Flatness-based control of a Timoshenko beam

An open loop control for a clamped Timoshenko beam, driven by a boundary torque, is presented. With the proposed method finite time transitions between two steady states can be achieved. The solution of the PDE is obtained using Mikusinski operators. The time dependent functions corresponding to the operators have compact support and can be represented using infinite series. When parametrizing the system by a flat output, the system trajectories can be written as definite integrals.