Experimental Evidence for Chaotic Response in a Feedback System

Abstract

In this paper, the dynamics of a one-degree-of-freedom mechanical positioning device with nonlinear stiffness and linear feedback are described. Experimental results show that chaotic dynamics can result due to an increase in control gain or shuttle frequency. Adding sufficient damping through velocity feedback gain, however, eliminated the chaos. In some chaotic motions, a one-dimensional delay map was obtained from the experimental time samples. The map was modeled by a piecewise linear function, which suggested that the third-order system might be modeled by a lower dimensional equation.