Control of flexible manipulators via serial-to-parallel transformation

It is shown that structure parameters of a flexible manipulator can be virt ually adjusted via tip-displacement feedback. By rearranging the structure parameters, transient performance can be significantly enhanced with the he lp of a collocated PD law. A procedure is developed to transform a lumped-p arameter flexible arm into a set of simple mass-spring pairs connected in p arallel to the base. The effect of tip-displacement feedback on each substr ucture can be visualized through this serial to-parallel transformation, an d the gain margin be readily found. It is seen that proportional feedback o f the tip displacement virtually scales up or down each of the lumped masse s and the lumped springs. A case study is provided to illustrate the design procedure and to demonstrate the performance of the proposed scheme.