Time-varying feedback linearization of magnetic bearing actuators

Magnetic bearings are a non-contact, lubricationless, and nearly frictionless bearing technology. For this reason, magnetic bearing devices enjoy an increasing popularity in applications whose harsh environment would lead to premature failure of conventional bearings. Magnetic bearings are fundamentally nonlinear devices. To handle nonlinearities, magnetic actuators are normally linearized by a Jacobian method. The resulting linear model of current and displacement expresses a simple relationship from bearing current input to actuator force output. This is an effective technique in some applications since the linear model comprises two parameters, both of which can be accurately measured. However, for cases when a large range of operation conditions is desired, such a technique is not powerful enough. With recent advances in nonlinear geometric control and digital computers, it has become desirable and practical to develop and implement a feedback linearization technique in control of magnetic bearings. Unlike Jacobian linearization for small currents and displacement, feedback linearization linearizes the actuator over a wide range of operating conditions. Furthermore, feedback linearization is capable of providing a framework for the control engineer to achieve better bearing load capacity, slew-rate, and power objectives while also guaranteeing controllability. Although this method has been applied to magnetic bearing systems, prior works offer no solution applicable to magnetic bearings levitating complex structures like a flexible rotor. Achieving this goal requires a new perspective wherein the bearing actuator is linearized independently of the rotor dynamics. First, the rotor states in the actuator equations are viewed as measured time-varying signals. Secondly, the system outputs are chosen as the actuator force and bias. With the aid of time-varying feedback linearization, the solveability criteria for the linearization problem are developed and understood within the context of magnetic bearings. Finally, as an illustration, several cases are examined with emphasis on practical concerns.