Manifold stabilization and path-following control for flat systems with application to a laboratory tower crane

This paper deals with the stabilization of manifolds for flat systems. Path-following control results as the special case of stabilizing a manifold with dimension one. The target manifold is defined in terms of the components of the flat output. A control strategy is developed which achieves the following objectives. Firstly, the error dynamics, which describe the deviation of the output from the target manifold, are to be asymptotically stabilized. Therefore, if the system is initialized such that all states of the error dynamics are zero, the invariance property holds. This means that in the nominal, undisturbed case the output of the system does not leave the target manifold for all future times. A further objective is that the movement of the system on the target manifold can be appropriately controlled. The degrees of freedom of this movement are given by the dimension of the manifold. Some nice features are gained by the restriction to flat systems. Amongst others, the controller which achieves the objectives of stabilization, invariance, and movement on the manifold can always be calculated in a systematic way. To this end, the equivalence of flat systems to linear controllable ones is exploited. The presented control methodology is applied to a laboratory experiment of a tower crane. The experimental results underline the feasibility of the proposed concept.