Coupling GRU and Adaptive PID Algorithm for Vehicle Tire Slip Angle Estimation

This paper presents a novel approach combining Gated Recurrent Unit (GRU) and adaptive Proportional-Integral-Derivative (PID) algorithm employed for predicting tire slip angles (TSA). In previous studies, research has shown successful prediction of tire slip angles using Recurrent Neural Network (RNN). Research has shown that when using only RNN for prediction, the model’s accuracy is low in untrained speed conditions. For this investigation, vehicle data under constant speed double lane change (DLC) conditions and S-Turn variable speed (STVS) scenarios were generated using the CarSim software. The dataset includes variables such as tire lateral force, tire longitudinal force, tire vertical force, vehicle TSA, and time. A total of three GRU models were utilized in this research. The first GRU model is employed for primary predictions, the second GRU model is utilized to predict the discrepancies between the first model’s predictions and the actual values, and the third GRU model is employed to learn variations in the PID weight parameters, facilitating further optimization of the predictions. The training of the GRU models is conducted using the TensorFlow framework. An adaptive PID was realized by utilizing the predicted PID parameter changes from the third GRU model, with the aim of further refining the prediction errors. In theory, the output values of GRU2 can be directly subtracted from GRU1. Simulation results showed that the GRU_APID algorithm performed better compared with GRU1 minus GRU2. Finally, the predictions generated by the first GRU model are combined with the corrective values generated by the last adaptive PID to obtain the ultimate TSA prediction. Simulation results have confirmed that this approach indeed enhances the model’s performance and increases TSA prediction accuracy under untrained speed conditions.