(Dr. William Singhose, advisor)

"Methods for Generating Deflection-Limiting Commands"

Abstract

Control of flexible systems is a challenging problem. Many methods have been developed to limit the residual vibration of these flexible systems, but in many cases, the large transient deflections can degrade the overall system performance. Recently, new classes of deflection-limiting commands have been developed to control both the residual vibration and transient deflection of flexible systems. These commands are limited only in the difficulties encountered when trying to create them. The optimal solution for the nonlinear constraint equations is sensitive to local minima and depends greatly on the initial guess.

This thesis details two methods used to create deflection-limiting commands. The first method uses an algorithm that produces the initial guesses for the optimization routine. Using the new initial guesses avoids the problem of sensitivity to local minima and assures convergence to the time-optimal, or nearly time-optimal, solution. The second method creates the shaper in the digital rather than the continuous domain. Working in the digital domain allows for a linearization of the problem, which greatly simplifies the optimization.