Nonlinear Control of a Planar Magnetic Levitation System

In this paper, we derive the model of a three-magnet positioning device and design a nonlinear control that stabilizes it. The motivation of this work is to develop tools that may have practical significance to, e.g., photolithography and to create a challenging nonlinear control problem which can be used to test novel nonlinear control approaches. The nonlinear controller designed here transforms the nonlinear system with three positive inputs into a linear system in controllable canonical form with two inputs. A simple linear controller (e.g., an LQR controller) can then be designed to stabilize the system. Finally, the nonlinear controller is robustified to handle uncertainties that affect planar levitation devices.