Comparative Analysis of Control Strategies for Tracking Periodic Sinusoidal References in Magnetic Levitation Systems

The dynamics associated with a magnetic levitation (Maglev) system are typically characterized by significant instability and nonlinear behavior. Consequently, the implementation of an effective control mechanism is imperative for achieving precise positioning of a ferromagnetic sphere. The majority of the extant literature primarily assesses the efficacy of the Maglev control system in response to a step input. This manuscript delineates a comparative analytical study contrasting synergetic control (SC) with backstepping control (BSC) in the context of a Maglev system aimed at tracking a periodic reference input. Periodic signals highlight how well the controller can achieve zero steady-state error (or minimal error) for non-constant references, which is harder than constant step tracking. The system's dynamics are articulated through the application of the Euler-Lagrange methodology. Utilizing the established nonlinear framework of the system, the control signals for both SC and BSC are formulated. Moreover, both control schemes were supplemented with the Grasshopper Optimization Algorithm (GOA), which was employed to systematically optimize the associated design parameters. The resultant optimized control systems are subjected to simulation utilizing MATLAB software. The findings from the simulations indicate that both proposed controllers effectively track the desired periodic reference input. Nevertheless, the quantitative analysis grounded in integral absolute error (IAE) metrics reveals that the performance of BSC surpasses that of SC.