Gain-scheduled control of a magnetic bearing with low bias flux

Conventional active magnetic bearings (AMB) use a bias current (or flux) to achieve greater linearity and dynamic capability. Bias, however, results in undesirable rotating losses and consequent rotor heating. Gain-scheduled control of a magnetic bearing with low bias is investigated. A single degree-of-freedom system consisting of a mass and two opposing electromagnets is considered. The nonlinear system is formulated as a quasi-LPV (linear parameter varying) system by linearizing the quadratic and the control input saturation nonlinearities. The gain-scheduled controller guarantees performance over a certain range of input saturation. The closed loop system is then transformed into linear fractional transformation (LFT) form with shared linear time varying (LTV) uncertainties and unshared multiplicative linear time invariant (LTI) uncertainty. The robust analysis consists of finding an upper bound via iteration between two minimizations, namely, a μ analysis problem and a scaled L₂ gain problem. The techniques developed may also be applied to many other applications which contain opposing quadratic actuators with limits on control input