Self–Sensing Magnetic Bearings Driven by a Switching Power Amplifier

Active magnetic bearings require some form of control, based on feedback of the position of the suspended object, to overcome open–loop instability and to achieve targeted system performance by modifying the bearing dynamics. In many applications of magnetic bearings, a need to eliminate discrete position sensors may arise either from economic or reliability considerations. Magnetic bearings which estimate the position from the information available in the electromagnet signals are referred to as “self–sensing”. Previously, there have been two mainstream approaches for developing self–sensing magnetic bearings. One approach is to use a Luenberger observer designed from a linearized state–space representation of voltage–controlled magnetic bearings. Due to the nonlinearities involved with the physics of the bearing, this approach has limited applicability. The other approach considers the air gap as a parameter of the system rather than a state. Previous attempts using parameter estimation were hampered by force feed–through (the infiltration of force information into the position estimates). In this dissertation, a nonlinear parameter estimation technique is presented by which the position of a rotor supported in magnetic bearings may be deduced from the bearing current waveform. The bearing currents are presumed to be developed by a bi–state switching amplifier which produces a substantial high frequency switching ripple. The amplitude of this ripple is a function of power supply voltage, switching duty cycle, and bearing inductance. Inductance is predominantly a function of the bearing air gap or, equivalently, the rotor position, while the duty cycle is fundamentally dependent upon the developed bearing force. Ideally, the estimator should exactly extract rotor position information while perfectly rejecting bearing force information. When the bearing is a perfect inductor, the aforementioned functional relationships are easily established and the gap dependence is monotonic. Since voltage and duty cycle are both easily measured, the relationships can be inverted with a non–linear parameter estimator to extract the rotor position. The estimator embeds a model of the bearing inductance parameterized by the air gap. This simulation is subject to the same switching voltage as the actual magnetic bearing coils. A feedback loop compares the simulated current waveform with the actual current and adjusts the gap length parameter until the two waveforms match. The performance of the estimator is evaluated both by computer simulation and experiment. The technique is demonstrated to produce a fairly wide bandwidth sensor (at least 1 kHz) with acceptably low feed–through of the bearing force. The estimator i also displays excellent linearity (less than 2 % deviation from linear). Nonidealities such as saturation, hysteresis, and eddy currents are investigated to assess their effects on the performance of the estimator. The embedded inductance model can easily incorporate these nonidealities without affecting the estimation performance.