Modelling and Stability Analysis for a Magnetically Levitated Slice Motor (MLSM) with Gyroscopic Effect and Non-Collocated Structure Based on the Extended Inverse Nyquist Stability Criterion

Abstract

Stability of the rotor motion is the precondition for the reliable operation of magnetically levitated slice motors (MLSMs). However, with gyroscopic effect and non-collocated structure existing simultaneously, its stability analysis faces a tremendous challenge, because the torsional motions couple with the radial translational ones, making MLSM a multiple-input and multiple-output (MIMO) system with high order. Therefore, in this paper, we first establish a novel MIMO rotor dynamics closed-loop model and further convert it into an equivalent single-input and single-out (SISO) feedback control system by constructing complex variables, meanwhile reducing the system order by half. Beneficial from the equivalence between the MIMO and SISO systems, the sufficient and necessary conditions of the absolute stability of MLSM are derived by the extended inverse Nyquist stability criterion in the complex domain. Additionally, the effectiveness of the proposed modelling and stability analysis method is evaluated by simulation and experimental results. Thus, apart from PID parameters, this paper demonstrates that the stability of MLSM is also affected by the coupling of gyroscopic effect and non-collocated structure, which should serve as an essential guideline for system regulation of MLSM.