Modeling and control of inverted magnetic needle: Energy based nonlinear controller for one degree of freedom system

Abstract

In this paper, we study the design of energy based controller to control the magnetic needle at desired location. The magnetic needle is allowed rotate about one axis, in the external magnetic field by pivoting its center. Due to attraction and repulsive forces between the magnetic needle and external magnetic field, the magnetic needle will have two equilibrium points, one is stable and the other is an unstable equilibrium point. The magnetic needle dynamics are derived by considering uniform and non-uniform external magnetic field. The controller is designed to control the magnetic needle at the desired location. Different control strategies are derived based on the Lyapunov's function. Different control strategies steady state and transient performance are compared based on the simulation results.