(Dr. William Singhose, advisor)

"Using Input Shaping to Optimize Point-to-Point Motions in PD Controlled Systems with Coulomb Friction"

Abstract

PD controlled systems with Coulomb friction are examined with the objective of optimizing point-to-point motion by varying the controller gains and input shaping the reference command. Specifically, the goal is to minimize percent overshoot, time to stick, and steady-state error. Coulomb friction adds non-linearity to the system dynamics that changes the shape of the response and creates a steady-state error. Increasing the proportional gain is typically used as a means of decreasing the steady-state error. However this often leads to the undesirable effects of increased vibration. Input shaping is a means of eliminating vibration from system response, but traditional input shaping techniques do not account for the non-linear effects of Coulomb friction. This study found an algorithm for creating a two-step command that would minimize time to stick and percent overshoot for any set of system parameters. These concepts were experimentally verified on a gantry robot.