Scaling laws for linear controllers of flexible link manipulators characterized by nondimensional groups

When constructing large robotic manipulators or space structures, it is advisable to begin with a small-scale prototype on which to perform the design, analysis, and debugging. To ensure that the results obtained on the scale-model apply directly to the actual manipulator, it is necessary that the prototype and the original robot are dynamically equivalent. This paper examines the single flexible link (SFL) manipulator. Dimensional analysis is used to identify the nondimensional groups for the SFL. 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 continuous-time and discrete-time controllers are developed for dynamically equivalent SFL systems. These theoretical scaling laws are verified experimentally for an H_∞ and a PD control strategy