Modeling and implementation of 1-D inverted magnetic needle system using a robust sliding mode controller

In this paper, we propose a novel problem in control systems area involving the control of a magnetic needle in the presence of an external magnetic field. A magnetic needle when restricted to rotate about a single axis in an external magnetic field, by pivoting its center will produce a stable and unstable equilibrium. Here, we present the detailed mathematical modeling of the 1-D inverted magnetic needle system and its control in the unstable equilibrium point. We use sliding mode controller (SMC) to achieve the control objectives. The simulation results are validated with the experimental results. For achieving a close match, we consider sensor and actuator nonlinearities. Further, its robust performance is compared with proportional-derivative (PD), proportional-integral-derivative (PID) controllers in the presence of system parameter uncertainty, disturbance, and sensor delay. We also study the effect of change in SMC parameters, proportional and derivative gains on the system performance. It is to be noted that the proposed experimental setup can be extended to a much more general and complex system, both in modeling as well as control design leading to a new benchmark problem in the control system.