Motion control of flexible beams is a well-studied problem, motivated by applications in space robotics and manufacturing, where fast and accurate positioning of manipulators is critical. These manipulators are usually designed to be as slender as possible to reduce mechanical inertia, leading the system to exhibit significant vibration and degrading performance.
This work employs the tools of differential flatness and distributed-parameter systems to address the issue. An overview of flatness and its extension to infinite-dimensional systems is given. The flexible beam is modeled from first principles, and its physical parameters experimentally identified. Using flatness, a smooth open-loop trajectory is computed, and a model-based closed-loop control is derived to track it despite disturbances and model uncertainty. A simulation framework based on the finite-element method is developed and experimentally validated. The last part develops a generalized beam model, and demonstrates motion planning for a magnetically levitated multi-input beam.
The material presented should be useful to anyone interested in the application of differential flatness to flexible beams.