Energy-Based Control of Spatially-Discretized Distributed Port-Hamiltonian Systems

The main contribution of this paper is a procedure for the control by energy shaping of high-order port-Hamiltonian systems obtained from the spatial discretization of infinite dimensional dynamics. Beside the intrinsic difficulties related to the large number of state variables, the finite element model is generally given in terms of a Dirac structure and is completely a-causal, which implies that the plant dynamics is not given in standard inputstate-output form, but as a set of DAEs. Consequently, the classical energy-Casimir method has to be extended in order to deal with dynamical systems with constraints, usually appearing in the form of Lagrangian multipliers. The general methodology is illustrated with the help of an examples, i.e. an hinged-hinged Timoshenko beam with actuators at both sides.