Modeling and nonlinear controller design of 1-D inverted magnetic needle in an nonuniform magnetic field

In this paper, we study the detailed modeling of the magnetic needle in a nonuniform external magnetic field. Center of the magnetic needle is pivoted so that it is allowed to rotate about one axis. A magnetic needle placed in an external magnetic field has two equilibrium points, one is stable and the other is unstable. A passivity based non-linear controller is designed for nonuniform external magnetic field system, and its tracking performance is studied at the unstable equilibrium point. The transient and steady state performance are compared between different control strategies in terms of settling time, peak overshoot, the steady state amplitude of oscillations. Further, the control strategies designed for uniform external magnetic field system are applied to the nonuniform external magnetic field system, to study the change in performance when compared to the designed controller for nonuniform external magnetic field system. The conclusions are made based on the simulation results.