Feedforward tracking control for non‐uniform Timoshenko beam models: combining differential flatness, modal analysis, and FEM

Abstract

AbstractThis paper considers the feedforward tracking control problem for flexible structures with spatially varying geometrical and material parameters. The design approach is illustrated for a Timoshenko beam model and is based on the Riesz spectral properties of the system operator, which allow to determine the modal system representation. This serves as the starting point for the derivation of an infinite‐dimensional inverse system description in terms of a so‐called flat output parameterizing modal states and input. Convergence of the resulting parameterizations can be ensured by appropriate motion planning. The feedforward control design methodology is further complemented to compute appropriate control commands directly from finite element approximations of the considered structure. As a result, feedforward tracking control design for flexible structures with complex geometry, boundary conditions, or material parameters can be performed within a general framework. Simulation scenarios for feedforward boundary control of a clamped‐free Timoshenko beam model with variable system parameters illustrate the usefulness of the approach.