Stability of Conventional Controller Design for Flexible Manipulators

Abstract

The paper investigates the independent joint control of flexible manipulators which are acted upon by gravity. Both finite-dimensional coordinates, and infinite-dimensional, spatially varying, distributed coordinates 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 nonlinear model. The use of infinite-dimensional coordinates is shown to be especially effective in obtaining the frequency domain characteristics of the linearized model because the exact frequency content of the 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 the flexible arm is demonstrated and various factors affecting the performance of the flexible manipulator, such as control gains and material damping, are studied.