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.

在最近的工作中（Shayak，2019），我提出了一种基于比较器的新型磁悬浮电机控制算法。转子动力学由六阶非线性微分方程控制，其稳定性分析如给定。在这里，我们从动力学系统的角度考虑该设备。我们首先提出一个简化的模型，它是一个二阶非线性延迟微分方程。然后，我们看到在该方程式中，在不存在控制的情况下不稳定的不动点在存在时转换为小幅度稳定的极限环。从简化模型推论，我们发现阻尼不足会产生不稳定性，但是可以通过增加逆变器电压，缩短逆变器开关周期并放宽位移容差值来解决。