Transfer Function Zeros in Noncollocated Flexible Rotor Models

Active magnetic bearing applications in rotating equipment often require that the feedback sensor be separated axially from the magnetic actuator. The stability of the resulting closed loop system can be understood by examining the nature of the plant transfer function between actuator and sensor. In this work, it is demonstrated that when the rotor has negligible damping, such transfer functions can have zeros in the right half of the complex plane, leading to very difficult stabilization and an inherent lack of robustness. This somewhat unexpected result is interpreted in terms of physical response. A computational approach is outlined for computing the zeros and validation is provided by companson to the exact solution for a uniform beam. In addition, the forced response of a more complex rotor is examined, illustrating the physical significance of real zeros.