Discrete-Time Fourier Series Neural Network Control for Nonlinear SISO Systems: Validated in a Magnetic Levitation Model

The control of nonlinear, open-loop unstable dynamics is a prevalent engineering challenge, often benchmarked through magnetic levitation (Maglev) systems. While continuous-time adaptive neural networks are commonly used to reject disturbances, their direct digital implementation often induces closed-loop instability due to unaccounted sampling effects. To address this, this paper proposes a discrete-time Fourier Series Neural Network (FSNN) control architecture for nonlinear Single-Input Single-Output (SISO) systems that can be transformed into the Brunovsky canonical form. The parameter adaptation laws are synthesized strictly in the discrete-time domain using Lyapunov stability theory. This approach yields an explicit upper bound for the digital sampling period, ensuring a proper implementation. Furthermore, it guarantees the Uniform Ultimate Boundedness (UUB) of the tracking error in the presence of bounded unmodeled dynamics and periodic disturbances. Numerical simulations of Maglev dynamics validate the theoretical bounds, demonstrating that the FSNN controller achieves rapid learning and generates a smooth control effort. Ultimately, by eliminating the instability risks of continuous-time approximations, this methodology bridges the gap between theoretical design and digital implementation, providing a practical framework for the robust control of electromagnetic actuators and other nonlinear industrial processes.