Effort- and flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems

The geometric formulation of general port-Hamiltonian systems is used in order to obtain two structure preserving reduction methods. The main idea is to construct a reduced-order Dirac structure corresponding to zero power flow in some of the energy-storage ports. This can be performed in two canonical ways, called the effort- and the flow-constraint methods. We show how the effort-constraint method can be regarded as a projection-based model reduction method. Both the effort- and flow-constraint reduction methods preserve the stability and passivity properties of the original system, as a consequence of preserving the port-Hamiltonian structure.