Robust-PID controller design for magnetic levitation system using parameter space approach

Recently, implementation of air magnetic suspension systems has become more challenging due to the growing demand for lightweight technologies, comfortable cabins, vehicle safety stability, and pollution control. Magnetic levitation, or Maglev, is the method of propelling a target into the air by adjusting different magnetic forces. The absence of contact and the avoidance of wear and friction phenomena are key considerations in the applications of magnetic levitation technology. Due to the high nonlinearity in the modelling process of such kind of systems, the stabilizing of magnetic levitation has been considered as a challenging task for many researchers in control engineering sector. The computation of all stabilizing PID gains controllers for the magnetic levitation benchmark ED-4810 (Maglev) is demonstrated in this paper using two different scenarios. In the first one, the tuning parameters of the classical PID controller (KP, KI, and KD) are assumed to be the uncertain parameters. The second scenario demonstrates the uncertainty in the transfer function of the system by using the resistance and the inductance as uncertain parameters. The characteristic polynomial of the linearized uncertain model is shown to be an unstable affine polynomial using the Zero Exclusion Theorem and the singular frequencies technique. The parameter space approach is used to illustrate the values of all PID parameters in order to achieve robust stability in the two scenarios. The effectiveness of the presented graphical technique has been verified through MATLAB simulation to obtain robust stability for magnetic levitation systems.