Optimum vibration control of distributed parameter rotor bearing systems by using electromagnetic bearing

Abstract

As the modern rotor systems have a tendency of being operated at high speed and designed to be lighter, the control of excessive vibration becomes more and more important because of increasing requirement in accuracy and reliability. Since the flexible rotor bearing system is a typical hyperbolic type distributed parameter system, the control, passive or active, not accounting for such a nature often does not yield satisfactory performance. The primary objective of this study is to develop efficient control design methods which account for and use the distributed parameter and isotropic properties. The output feedback control scheme accounts for the practical aspects such as the observation and related stability problems caused by spillover effects, while the optimal design deals mainly with the theoretical and numerical aspects. Optimal pole assignment in distributed parameter control systems is established and the existence of optimal solution is proven in case of compact linear feedback. The method, an extension of the finite dimensional design, gives the solution of the operator Riccati equation, which is known to be one of the most difficult problems faced by the designers. By adopting the complex notation for the isotropic systems, it is shown that the closed loop eigenstructure is determined, contrary to the real field design, so as to preserve the isotropic property. In order to utilize the symmetric property between the two directional vibrations: vertical and horizontal or forward and backward, a new control scheme is designed by introducing the complex state for the systems having the isotropic property. The algebraic relations concerning distribution of the eigenvalues of complex matrices are developed so as to cluster the poles into specified regions, rather than fixed positions, imposing the relative stability margin, e.g.. uniform damping or uniform damping ratio. The closed loop eigenstructure has the direct one-to-one relation with the physic...