Modeling Method for Flexible Multibody Systems with Arbitrary Boundary Conditions by Using Extended Reduced-Order Physical Model (2nd Report, Motion and Vibration Control of a Two-link Flexible Robot Arm)

Abstract

This paper deals with the effectiveness of an Extended Reduced-Order Physical Model (Extended Model) with arbitrary boundary condition for motion and vibration control system design. The Extended Model is proposed to apply to the simultaneous motion and vibration control of elastic structures. The Extended Model consists of some rigid bodies which are called as rigid body elements and stiffness elements. To design rigid body elements, four dynamical conditions are used (1) Total mass and Total moments of inertia, (2) Position of center of gravity, (3) Modal mass and Orthogonality, (4) Modal momentum and Modal angular momentum. The (1) - (4) values of a modeling object are needed to identify masses and moments of inertia of rigid body elements. In the case of that an elastic body has general boundary conditions, the Modal momentum and the Modal angular momentum are not zero and needed to be identified by any means. However, it is not always easy to identify these values. Therefore, a novel formulation to identify mass and inertia matrices is presented that utilizes dynamical conditions for the original object. subjected to free boundary conditions. The presented formulation is applied to the modeling of the two-link flexible robot arm. Each flexible link is modeled by using the proposed modeling method. The two-link flexible robot arm is built by combining two independently identified link models. The effectiveness of “an Extended Model with an arbitrary boundary condition” is shown through the simulation and experimental control results.