Nonlinear compensation of active electrostatic bearings supporting a spherical rotor

This paper proposes a nonlinear compensation scheme to deal with the nonlinear, uncertain dynamics of electrostatic bearing systems. A feedback linearization technique that utilizes the approximate nonlinear model of the electric field distribution is employed to compensate for the unstable position stiffness inherent in electrostatic suspension for global stability and enhanced dynamic performance. Robustness of the nonlinear compensation to the model uncertainty is analytically verified in an effort to obtain a more consistent and predictable performance. Theoretical relationship is also developed to relate the characteristics of the proportional-integral-derivative (PID) controller to the dynamic stiffness properties of the linearized electrostatic bearing system. The performance of the proposed nonlinear compensation algorithm is experimentally investigated on a three-degree-of-freedom (3-DOF) electrostatic bearing supporting a spherical rotor. The experimental results demonstrate the superiority of the nonlinear controller over a classical linear control system in transient response, stability, dynamic stiffness, and force-disturbance rejection performance.