Parameter Sensitivity Analysis of a Tractor and Single Axle Grain Cart Dynamic System Model
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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 variation on system responses and to identify the most critical system parameters. Sensitivity analysis was performed with respect to three tire cornering stiffness parameters, three tire relaxation length parameters, and two implement inertial parameters. Overall, the system was most sensitive to the tire cornering stiffness parameters and least sensitive to the implement inertial parameters. In general, the variation in the input parameters and the system state variables were related in a non-linear fashion. With the nominal parameter values for a MFWD tractor, a single axle grain cart, and corn stubble surface conditions, a 10% variation in cornering stiffness parameters caused a 5% average variation in the system responses whereas an 80% change in cornering stiffness parameters caused an 80% average variation at 4.5 m/s forward velocity. If a 10% average variation in system responses is acceptable, the cornering stiffness parameters and implement inertial parameters must be estimated within 20% and 30% of actual/nominal values respectively. The relaxation length parameters have to be within 75% of the nominal values.