Flatness of heavy chain systems (Q2753214)

The paper deals with systems that consist of a fixed length heavy chain suspended from a cart moving along an horizontal line. The whole system is controlled by the motion of the cart. Various types of chains are considered: simple homogeneous chains and variable density chains with or without a weight attached to its free end. Under small angle approximations, these systems are described by one-dimensional partial differential wave equations. The resulting PDE control systems are shown to be flat by producing transformations that map the flat output (the trajectory of the free end of the chain) to the trajectory of the whole system. Since these transformations are given as explicit formulae, they are very useful for motion planning.