Synthesis of controllers based on linear matrix inequalities for a magnetic levitation system

Abstract

This paper presents the results of synthesizing controllers based on Linear Matrix Inequalities (LMIs) for a magnetic levitation system with a strongly nonlinear mathematical model: integral-state feedback control and sliding mode control. Comparative simulation results and evaluations of the controllers in MATLAB/Simulink software have demonstrated that the controllers perform well and are robust to changes in the mass of the object, with the object's position closely following the setpoint signal. However, in cases where system parameters change significantly, the control system with the integral-state feedback controller may operate inaccurately or even become unstable, whereas the sliding mode controller still ensures stability and robustness against changes in system parameters.