Infinite Dimensional Pole Optimization Control Design for Flexible Structures Using the Transfer Matrix Method

Abstract

This paper presents an approach to control design for flexible structures based on the transfer matrix method (TMM). The approach optimizes the closedloop pole locations while working directly on the infinitedimensional TMM model. The approach avoids spatial discretization, eliminating the possibility of modal spillover. The design strategy is based on an iterative process of optimizing the closedloop pole locations using a NelderMead simplex algorithm and then performing hardwareintheloop experiments to see how the pole locations are affecting the closedloop step response. The evolution of the cost function used to optimized the pole locations is discussed. Contour plots (three dimensional Bode plots) in the complex splane are used to visualize the pole locations. A computationally efficient methodology for finding the closedloop pole locations during the optimization is presented. The technique is applied to a singleflexiblelink robot and experimental results show that the optimization procedure improves upon an initial, Bodebased compensator design, leading to a lower settling time.