Pareto Optimal Decentralized Control of a Rotor in Electromagnetic Bearings

Abstract

The problem of the optimal stabilization of a vertical rigid rotor rotating in two electromagnetic bearings is considered. A quantitative estimate of transient processes is based on the maximal deviation of the rotor from the equilibrium state and the maximal value of the current intensity in the windings of electromagnets. The use of linear matrix inequalities allow synthesizing the Pareto optimal control laws in the form of linear state-feedback, as well as decentralized control laws, which are defined by the displacements of the rotor in each electromagnetic bearing. The Pareto optimal criteria for centralized and decentralized control laws are compared. It is shown that utilization of simple easily realizable decentralized control laws only slightly worsens transient processes.