Lumped Parameter Port-Hamiltonian Modeling and Order Reduction of Flexible Structures (I)

In this work, we consider a scalable lumped-parameter model of the flexible structure in the port-Hamiltonian framework. We then propose a structure-preserving model reduction approach in the contraction framework. The contraction framework facilitates performing model reduction not around an equilibrium point, but rather along a trajectory of the system. As the interconnection matrix and the dissipation matrix are constant for the discretized model, the variational system provides the flexibility to preserve the port-Hamiltonian structure for the reduced-order model along a trajectory.