{'fraction_non_alphanumeric': 0.024355300859598854, 'fraction_numerical': 0.0028653295128939827, 'mean_word_length': 5.652380952380953, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An Efficient High-Order Time-Step Algorithm With Proportional-Integral Control Strategy for Semirecursive Vehicle Dynamics

Dynamics of complex mechanical systems can be modeled and solved efficiently, often even in faster-than-real-time by employing semi-recursive formulations and their various versions. To simulate complex mechanical systems accurately and efficiently, an optimal combination of a multibody formulation and a numerical time integration scheme is critical. To this end, this paper introduces a procedure based on the double-step semi-recursive formulation and adaptive time-step algorithm. The introduced adaptive time-step is based on proportional-integral controller that is particularly suitable for efficient computation of vehicle dynamics. The introduced proportional integral control strategy accounts the local truncation error and recent alteration concerning the local truncation error which improves the numerical stability and efficiency. As numerical examples, a 15-degree-of-freedom sedan vehicle model and a 17-degrees-of-freedom light truck model are analyzed by using the double-step semi-recursive formulation with an adaptive time-step algorithm. The results highlight the efficiency gain of the presented adaptive time-step algorithm. It can be concluded that the introduced approach is suitable for efficient simulation of highly nonlinear dynamics model.