Dynamics modeling and Causal Ordering Graph representation of a non minimum phase flexible arm fixed on a cart

摘要

The dynamics of a flexible system is studied in this paper. The system considered is modeled by an Euler-Bernoulli flexible beam fixed on a moving cart for which the effect of beam's translation is included in the overall dynamics. Modal analysis is used to derive the exact eigensolutions which satisfy the described geometric boundaries conditions The equations of motion are determined using the Assumed Mode Method A criterion is proposed to prove the non-minimum phase nature of such flexible structure. An improved Lumped Constants model is suggested to represent the behavior of the system which replaces the classical two mass-spring model. A link between the parameters of the flexible model and the suggested Lumped Constants model is then given. The equation of motion of the Lumped Constants model is expressed in a Causal Ordering Graph representation and numerical simulations of the open-loop response of the system are carried out to show the influence of the system's parameters. This method has been applied to the modeling of an industrial robot.