History-of-Error Neural Network Disturbance Rejection With Application to Motion Control of a Cylindrical Robot

Precision motion control is essential for the reliable and efficient operation of industrial and autonomous systems. This article presents an adaptive neural network (NN) controller that achieves high-accuracy trajectory tracking and disturbance rejection in the presence of nonlinear effects, such as cogging and friction forces. The key contribution lies in incorporating ahistory-of-error learning mechanisminto the NN objective function, enabling the controller to adapt based on both instantaneous and past tracking dynamics. This temporal formulation enhances learning efficiency and disturbance suppression compared to conventional instantaneous-error methods. The controller employs a single-layer feedforward NN to estimate unknown dynamics, with a modified backpropagation algorithm and e-modification ensuring stable weight adaptation. A Lyapunov-based stability analysis is presented that guarantees bounded tracking errors and weight convergence. The resulting control law achieves robust real-time implementation without compromising computational efficiency. Experimental results on a cylindrical robot subjected to friction and cogging torque disturbances show over 60% improvement in tracking accuracy and up to 40% enhancement in disturbance rejection relative to NN and proportional integral derivative (PID) baselines. These results confirm the effectiveness of the proposed history-enhanced adaptive neural control framework for precision motion systems.