Flatness-based control of a horizontally moving erected beam with a point mass

A mechanism consisting of a horizontally moving cart that carries an erected flexible beam with a point mass - as occurring in placement machines or stacker cranes - is considered. An explicitly parametrized feed-forward control law is designed using a flatness-based approach. Nominally, this control law allows one to perform fast placement motions although avoiding residual oscillations at the arrival. The efficiency of this approach and sensitivity with respect to parametric uncertainties are investigated numerically using both finite element and finite difference models. An experimental set-up is presented and some experimental results demonstrate the usefulness of the approach.