Pseudospectral Optimal Control of Active Magnetic Bearing Systems

In this paper the optimal control framework is formed to control rotor-active magnetic bearing (AMB) systems. The multi-input–multi-output non-affine model of AMBs is well established in the literature and represents a challenging problem for control design, where the design requirement is to keep the rotor at the bearing centre in the presence of external disturbances. To satisfy the constraints on the states and the control inputs of the AMB nonlinear dynamics, a nonlinear optimal controller is formed to minimizethe tracking error between the current and desired position of rotor. To solve the resulted nonlinear constrained optimal control problem, the Gauss pseudospectral collocation method (GPCM) is used to transcribe the optimal control problem into a nonlinear programming problem (NLP) by discretization of states and controls. The resulted NLP is then solved by a well-developed algorithm known as SNOPT. The procedure for modeling, compilation and solving of resulted optimal control problem is done in Matlab optimal control software known as PROPT. The results illustrate the effectiveness of the proposed approach to deal with the control of AMBs.