S. Cetinkunt et Wl. Yu, ACCURACY OF FINITE DIMENSIONAL DYNAMIC-MODELS OF FLEXIBLE MANIPULATORS FOR CONTROLLER-DESIGN, Journal of robotic systems, 9(3), 1992, pp. 327-350
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.