M. Ghanekar et al., SCALING LAWS FOR LINEAR CONTROLLERS OF FLEXIBLE LINK MANIPULATORS CHARACTERIZED BY NONDIMENSIONAL GROUPS, IEEE transactions on robotics and automation, 13(1), 1997, pp. 117-127
When constructing large robotic manipulators or space structures, it i
s advisable to begin with a small-scale prototype on which to perform
the design, analysis, and debugging, To ensure that the results obtain
ed on the scale-model apply directly to the actual manipulator, it is
necessary that the prototype and the original robot are dynamically eq
uivalent. As an initial investigation, this paper examines the single
flexible link (SFL) manipulator, Dimensional analysis is used to ident
ify the nondimensional groups for the SPL. These groups are present in
the corresponding nondimensional equations of motion, which are also
derived, To account for inherent manufacturing imprecision, tolerances
are developed for the nondimensional groups, Scaling laws for continu
ous-time and discrete-time controllers are developed for dynamically e
quivalent SFL systems, These theoretical scaling laws are verified exp
erimentally for an H-infinity and a PD control strategy.