Model-Reconstructed RBFNN-DOB for FJR Trajectory Control with External Disturbances

Parameter uncertainties and fluctuating disturbances have posed significant challenges to the smooth and precise control of Flexible Joint Robots (FJRs) in industrial environments. To mitigate such disturbances, Disturbance Observers (DOBs) are commonly employed; however, the model uncertainties inherent in FJR systems make accurate dynamic modeling challenging, and the efficacy of DOBs hinges heavily on the accuracy of the dynamic model, which limits their applicability to FJR control. This paper presents a hybrid RBFNN-based Disturbance Observer (RBFNNDOB) state feedback controller for FJRs. By combining a nominal model-based DOB with an RBFNN, this method effectively addresses the unknown dynamics of FJRs while simultaneously compensating for external time-varying disturbances. In this framework, an adaptive neural network weight update law is formulated using Lyapunov stability theory. This enables the RBFNN to selectively estimate the unmodeled uncertainties in FJR dynamics, thereby minimizing computational redundancy in model estimation while allowing dynamic compensation for residual uncertainties beyond the nominal model and DOB estimation errors—ultimately enhancing computational efficiency and achieving robust compensation for rapidly changing disturbances. The boundedness of the tracking error is proven using the Lyapunov approach, and experimental validation is conducted on the FJR system to confirm the efficacy of the proposed control method.