Complex-model-space control of rotating disk vibrations

Abstract

The dynamic characteristics of rotating disks are spin speed dependent and excessive vibrations are likely to take place as the spin speed increases toward the critical speed. At the critical speed, constant stationary force excites resonance of the backward travelling wave which forms nodal diameters together with the forward travelling wave in a mode. In the past, much experimental efforts have been placed on suppressing the measured vibrations of the rotating disk. without fully understanding the behavior of the closed-loop control systems. In the control of rotating disk system, which is a typical distributed-parameter system (DPS), instability of the controlled system is indeed the most important problem to be resolved. Modal state feedback is one of the DPS control schemes which not only guarantees the stability of the closed-loos system but also provides the deep insights into the behaviors of the controlled system. In this work, complex-modal-space control of rotating disk vibrations is presented. Adoption of complex notation reduces the order of the modal equations of isotropic rotating systems and controller design in complex field ensures the isotropic nature of the closed-loop system. In addition, decoupled wave coordinates play a key role in analyzing the controlled behaviors of travelling waves. Three deterministic control schemes, pole assignment, optimal control and proportional and derivative (P_D) control, are separately formulated and analyzed in complex modal space. Pole assignment design is established with four independent real gains. The feedback gain matrix is uniquely determined in complex field because preservatoin of the isotropic nature in the uncontrolled and controlled modal system only allows the assignment of the isotropic eigenstructure. The obtained gain matrix is control energy efficient and shows smallest transient magnitudes of state variables with the prescribed eigenvalues. Optimal modal-space control and modal P-D control...