An optimal proportional integral derivative tuning for a magnetic levitation system using metamodeling approach

A magnetic levitation system (MLS) is a complex nonlinear system that requires an electromagnetic force to levitate an object in the air. The electromagnetic field is extremely sensitive to noise which can cause the acceleration on the spherical object, leading it to move into the unbalanced region. This paper presents a comparative assessment of controllers for the magnetic levitation system using proportional integral derivative (PID) controller based optimal tuning. The analysis was started by deriving the mathematical model followed by the implementation of radial basis function neural network (RBFNN) based metamodel. The optimal tuning of the PID controller has offered better transient responses with the improvement of overshoot and the rise time as compared to the standard optimization methods. It is more robust and tolerant as compared to gradient descent method. The simulation output using the radial basis based metamodel approach showed an overshoot of 9.34% and rise time of 9.84 ms, which are better than the gradient descent (GD) and conventional PID methods. For the verification purpose, a Simscape model has been developed which mimic the real model. It was found that the model has produced about similar performance as what has been obtained from the Matlab simulation