Regulation and vibration control of an FEM-based single-link flexible arm using sliding-mode theory

Compared to the assumed-mode method (AMM), the finite-element method (FEM) is not only more applicable to the modeling of various kinds of flexible structures but also better in estimating the natural frequencies. Motivated from these features and modified from the work of Yeung and Chen for an AMM-based model, the sliding-mode controller introduced in this paper is developed to deal with the regulation problem and vibration suppression of an FEM-based single-link flexible arm. This paper will focus on the issue of how to change the FEM-based model into a form similar to the AMM-based model via the Schur decomposition. A technique to measure the well-estimated state variables required for the control is also presented. Finally, numerical simulation results are given to verify the robustness of the modified sliding-mode controller against payload variation.