Quantifying the Effect of Initialization Errors for Enabling Accurate Online Drivetrain Simulations 2019-01-0347

Decisions are routinely made in vehicle controls based on simulations executed by on-board modules. An advanced vehicle control strategy program needs to include mathematical models of sub-systems and components for real-time analysis. The rapid advancement of on-board control hardware makes online simulation of a complex dynamic system such as an automatic transmission feasible for predicting future system states for numerous control applications. Implementation of online simulations necessitates model initialization at the current drivetrain state. However, sensor signals and estimated variables used to obtain the current drivetrain state are susceptible to error, compromising accuracy of future state prediction as error propagates through numerical integration process. This article describes drivetrain modeling and analysis to account for initialization error for accurate online simulations. First, a torsional drivetrain model is developed to study the dynamics of drivetrain up-shifts from first to second gear using the Hybrid Dynamical System paradigm. The model is constructed in an analytical form to assist mathematical analysis on-the-fly. Then a methodology is introduced to quantify the effects of initialization error online based on eigenvalue analysis. The outcomes of this study show promise for enabling accurate online predictive drivetrain simulations.