Design of an Actuated Flexible Arm for Improved Vibration Properties

Abstract

In this paper, a multi-objective optimization index is introduced for improving the dynamic behavior of an actuated structurally flexible arm through geometric shape design. The improvement in the dynamic behavior is achieved by defining a vector optimization cost function. This cost function is associated with the frequency of the lowest system zero when joint angles are taken as outputs, the gain sensitivity of open-loop system modes, and the gain sensitivity of the closed-loop system modes at its transmission zeros. Moreover, a general relationship is obtained between the system pole and zero locations. In particular, it is shown that the magnitude of each system zero is smaller than a corresponding flexural mode and thus the smallest zero always occurs before the smallest pole and should therefore be considered in structural shape design. The design method is applied for finding an optimized structural shape for a single-link flexible arm. The optimized link is shown to yield superior robustness and performance characteristics in a closed-loop system when compared to the non-optimized uniform link. Thus, simpler control schemes can be utilized for the optimized flexible-link system compared to the non-optimized case.