Study on stability and rotating speed stable region of magnetically suspended rigid rotors using extended Nyquist criterion and gain-stable region theory

This paper presents a novel and simple method to analyze the absolute stability and the rotor speed stable region of a magnetically suspended rotor (MSR). At the beginning of the paper, a complex variable is introduced to describe the movement of the MSR and a complex coefficient transfer function is obtained accordingly. The equivalent stability relationship between this new variable and the two traditional deflection angles is also demonstrated in a simple way. The detailed characteristics of the open-loop MSR system with time delay are studied carefully based on the characteristics of its Nyquist curve. A sufficient and necessary condition of absolute stability is then deduced by using an extended complex Nyquist stability criterion for MSRs. Based on the relationship between the rotor speed and gain-stable region proposed in this paper, the rotor speed stable region can be solved simply and directly. The usefulness and effectiveness of the proposed approaches are validated by examples and simulations. •A simple method is proposed to analyze the absolute stability and the speed stable region of magnetically suspended rotors.•Complex variables and complex transfer functions are employed to describe the movement and dynamics of MSRs.•A sufficient and necessary condition of absolute stability is deduced by using an extended Nyquist stability criterion.•Based on the relationships between rotor speed and gain-stable region, the rotor speed stable region is calculated.