This paper deals with rotor systems that suffer harmonic base excitation when supported on magnetic bearings. Magnetic bearings using conventional control techniques perform poorly in such situations mainly due to their highly nonlinear characteristics. The compensation method presented here is a novel optimal control procedure with a combination of conventional, proportional, and differential feedback control. A four-degree-of-freedom model is used for the rotor system, and the bearings are modeled by nonlinear expressions. Each disturbance frequency is expected to produce a multiharmonic system response, a characteristic of nonlinear systems. We apply optimal control choosing to minimize a performance index, which leads to the optimization of the trigonometric coefficients in the correction current function. Results show that the control technique suppresses rotor vibration to amplitudes that were significantly smaller than the disturbance amplitudes for the entire range of disturbance frequencies applied. The control technique explored in this paper is a promising step towards the successful application of magnetic bearings to systems mounted on moving platforms.

Magnetic bearings are non-contacting, with the rotor being suspended between electromagnets, and therefore they can eliminate the need for lube oil and reduce machinery wear. The magnetic bearing is naturally unstable, and very nonlinear. This paper proposes a method designed to suppress the motion of a nonlinear magnetic bearing system rotor due to base excitation. The method combines PD feedback with feedforward optimal control, where a measured base motion is used to select a control signal designed to suppress the rotor response. The signal is generated from a combination of subharmonic frequencies and optimized coefficients stored in a lookup table. The trigonometric collocation method (TCM) is used to generate solutions for the four degree-of-freedom system made up of a shaft suspended at each end by a magnetic bearing. The TCM method uses a trigonometric series to simulate the multiharmonic behavior of each degree-of-freedom of strongly nonlinear systems. The method is easy to use and its advantage over numerical methods is that it demands less computation, particularly with higher numbers of degrees-of-freedom.

This paper considers a one degree of freedom rotor supported on an electromagnetic bearing in a feedback control loop. A nonlinear model of an electromagnetic bearing is developed and a nondimensional model is derived for the system with two distinct parameters corresponding to the controller gain and the static load. Nonlinear analysis is carried out as a function of these two parameters and bifurcation diagrams are derived. The results reveal a very interesting panoply of fixed points with varying stability conditions. Numerical simulations are carried out to confirm the results of nonlinear analysis. Practical implications of the nonlinear analysis results are discussed.

The paper deals with rotor systems that suffer harmonic base excitation when supported on magnetic bearings. Magnetic bearings using conventional control techniques perform poorly in such situations mainly due to their highly nonlinear characteristics. The compensation method presented here is a novel optimal control procedure with a combination of conventional, proportional and differential feedback control. A four degree of freedom model is used for the rotor system, and the bearings are modeled by nonlinear expressions. Each disturbance frequency is exprcted to produce a multi-harmonic system response, a characteristic of nonlinear systems. We apply optimal control choosing to minimize a performance index, which leads to the optimization of the trigonometric coefficients in the correction current function. Results show that the control technique suppresses rotor vibration to amplitudes that were significantly smaller than the disturbance amplitudes for the entire range of disturbance frequencies applied. The control technique explored in this paper is a promising step towards the successful application of magnetic bearings to systems mounted on moving platforms.