Dynamic modeling, input-shaped maneuvering and vibration suppression of flexible body using quasi-coordinates and euler parameters

Abstract

In dealing with the dynamics of a flexible body, the rigid-body motions and elastic vibrations are analyzed separately. However, rigidbody motions cause vibrations, and elastic vibrations affect rigid-body motions, indicating the inherent coupling between rigid-body motions and elastic vibrations. The coupled equations of motion for a flexible body can be derived by means of Lagrange’s equations in terms of quasi-coordinates. The resulting equations of motion are hybrid and nonlinear. This paper proposes a unified approach for the equations of motion for a flexible body based on the perturbation method and the Lagrange’s equations of motion in terms of quasicoordinates and Euler parameters to analyze a more general case maneuvering. The resulting equations consist of zero-order nonlinear equations of motion which depict rigid-body motions and first-order time-varying linear equations of motion which depict perturbed rigid-body motions and elastic vibration. Hence, the input-shaped maneuvering can be applied to the zero-order equation considering the induced vibrations. Since the input-shaped maneuvering alone cannot achieve vibration suppression, the vibration suppression controller combined with the input-shaped maneuvering is proposed in this study. As a numerical example, a hub with elastic appendages is considered. Numerical results show that the unified modeling approach proposed in this paper is effective in numerical simulation and control design.