Optimal PID-Based Super-Twisting Sliding Mode Control for Magnetic Levitation Systems With Real-Time Implementation

This paper presents the design and experimental validation of an optimal proportional–integral–derivative (PID)-based super-twisting sliding mode control (STSMC) strategy for precise position tracking of a magnetic levitation system (MLS). The parameters of the PID-based sliding surface are optimally tuned using a genetic algorithm (GA) to enhance transient response and tracking accuracy. The super-twisting algorithm ensures robust performance while mitigating chattering and providing smooth control action. Closed-loop stability is rigorously established; unlike conventional Lyapunov approaches in sliding mode control (SMC), a strict Lyapunov stability (SLS) framework is employed to guarantee the finite-time convergence of the sliding variable. In addition, discrete-time stability analysis is performed to verify the practical applicability of the proposed controller. The controller performance is evaluated through numerical simulations in MATLAB/Simulink and real-time experiments on the ECP Model 730 MLS platform, which uses a digital signal processor (DSP). Simulation results show that the proposed STSMC reduces the settling time ( $\mathrm {t_{s}}$ ) to $0.201~{\mathrm {s}}$ , achieving improvements of 59% and 38% compared to IOFL and SMC, respectively. Moreover, the overshoot (OS) is eliminated, and a minimal integral absolute error (IAE) of $0.231~{\mathrm {cm \cdot s}}$ is obtained, corresponding to improvements of 98% and 56%, respectively. Experimental results further validate the effectiveness of the proposed approach, achieving $\mathrm {t_{s}}$ of $0.317~{\mathrm {s}}$ with improvements of 25% and 35%, respectively. In addition, the controller exhibits negligible OS (0.7%) compared to 14% and 6%, and achieves the lowest tracking error ( $\mathrm {IAE} = 0.313~ {\mathrm {cm \cdot s}}$ ), corresponding to improvements of 53% and 47%, respectively. These results demonstrate that the proposed STSMC strategy provides superior tracking performance, enhanced robustness, and practical feasibility for real-time MLS position control.