Closed-Loop Displacement Control of a One-Link Flexible Arm with a Tip Mass

Abstract

A theoretical and experimental study is presented for the displacement control of a one-link flexible arm with an end-point payload, The tip displacement of the arm is measured by a gap sensor fixed in space and controlled by a D. C. motor located at the other end of the arm, where the motor is driven by a feedback signal composed of the tip displacement and the velocity. As an example, the problem of shifting the end-point of the arm from its initial position to the commanded position by the amount of w^*_d is considered. Solutions derived by applying the method of the Laplace transform to the governing equations are calculated by the method of numerical inversion. Experimental results are obtained and compared with the theoretical ones, showing both results in good agreement for a wide range of parameters.