Nonlinear Control Design for a Magnetic Levitation System

This thesis presents the design of two magnetically levitated high precision positioning systems based on permanent magnet linear synchronous motors (PMLSMs). Magnetic levitation based on PMLSMs requires the motors to operate with a variable airgap length but previous research in the field has studied mainly motors fastened by bearings; therefore, this work first models a motor with free normal dynamics. A 3-DOF levitation device is then designed with basis on the resulting model of the motor. The nature of that system conveys the need for restricting its state in order to guarantee well-definiteness of the controls. Simulations then evaluate the performance of three different stabilization approaches: LQR, standard nonlinear control, and invariance control. Because that 3-DOF device neither controls nor constrains rotation, a more complex machine is introduced in order to regulate five DOF. An invariance controller completes the design of this 5-DOF levitation device.