H-infinity controller design for active magnetic bearings considering nonlinear vibrational rotordynamics

摘要

This paper deals with optimal controller design for active magnetic bearing (AMB) systems for which nonlinear rotordynamic behavior is evident, and so vibration predicted by operating point linearization differs substantially to that which actually occurs. Nonlinear H-infinity control theory is applied with a rotordynamic model involving nonlinear stiffness and/or damping terms. The associated Hamilton-Jacobi-Isaacs (HJI) equation is formulated and solved to obtain a state feedback control law achieving specified vibration attenuation performance in terms of the peak L2 gain of the nonlinear system. The method is applied in case study to a flexible rotor/AMB system that exhibits nonlinear stiffness properties owing to rotor interaction with a clearance bearing. Simulations are performed to quantify RMS vibration due to harmonic disturbances and the results compared with the norm-bound values embedded in the HJI equations. A feedback controller design method is then presented that is similar in approach to the standard loop-shaping/mixed-sensitivity methods used for linear systems, and involves augmenting the system model with weighting transfer functions. Experiments are undertaken to compare controller performance for design based on nonlinear and linearized models. The results highlight the shortcomings of applying linear optimal control methods with rotor systems exhibiting nonlinear stiffness properties as large amplitude vibration and loss of rotordynamic stability can occur. Application of the described nonlinear H-infinity control method is shown to overcome these problems, albeit at the expense of vibration attenuation performance for operation in linear regimes.