Super-Twisting-Based Online Learning in High-Order Neural Networks for Robust Backstepping Control of DC Motors Under Uncertainty

This paper addresses the speed control problem of a DC motor in the presence of nonlinearities, disturbances, and unmodeled dynamics by proposing a neural backstepping control scheme based on a Recurrent High-Order Neural Network (RHONN). The proposed RHONN serves as an online approximator to compensate for uncertain nonlinear dynamics in a PD-based backstepping controller, enabling the system to handle disturbances, modeling errors, and unmodeled dynamics. Instead of relying on the traditional Extended Kalman Filter (EKF) for RHONN weight adaptation, the neural parameters are updated online using a Super-Twisting Algorithm (STA). As a result, the proposed STA-based learning law provides a simpler and robust covariance-free adaptation mechanism with practical finite-time convergence properties, making it suitable for real-time embedded implementations. The proposed method was evaluated through numerical simulations and implemented on an embedded microcontroller to assess its real-time performance. Simulation results show reductions between 0.04% and 2.04% in steady-state and integral error metrics compared with a tuned PD controller, and improvements up to 25.66% and 23.82% over LQR and MPC in the IMSE index. Experimental results demonstrate good tracking performance, robustness under varying load conditions, and low computational requirements, confirming the practical feasibility.