Integral Resonant Controller to Suppress the Nonlinear Oscillations of a Two-Degree-of-Freedom Rotor Active Magnetic Bearing System

Abstract

Within this article, the nonlinear vibration control of the rotor active magnetic bearings system is tackled utilizing the integral resonant controller for the first time. Two integral resonant controllers are proposed to mitigate the system lateral oscillations in the horizontal and vertical directions. Based on the suggested control technique, the whole system dynamical model is derived as a two-degree-of-freedom nonlinear system (i.e., rotor system) coupled linearly to two first-order filters (i.e., the integral resonant controllers). The nonlinear autonomous system that governs the oscillation amplitudes of the controlled system as a function of the control parameters is extracted by applying perturbation analysis. The obtained autonomous system showed that the linear damping coefficients of the rotor system are functions of the control gains, feedback gains, and internal loop feedback gains of the coupled controller. Accordingly, the sensitivity of the rotor oscillation amplitudes to the different control parameters is explored. The stability margins and the optimal control gains are reported via plotting the different stability charts in two-dimensional space. The main acquired results demonstrated that the vibration suppression efficiency of the proposed controller is proportional to the product of both the control and feedback signal gains, and inversely proportional to the square of the internal loop feedback gains. In addition, the analytical investigations confirmed that the proposed integral resonant control method can force the rotor system to respond as a linear one with a single periodic attractor when the control parameters are designed properly. Finally, numerical simulations are performed that have illustrated the excellent correspondence with the obtained analytical results.