Accuracy of finite dimensional dynamic models of flexible manipulators for controller design

Abstract

Abstract The dynamics of mechanical systems with distributed flexibility are described by infinite dimensional mathematical models, yet a real controller must be finite dimensional due to the limited bandwidth capabilities of the sensor‐actuator system and real‐time control computer hardware. Therefore, simplified finite dimensional dynamic models must be obtained for the purpose of controller design. This article addresses the issue of selecting the shape and number of mode functions in developing finite order models using a flexible robot arm as an example. The results of this work have consistently shown that the clamped‐free mode shape predicts the closed‐loop system dynamics under a feedback controller much more accurately than pinned‐free mode shapes. However, as the hub inertia increases relative to the flexible beam inertia the difference between the clamped‐free and pinned‐free mode shape model predictions becomes smaller.