Delay dynamics of a levitating motor with two-limit control strategy

Abstract

In a recent work (Shayak, 2019), I have proposed a new comparator-based control algorithm for a magnetically levitated motor. The rotor dynamics are governed by a sixth order nonlinear differential equation, whose stability analysis is treated as given. Here we consider this device from a dynamical systems viewpoint. We first present a simplified model which is a second order nonlinear delay differential equation. We then see that in this equation, a fixed point which is unstable in the absence of control gets converted to a small-amplitude stable limit cycle in its presence. Extrapolating from the simplified model, we find that insufficient damping can create an instability but it can be countered by increasing the inverter voltage, decreasing the inverter switching period, and relaxing the displacement tolerance value. Extensive simulation results show that all predictions made on the basis of the simplified model are applicable to the original system.