Nonlinear oscillation of active magnetic bearing-rotor systems with a time-delayed proportional-derivative controller

A time-delayed proportional-derivative controller is applied to suppress the nonlinear vibration of a rigid rotor suspended by the active magnetic bearing (AMB) subjected to multiple excitations. The rotor eccentricity, the parametric excitations, the gravity of the rotor, and the coupling of the electromagnetic force between horizontal and vertical directions are taken into consideration in the dimensionless governing equation. The method of multiple scales is applied to obtain the approximate solution. Based on the Routh-Hurwitz stability criterion, the stability of steady-state solutions is discussed. Then, the influence of the control parameters and the time delay in the proportional and derivative control loop on the system is studied. And the optimal operating conditions are given. The results show that there exist multi-solutions and jump phenomena under certain conditions. Finally, the numerical solutions are obtained by applying ODE45 and DDE23 MATLAB solvers. And the analytical solutions have an excellent agreement with the numerical solutions.

Automated summary

In this study, a time-delayed proportional-derivative controller is applied to suppress the nonlinear vibration of a rigid rotor suspended by active magnetic bearings (AMB) under multiple excitations. The governing equation considers the rotor eccentricity, parametric excitations, rotor gravity, and electromagnetic force coupling in horizontal and vertical directions. The method of multiple scales is used to obtain the approximate solution, and the stability of the steady-state solutions is analyzed using the Routh-Hurwitz stability criterion. The influence of control parameters and time delay on the system is investigated, and optimal operating conditions are determined. The results show the existence of multiple solutions and jump phenomena under certain conditions. Numerical solutions obtained using ODE45 and DDE23 MATLAB solvers demonstrate excellent agreement with the analytical solutions.