Robust Control under Uncertain Equilibrium States: Application to Magnetic Levitation Systems

A robust output derivative feedback controller is investigated for the local stabilization of dynamic systems under uncertain or unknown equilibrium states. The proposed controller is designed such that the closed-loop system exponentially converges to the equilibrium states of the system, even when the location of such equilibrium is unknown to the controller. For the case when norm-bounded dynamic uncertainty is present in the system model, robust stability conditions are derived in the linear matrix inequality form to guarantee the robust stability of the closed-loop system. The proposed solution is evaluated on a magnetic levitation system, in which two magnetic disk are to be levitated at an uncertain magnetic equilibrium. Experimental results demonstrate the effectiveness and robustness of the proposed output derivative feedback controller.