2-D Inverted Magnetic Needle Modeling and it's Control: A Novel Benchmark Problem in Control System

In this paper we introduce a novel benchmark problem to study the control of magnetic needle with two degrees of rotational freedom in a uniform magnetic field. Magnetic needle in an external magnetic field has stable and unstable equilibrium points, which depends on it's orientation. Our idea is to control the magnetic needle near it's unstable equilibrium point. Dynamics of the system is derived using Lagrangian energy based technique. The nonlinear system dynamics are linearized at unstable equilibrium point and the controllers are designed for this linear system, and the same controllers are applied to nonlinear system. The difference in tracking performance for linear and nonlinear system is observed using PD, PID, lead, lead lag compensators and state feedback, feed forward integral controller and H∞, quantitative feedback controllers. Further, control effort for all the above controllers are computed.