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Open and Closed Loop System Characteristics of a Tractor and an Implement Dynamic Model

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan

Citation:  2008 Providence, Rhode Island, June 29 – July 2, 2008  084761.(doi:10.13031/2013.25208)
Authors:   Manoj Karkee, Brian L Steward
Keywords:   dynamic vehicle model, implement guidance, automatic guidance, LQR design, relaxation length

Accurate guidance of towed implements is important for performing agricultural field operations and for gaining the ultimate benefit from an agricultural automatic guidance system. The study of open and closed loop system responses can be helpful in the design of practical guidance controllers. A dynamic model of a tractor and a towed implement system was developed. Open loop analysis of the kinematic and dynamic models revealed that the dynamic model was essential for capturing the higher order dynamics of the tractor and implement system at higher operating velocities. In addition, a higher fidelity dynamic model was also developed by incorporating steering dynamics and tire relaxation length dynamics. Closed loop system characteristics were studied by using a linear quadratic regulator (LQR) controller. The tractor position and heading and implement heading states along with respective rate states were fed back to close the loop. The higher fidelity closed loop system used a practical range of steering angles and rates to keep the response within nominal off-road vehicle guidance controller design specifications in the forward velocity range of 0.5 m/s to 10 m/s (1.8 km/h to 36 km/h). These simulation studies provided understanding about the characteristics of the tractor and towed implement system and showed promise in assisting in the development of automatic guidance controllers.

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