State feedback and proportional-integral-derivative control of a magnetic levitation system

The paper presents the design of two low-cost control solutions (CSs) for a laboratory equipment, a state feedback CS and a proportional-integral-derivative CS. The two CSs are dedicated to the position control of a ferromagnetic sphere in a Magnetic Levitation System with Two Electromagnets (MLS2EM) and are designed in order to stabilize and to ensure the zero steady-state control error. The nonlinear mathematical model (MM) of the MLS2EM is derived on the basis of the first principles equations with experimentally identified parameters. This unstable and nonlinear MM is next linearized at seven operating points. A system response performance analysis of the best state feedback gain matrix expressed as very good dynamics behavior and settling time is done in order to validate the proposed CSs. Some real-time experimental results are presented in order to validate the proposed control solutions.