Nonlinear dynamics and static bifurcations control of the 12-pole magnetic bearings system utilizing the integral resonant control strategy

Abstract

In this study, the Integral Resonant Controller (IRC) is presented along with the Proportional-Derivative (PD) controller as a novel control technique to control the dynamical behaviors of the 12-pole rotor active magnetic bearing system. According to the proposed control strategy, the system model has been derived as a two-degree-of-freedom nonlinear dynamical system coupled with two first-order filters. The obtained mathematical model has been analyzed utilizing the asymptotic analysis. The nonlinear algebraic system that governs the steady-state vibration amplitudes and corresponding phase angles of the considered system has been extracted. The influence of the IRC control parameters on the rotor dynamics has been explored by plotting the different bifurcation diagrams. The analytical investigations demonstrated that the vibration suppression efficiency of the combined controller (i.e., PD and IRC) is proportional to the product of control and feedback gains of the IRC as well as the derivative gain of the PD-controller. In addition, it is found that the controller efficiency is inversely proportional to both the square of the internal loop feedback gain of the IRC and the position gain of the PD-controller. Accordingly, an objective function has been derived to design the best control gains of the proposed controller strategy. The analytical and numerical simulations confirmed that the suggested control method can suppress the system vibration and eliminate the catastrophic bifurcation behaviors if the control gains are selected according to the proposed objective function. Finally, the effect of failing one of the coupled integral resonant controllers on the rotor dynamics has been explored as a precautionary procedure. It is found that the failure of one of the coupled integral resonant controllers may breakdown the bifurcation symmetry of the rotor system, but the system does not lose its stability.