Quantifying the Effect of Initialization Errors for Enabling Accurate Online Drivetrain Simulations

Simulations conducted on-board in a vehicle control module can offer valuable information to control strategies. Continued improvements to on-board computing hardware make online simulations of complex dynamic systems such as drivetrains within reach. This capability enables predictions of the system response to various control actions and disturbances. Implementation of online simulations requires model initialization that is consistent with the physical drivetrain state. However, sensor signals and estimated variables are susceptible to errors, compromising the accuracy of the initialization and any future state predictions as the simulation proceeds through the numerical integration process. This paper describes a drivetrain modeling and analysis method that accounts for initialization errors, thereby enabling accurate simulations of system behaviors. First, the hybrid dynamical system paradigm is employed to develop a torsional drivetrain model that captures the dynamics during a gear shift. The model is constructed in an analytical form and linearized to enable online mathematical analysis. Then a methodology is introduced to quantify the effect of initialization errors online. Finally, a procedure to systematically account for initialization errors is discussed. The outcome of this study demonstrates the capability for enabling accurate online simulations in the presence of sensor and state estimation errors in drivetrain applications and beyond.