Chaotic dynamics and control of nonlinear and flexible arm robotic devices.

摘要

Dynamical behavior and control of high speed robotic type mechanisms is the main focus of this dissertation with the major emphasis on the existence of chaotic oscillations associated with stiffness, Coriolis, inertia, and centripetal nonlinearities.;In the one degree of freedom problem, experimental and numerical results provided evidence that upon increasing the desired cycle frequency and or proportional control gain, the possibility of chaotic output, even when the input control was deterministic, would increase. Adding proper damping through velocity feedback gain, however, eliminated chaos and resulted in the positioning of the motion. In some cases, 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 three dimensional system could be modeled by a lower dimensional equation.;The work in part two which considered a flexible arm robotic device undergoing planar motion, was an extension of studies on the one dimensional system discussed in part one. Numerical studies in this case, indicated the presence of chaotic behavior. The routes to chaos contained subharmonic bifurcations and quasi-periodic motions. The chaotic motions occurred when the cyclic forcing frequency or amplitude were increased. Although the numerical model revealed similar qualitative behaviors as the experiment, chaotic solutions were not observed in the experiment due to the limitations of the apparatus. However, other nonlinear oscillations were observed in the experiments such as: subharmonic, quasi-periodic, and combination resonances. These phenomena were successfully predicted by analysis.;The two variable expansion perturbation scheme was used to describe the motions at internal and primary resonances. The perturbation solutions showed the existence of a jump phenomenon at the primary resonance when 2:1 internal resonance prevailed. This phenomenon was observed in the experiment, hence, proving the accuracy of the perturbation solution.;The work is divided into two catagories. In the first part the behavior of a one degree of freedom mechanical positioning device with nonlinear stiffness, subject to linear feedback, is described. In the second part, the effects of kinematic nonlinearities such as inertia, coriolis, and centripetal forces, on the motion of a multi-degree of freedom high speed flexible arm robot, is considered.;The chaotic vibrations which limited the upper frequency of operation were eliminated with feedback control.