Robust–optimal control of electromagnetic levitation system with matched and unmatched uncertainties: experimental validation

The electromagnetic levitation system (EMLS) serves as the most important part of any magnetic levitation system. However, its characteristics are defined by its highly nonlinear dynamics and instability. Furthermore, the uncertainties in the dynamics of an electromagnetic levitation system make the controller design more difficult. Therefore, it is necessary to design a robust control law that will ensure the system’s stability in the presence of these uncertainties. In this framework, the dynamics of an electromagnetic levitation system are addressed in terms of matched and unmatched uncertainties. The robust control problem is translated into the optimal control problem, where the uncertainties of the electromagnetic levitation system are directly reflected in the cost function. The optimal control method is used to solve the robust control problem. The solution to the optimal control problem for the electromagnetic levitation system is indeed a solution to the robust control problem of the electromagnetic levitation system under matched and unmatched uncertainties. The simulation and experimental results demonstrate the performance of the designed control scheme. The performance indices such as integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE), and integral time square error (ITSE) are compared for both uncertainties to showcase the robustness of the designed control scheme.