Local and global sensitivity analysis of a tractor and single axle grain cart dynamic system model

Tractor and towed implement system models have become increasingly important for model-based guidance controller design, virtual prototyping, and operator-and-hardware-in-loop simulation. Various tractor and towed implement models have been proposed in the literature which contain uncertain or time-varying parameters. Sensitivity analysis was used to identify the effect of system parameter uncertainty/variation on system responses and to identify the most critical parameters of the lateral dynamics model for a tractor and single axle grain cart system. Both local and global sensitivity analyses were performed with respect to three tyre cornering stiffness parameters, three tyre relaxation length parameters, and two implement inertial parameters. Overall, the system was most sensitive to the tyre cornering stiffness parameters and least sensitive to the implement inertial parameters. In general, the uncertainty in the input parameters and the system output responses were related in a non-linear fashion. With the nominal parameter values for a Mechanical Front Wheel Drive (MFWD) tractor, a single axle grain cart, and maize stubble surface conditions, a 10% uncertainty in cornering stiffness parameters caused a 2% average uncertainty in the system responses whereas a 50% uncertainty in cornering stiffness parameters caused a 20% average uncertainty at 4.5 m s−1 forward velocity. If a 5% average uncertainty in system responses is acceptable, the cornering stiffness parameters must be estimated within 25% of actual/nominal values. The output uncertainty increased as the forward velocity was increased.