Modeling and Control of Single-Link Flexible Arms With Lumped Masses

Abstract

This paper deals with the modeling and control of a special class of single-link flexible arms. These arms consist of flexible massless structures having some masses concentrated at certain points of the beam. In this paper, the dynamic model of such flexible arms is developed and some of the control properties are deduced. A robust control scheme to remove the effects of friction in the joins is proposed. The control scheme consists of two nested feedback loops, an inner loop to control the position of the motor and an outer loop to control the tip position. The inner loop is described in other publications. A simple feedforward-feedback controller is designed for the outer loop to drive the beam accurately along a desired trajectory. Effects of the changes in the tip’s mass are studied. This modeling and control method is then generalized to the distributed-mass flexible beam case. Finally, experimental results are presented.

Strain gauge based control of single-link flexible very lightweight robots robust to payload changes

“…This proposed feedforward has been successfully tested in previous experimental works where it was implemented with direct driven motors as in [15,18], and in motors with reduction gears [16,19]. The block diagram of the PD inner loop control system is represented in Fig.…”

Control of Flexible Manipulators. Theory and Practice

“…3), where the inertia produced by the point mass rotations is rejected. An example of this technique can be found in (Feliu et al, 1992). Fig.…”

“…The objective is to obtain a simplified model (finite number of vibration modes) of the differential equation that characterizes the dynamics of the link. A number of models can be found in the literatures obtained from methods such as the truncation of the infinite dimensional model (Cannon & Schmitz, 1984); the discretization of the link based on finite elements (Bayo, 1987); or directly from concentrated mass models (Feliu et al, 1992). The hypothesis of negligible gravity effect and horizontal motion are considered in the deduction of the model equations.…”

“…The dynamic model of the flexible link is obtained from some geometric and dynamic equations as follows (see (Feliu et al, 1992) for more details):…”

Experimental Validation of Nonlinear Dynamic Models for Single-Link Very Flexible Arms

“…Different dynamic models have been proposed for analysis and control of these robots: the basic spring-mass discrete model ( [2], e.g. ), lumped masses models ( [3], e.g.) linear Euler-Bernoulli PDE ( [4], e.g.…”