STABILITY OF CONVENTIONAL CONTROLLER-DESIGN FOR FLEXIBLE MANIPULATORS

The paper investigates the independent joint control of flexible manip ulators which are acted upon by gravity. Both finite-dimensional coord inates, and infinite-dimensional, spatially varying, distributed coord inates are used to describe the deformation of the flexible links. The effects of the flexibility on the closed-loop system behavior in the presence of both derivative and integral feedback control are studied both in the Laplace transform domain using the linearized model of the original nonlinear system and in the time domain using the original n onlinear model. The use of infinite-dimensional coordinates is shown t o be especially effective in obtaining the frequency domain characteri stics of the linearized model because the exact frequency content of t he linearized system may be extracted without involving the difficult order reduction problem. The problem of convergence onto an incorrect solution which is associated with using the eigenvectors of a clamped- free beam as the comparison functions in approximating the motion of t he flexible arm is demonstrated and various factors affecting the perf ormance of the flexible manipulator, such as control gains and materia l damping, are studied.