ACCURACY OF FINITE DIMENSIONAL DYNAMIC-MODELS OF FLEXIBLE MANIPULATORS FOR CONTROLLER-DESIGN

The dynamics of mechanical systems with distributed flexibility are de scribed by infinite dimensional mathematical models, yet a real contro ller must be finite dimensional due to the limited bandwidth capabilit ies of the sensor-actuator system and real-time control computer hardw are. Therefore, simplified finite dimensional dynamic models must be o btained for the purpose of controller design. This article addresses t he issue of selecting the shape and number of mode functions in develo ping finite order models using a flexible robot arm as an example. The results of this work have consistently shown that the clamped-free mo de shape predicts the closed-loop system dynamics under a feedback con troller much more accurately than pinned-free mode shapes. However, as the hub inertia increases relative to the flexible beam inertia the d ifference between the clamped-free and pinned-free mode shape model pr edictions becomes smaller.