Modeling, identification and analysis of tractor and single axle towed implement system
Increased and sustained agricultural productivity is a key to meet the globally increasing demands for food and energy. Automation of agricultural machinery is one of the ways to improve the efficiency and productivity of various field operations. Because a field implement performs most of these operations, accurate implement guidance is needed to reduce production cost, increase yield, and improve sustainability. Model-based guidance controller design and virtual prototyping techniques can be used in automatic guidance controller development to improve the accuracy and robustness of the guidance controller while reducing the development time and cost. Hence, development and analysis of accurate tractor and implement system models are needed to support automatic tractor and implement guidance controller development. Real-time vehicle model simulation capability allows engineers and users to intuitively interact with the realistic virtual prototypes and to evaluate the performance of physical hardware. As the model complexity is increased to improve the model accuracy and/or fidelity, the computational need will also increases thus increasing the challenge to meet real-time constraints. In this regard, it is important to minimize the computational load to a Virtual Reality (VR)-based real-time dynamics model simulation system.
In this dissertation, various strategies were investigated to reduce the computational burden on the dynamics model simulation so that real-time simulation could be achieved for increasingly complex models. A distributed architecture was developed for a virtual reality-based off-road vehicle real-time simulator to distribute the overall computational load of the system across multiple machines. Multi-rate model simulation was also used to simulate various system dynamics with different integration time steps so that the computational power can be distributed more intelligently.
It is also important to study the trade-off between the model accuracy/fidelity and model complexity. Three different tractor-and-single-axle-towed-implement system models with varying degrees of fidelity, namely a kinematic model, a dynamic model, and a dynamic model with tire relaxation length, were developed, and the simulated transient and steady state responses were compared at various forward velocities and input frequencies. Both open and closed loop system characteristics were studied. Field experiments were also carried out to characterize the input-output relationship of the tractor-implement steering system. The responses from all three models were similar at lower forward velocities and with low frequency steering inputs (< 0.2 Hz). However, when the system was operated at higher forward velocities or with higher frequency steering inputs, the responses from the three models varied substantially. In this case, the dynamic model with tire relaxation length best represented the experimental system responses.
The system model contained various uncertain or varying parameters. It was important to understand and quantify the effect of parameter variation on system responses. Sensitivity analysis was used to identify the effect of variation in tire cornering stiffness, tire relaxation length, and implement inertial parameters on simulated system responses. Overall, the system was most sensitive to the tire cornering stiffness and least sensitive to the implement inertial parameters. In general, the uncertainty in the input parameters and the output variables were related in a non-linear fashion. At 4.5 m/s forward velocity, a 10% uncertainty in cornering stiffness caused a 2% average output uncertainty whereas a 50% uncertainty in cornering stiffness caused a 20% output uncertainty. Finally, a parameter identification method was used to estimate the uncertain model parameters from measured field data. The accuracy of the model responses improved substantially when the model was simulated with the estimated parameters.
It was concluded that a dynamic model with tire relaxation length will represent a tractor and single axle towed implement system with reasonable accuracy. The study also helped improve the understanding of the relative importance of various model parameters, which will help to more judiciously allocate resources for estimating system parameters. Moreover, the analysis indicated that various vehicle parameters can be estimated with reasonable accuracy using a dynamic model, experimental data, and a parameter estimation method. The work will provide a framework for off-road vehicle and implement simulation through which engineers and scientists can determine to which parameters the system is most sensitive and how a model would perform with estimated model parameters.