Flatness-based open and closed-loop control of a flexible beam system

Open and closed-loop flatness-based tracking control of flexible beams is considered. A rotating beam system is modeled using an Euler-Bernoulli partial differential equation. Flatness is used to derive an open-loop control by introducing a so-called flat output which parameterizes the system state and input in terms of an infinite series depending on the flat output and its time derivatives. The series are truncated to derive finite-dimensional state-space form system approximations for which linear estimated state feedback tracking laws are applied. A finite-element analysis model, required to simulate the performance of the proposed closed-loop design, is derived and implemented. Both open and closed-loop controls are successfully validated experimentally on a test stand. Generalization of the open-loop control for rotating beam systems with tip payload are presented, and a superposition-based open-loop control for a levitated beam is described.