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Agricultural machines, bulldozers and tractors use a hydrostatic transmission (HST) to turn engine power into motion. The HST’s “stroke,” or piston travel, must be precisely controlled to save energy and adapt to changing terrain. Traditionally, engineers rely on a multiple model predictive controller (MPC) that forecasts the best action ahead of time. Now, a research team has built a new controller based on an artificial neural network (ANN) that mimics the MPC’s behavior.

In tests, the ANN had to follow complex stroke trajectories for both primary (power) and secondary (speed) regulation while coping with real disturbances like engine torque variations and load changes caused by the ground. Results show the ANN is more robust to white‑noise, less sensitive to modeling errors, and requires fewer calculations than the MPC. Its multi‑input‑multi‑output architecture also fits well with complex systems like HSTs.

In practice, this could make heavy vehicles more efficient, consume less fuel, and react faster to sudden terrain changes, all thanks to a simpler, faster‑to‑run AI algorithm that can work in real time.

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The hydrostatic transmission's mathematical model is typically nonlinear and time‑varying due to fluid viscosity dependencies, load pressure, and piston slip conditions. MPC employs a series of locally linearized models, each valid in a sub‑space of the state, to predict stroke evolution and optimize a cost function penalizing deviations from the desired trajectory and excessive energy use. However, solving a quadratic programming problem at every sampling step makes MPC computationally heavy, especially for high‑frequency MIMO systems.

The proposed ANN is a multi‑layer feed‑forward network trained offline with data generated by an HST simulator under diverse operating conditions (engine torque variations, variable loads, white noise). Training uses back‑propagation with L2 regularization to prevent over‑fitting. Once trained, the network directly outputs the stroke command based on the current state (pressure, speed, torque) without solving an optimization problem.

Processor‑in‑the‑Loop (PIL) simulations showed that the root‑mean‑square error (RMSE) between the reference trajectory and the ANN output is 12% lower than MPC, with per‑cycle computation time reduced by 78%. Moreover, the ANN remains stable when the system model is perturbed by ±15% from the nominal model, demonstrating good robustness to parametric uncertainties. These traits suggest the ANN can be deployed on low‑power microcontrollers, paving the way for more efficient real‑time control in heavy vehicles.

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Authors:
Hakan Ülker
Date Published:
Original Article www.mdpi.com
Fact-check verified on 17/12/2025
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Creative Commons License CC BY-NC-SA 4.0

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