Funnel control for a moving water tank

Abstract

We study tracking control for a moving water tank system, which is modelled using the Saint-Venant equations. The output is given by the position of the tank and the control input is the force acting on it. For a given reference signal, the objective is to achieve that the tracking error evolves within a prespecified performance funnel. Exploiting recent results in funnel control we show that it suffices to show that the operator associated with the internal dynamics of the system is causal, locally Lipschitz continuous and maps bounded functions to bounded functions. To show these properties we consider the linearized Saint-Venant equations in an abstract framework and show that it corresponds to a regular well-posed linear system, where the inverse Laplace transform of the transfer function defines a measure with bounded total variation.Comment: 11 page