Nonlinear Control of a Benchmark Beam

Magnetic bearing control schemes frequently use a bias current together with a superimposed control current to improve actuator gain and linearity. However, even in no load conditions, there is power loss due to the bias currents. There are ohmic losses in the coils, and in high-speed machines there are eddy-current and hys-teresis losses in the rotor because of the bias uxes. The force slew-rate limit of magnetic bearings is determined by a combination of ampliier saturation voltage and ux bias in the bearings. Higher bias levels imply better slew-rate performance. The desired slew-rate limit is often used to set the bias level and knowledge of disturbance forces is important. In this paper a variable bias scheme is developed to reduce electrical power loss while maintaining the control performance similar to conventional bias control. Two diierent bias schemes are proposed in this paper { (1) A linear bias scheme (2) A hyperbolic bias scheme. A bias-dependent feedback linearization approach is applied to both systems to make the input/output (i/o) relation of the system linear, and an observer-based stabilizing controller is designed to stabilize the nominal closed loop system. The resulting closed loop system dynamics are independent of bias except for ampliier saturation. The bias is minimized while avoiding ampliier saturation and singular-ity in feedback linearization with a separate bias control loop.