Vibration reduction of flexible structures using torque wheel mechanism

Abstract

A technique is presented and experimentally validated for reducing motion-induced vibration of a flexible structure system during and after a motion. The proposed method utilizes wheel-like rigid bodies, which are denoted as torque wheels. The wheels are to generate the torque that is required in canceling out unwanted vibration modes of the manipulator. If, for example, a flexible link rotates suddenly, the link deforms due to its inertia and the deformation may bring undesirable vibration during and after the rotation. A torque wheel is introduced to neutralize the rotation-induced force, so its vibration as well as deformation is minimized. Lets consider a multi-link flexible manipulator which is described by a mathematical model having m d.o.f.s. To make the motion-induce force of the system be perfect zero requires the same number of torque wheels as the d.o.f.s. In order to reduce the d.o.f.s of the model without loss of accuracy, lets apply a concept of modal space to this system. In general, a modal space is defined as a space spanned by eigenmodes from a linear time invariant system. The multi-link manipulator dynamics is basically nonlinear and becomes at least a linear time variant problem if linearized about a nominal trajectory. Therefore, a concept of instantaneous eigenproblem defined at a specific time is introduced and finally the original nonlinear model is approximated by a series of instantaneous linear time invariant models along the nominal trajectory. The driving torque of the wheels whose reactive torque eliminates the motion-induced modal force of the manipulator is consecutively obtained through an instantaneous eigenproblem given at every time step. The entire torque profile is to be synthesized with the discrete torque values. In this study, an experimental two-link flexible manipulator system has been built to study the dynamics and vibration control of a multi-link system. The arm consists of two flexible steel links, a rigid wheel...