Nonlinear Compensation for Flexible Manipulators

Abstract

This paper presents an analysis on the use of nonlinear feedback to control the tip position of a single-link flexible manipulator. This form of feedback uses products of state variables to obtain a lightly damped system in the beginning of a step response and a more heavily damped system when it is close to the steady state position. This scheme results in faster rise and settling times than those obtained with an optimal linear controller while maintaining a comparable amount of control effort. The model used in the analysis is a single Bernouli-Euler beam moving in a horizontal plane, considering only a rigid mode plus two vibrating modes. A heuristic method to tune the nonlinear feedback gains is proposed. This method results in a design that, compared to a linear optimal controller, reduces the settling time by 32 percent without increasing the percent overshoot.