Robust Integral Optimal Sliding Mode Control Design for Electromagnetic Levitation System with Matched Uncertainties

Recently, there has been a rapid increase in the demand for magnetic levitation systems. Since they are utilized in many levitation-based systems, one such application is in magnetic levitated (Maglev) trains. Moreover, these systems are complicated to control due to their nonlinear characteristics, susceptibility to external disturbances, and model uncertainties. This article proposes an enhanced integral sliding mode control (ISMC) strategy with a robust optimal framework designed for electromagnetic levitation systems (EMLSs). Traditional sliding mode control (SMC) often suffers from a high-frequency phenomenon in the input, thereby necessitating the development of a more robust controller. This requirement is addressed through the implementation of a comprehensive integral robust optimal sliding mode control strategy. The proposed controller effectively mitigates the chattering phenomenon while simultaneously enhancing the system’s robustness against uncertainties. The robust optimal approach is specifically designed to handle the matched uncertainties inherent in the system dynamics, thereby facilitating an appropriate feedback control mechanism. The Hamilton–Jacobi–Bellman (HJB) equation is used to achieve the robust control design. This feedback control is integrated with the ISMC to execute the desired control action effectively. The simulation results highlight the effectiveness of the proposed control scheme, presenting a comparative analysis of performance indices, including integral time absolute error (ITAE), integral absolute error (IAE), integral squared error (ISE), and integral time squared error (ITSE). These indices collectively underscore the robustness of the control design.