On the feedforward control problem for discretized port-Hamiltonian systems

The boundary feedforward control problem for a class of distributedparameter port-Hamiltonian systems in one spatial dimension is addressed. The considered hyperbolic systems of two conservation laws (with dissipation) are discretized in the spatial coordinate using an energy-based, structure preserving discretization scheme. The resulting finite-dimensional approximate state representation has a feedthrough term which allows to directly express the differential equation for the inverse dynamics. The inverse system needs to be solved in order to determine the control inputs for given desired output trajectories. For non-collocated pairs of boundary inand outputs the magnitude of dissipation determines whether the inverse discretized models are stable or not. In the unstable case, the problem at hand can be attacked with classical approaches for the dynamic inversion of nonminimum phase systems.