Effect of Payload on the Dynamics of a Flexible Manipulator—Modeling for Control

Abstract

The “exact” and pole/zero transfer functions are developed for a flexible beam-like single link arm with actuator on one end and payload on the other. This model represents a broader class of actuator hub and payload mass properties than is found in prior literature. The dependence of dynamics on the hub and payload inertia characteristics are studied and graphs are provided to facilitate estimation of poles and zeroes for any similar plant. It is shown that a 10:1 reduction in fundamental frequency and substantial change in the zeroes results from variations in payload through a practical range. Payload rotary inertia is shown to cause a qualitative change in the arm tip zeroes resulting in loss of observability/controllability in some cases. Results provide insight into the two-link problem and it is shown that complex values zeroes may result if the second arm is allowed to “fold back.” Implications to plant modeling and control design are discussed including sensor placement and model order reduction issues. Analytical results are compared to those measured on an experimental arm and show very good agreement in modal frequency and shape.

Prototyping a simple small smart robotic arm — Manipulator

“…Hence, the existing heavy rigid manipulators are shown to be inefficient in terms of power consumption or speed with respect to the operating payload [2]. Also, the operation of high precision robots is severely limited by their dynamic deflection, which persists for a period of time after a move is completed [3]. These conflicting requirements.…”

Modeling of a One Flexible Link Manipulator

“…In contrast with most studies, the frequencies were under-estimated because the model did not include the base and load inertias. Parametric and simulation studies were also performed to investigate the influence of different system parameters on the natural frequencies (Li et al, 1998) or on the zeros and the poles of the transfer functions of a flexible link (Parks & Pak, 1991). To validate the models of multilink flexible manipulators, experimental frequency response results are generally compared to linearized model responses (Nicosia et al, 1996) or to simplified model responses (Book & Obergfell, 2000;Stanway et al, 1998).…”