MSCSG转子系统的扩展双频Bode图稳定性分析方法

为分析洛伦兹力磁轴承驱动磁悬浮控制敏感陀螺（MSCSG）转子偏转过程中的稳定性，针对现有双频Bode图稳定性判据方法仅适用于最小相位系统的不足，提出一种基于扩展双频Bode图的稳定性分析方法。根据洛伦兹力磁轴承工作原理建立了MSCSG转子偏转系统动力学模型；通过变量重构，将实系数双输入双输出系统等效变换为复系数单输入单输出系统；在分析Nyquist曲线与Bode图关联性的基础上，提出针对非最小相位系统的扩展双频Bode图稳定性判据，对不同转速下MSCSG转子系统稳定性进行预测，并通过转速根轨迹曲线预测转子系统的转速稳定区间。所提出的扩展双频Bode图稳定判据结果与时域仿真校验结果相一致，验证了本文所提出的稳定性分析方法的正确性和有效性。

Stability Analysis Method with Extended Double frequency Bode Diagram For Rotor of MSCSG

To analyze the stability in the process when a rotor in magnetically suspended control & sensing gyroscope (MSCSG) is tilted by Lorentz force magnetic bearing, an extended double-frequency Bode diagram is proposed. It can remedy the limitation that the classical double-frequency bode diagram which is only available for minimum-phase system. Based on the working principle of the Lorentz force magnetic bearing, the dynamic model for rotor tilting is established. The real coefficient two-input-two-output system is transformed into the complex coefficient single-input-single-output system by variable reconstruction. In addition, the correlation between the Nyquist curve and the Bode diagram is analyzed. On this basis, a new stability analysis method by extended double-frequency Bode diagram is proposed for the non-minimum phase system, and the stability of the rotor system with different rotation speeds is estimated by this method. The stable rotation speed region is estimated by the speed root locus curve. The time-domain simulation results are consistent with the results estimated by the proposed method. This verifies the correctness and validity of the proposed stability analysis method.