Performance enhancement of a 12-pole AMB model via robust control approach

In this study, I investigated the energetic behavior of a twelve-pole active magnetic bearing (AMB) framework with a nonlinear proportional derivative cubic velocity feedback (NPDCVF) controller in the presence of mixed excitations and primary resonance ( $\Omega \cong {\omega }_1,\Omega \cong {\omega }_2$). The controller combines classic proportional-derivative (PD) control with nonlinear cubic velocity feedback to improve stability, reduce rotor oscillations, and increase robustness. A detailed mathematical framework of the 12-pole AMB system was developed, accounting for magnetic force nonlinearity, dynamic interactions between poles, and the effects of rotor eccentricity. The motion equations (ME) were investigated using the multiple time scales approach (MTSA), and the approximation solutions (AS) were numerically validated with the fourth-order Runge-Kutta (4RK) method. Simulations were performed to compare five controllers: PD, integral resonant controller (IRC), positive position feedback (PPF), nonlinear integral positive position feedback (NIPPF), and the proposed NPDCVF scheme. MATLAB 18.2 numerical simulations (4RK) were employed to analyze time-history responses, the effects of system parameters, and the performance of controllers. The time-domain results showed that the NPDCVF controller delivers the quickest vibration reduction, the least overshoot, and increased robustness to disturbances and parameter changes. Time-domain, frequency-response, and phase-plane analyses confirmed wider stability margins and increased damping effectiveness. Additional nonlinear dynamical assessments, such as bifurcation charts, frequency response curves, and stable and unstable zones, showed that nonlinear oscillations have been successfully reduced and the AMB system has stabilized reliably.