Constrained control for electromagnetic levitation system with matched and mismatched uncertainties via robust optimal design

In the magnetic levitation (Maglev) train and in many levitation applications, the electromagnet levitation system (EMLS) is the main control element. Its highly nonlinear dynamics and innate instability define its nature. Furthermore, the controller design for this system is further complicated by many external perturbations and modelling uncertainties. To fade away from this drawback, a constrained control for an electromagnetic levitation system with matched and mismatched uncertainties via robust optimal design is proposed in this article. The optimal control approach based on the Hamilton–Jacobi–Bellman (HJB) equation is designed for the bounded robust control problem. A non-quadratic term is added in the performance function to address the range of the constraint control input incorporated by the (HJB) equation. The parametric uncertainties and external disturbances are directly addressed in the cost function. The direct Lyapunov stability theorem is utilised to prove the optimality of the designed controller concerning the performance function that incorporates the additional control effort and highest bound on the matched and mismatched uncertainties. The upper bound of the system uncertainties should be known to the constrained control effort. The stability is proved using the actual dynamics of the EMS. The results obtained from the simulation demonstrate the performance of the proposed controller design. The integral performance indices are compared for matched and mismatched uncertainties with and without constrained control to highlight the resilience of the proposed control technique.