Sub-Optimal Control Law for Active Magnetic Bearings Suspension

This paper deals with the comparison of three types of sub-optimal control law for the stable levitation of a turbojet shaft, sustained by two radial active magnetic bearings (AMBs). Shaft is considered rigid for the procedure simplification. The utilized approach leads to development of different sub-optimal control laws to use in speed-varying simulations in the angular speed of the shaft. The first control matrix is obtained by explicit relationships of the parameters of the control law vs. speed, obtained using a curve-fitting procedure neglecting the speed-varying elements out of the main diagonal of each single block constituting the entire control matrix. The second control law is obtained by control matrix set to zero angular speed during speed-varying simulations. The third control matrix is obtained by the second neglecting the elements out of main diagonal. Time response to the step input shows difference in performance of the AMBs when varying the control law. All control laws are tested by means of simulation. The study allows showing like a polynomial representation of the control matrix, developed to the variation of angular speed, is able to maintain stable the magnetic levitation.