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

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 dewloped 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 fedforward-feedback controller is designed for the outer loop to driw the beam accurately along a desired trajectoty. 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, experimentaf results are presented. This paper deals with the modeling and control of a special class of single-link, lumped-mass, flexible arms. These arms consist of massless flexible structures that have masses concentrated at certain points of the beam (see Fig. 1). Although the translations of these masses produce stresses in the flexible structure, their rotations do not generate any torque in the beam. Therefore, the number of vibrational modes in the structure coincides with the number of lumped masses. Book (1979) studied the case of two rigid masses connected by a chain of massless beams having an arbitrary number of rotation joints. Our problem differs from this in the sense that our structure has only one rotation joint and an arbitrary number of lumped masses. These two particular structures are studied because: Some lightweight robots and other applications can be reasonably approximated by these models. Their dynamics may be easily modeled as compared to distributed-mass flexible arms. Interesting properties for the control of flexible arms are deduced from their dynamic models. A method to control these arms is inferred from the structure of the model. The influence of changes in the tip’s mass are easily characterized. Given a distributed-mass flexible arm, there always exits a truncated dynamic model which is of the same form as the lumped-mass flexible arm model and which reproduces the dynamics of the measured variables. This allows us to generate the above mentioned control method to the case of distributed-mass flexible arms. - Contributed by the Dynamic Systems and Control Division for publication