamics application investigates threshold and maximum-value optimization criteria in direct representation using AD for the sensitivity analysis. Secondly, an adaptive cruise controller of a vehicle convoy is optimized with respect to control error and control effort. Two experimental cars equipped with state-of-the-art sensors and actuators are used to verify the designed controllers. Since the engine voltage of the actuator is restricted to +/-10 V, there are non-differentiable points in the time trajectory, but AD techniques can still be used. Thirdly, AD is used for the evaluation of constitutive relations for hyperelastic materials. Some important continuum mechanical quantities correspond to the first and second derivatives of the scalar stored energy function with respect to the strain tensor. These quantities can be derived analytically using complicated analysis but it is fascinating that with minimal preparation and only few mathematical insight exactly the same values can also be computed using AD methods.