Explicit port-Hamiltonian formulation of bond graphs with dependent storages

Explicit port-Hamiltonian systems (PHSs) are the starting point for many
powerful controller and observer design methods. It is well-known that explicit PHSs can be
formulated on the basis of bond graphs. Indeed, the port-Hamiltonian formulation of bond
graphs without dependent storages has been well investigated. However, little effort has been
made towards bond graphs with dependent storages. This is a problem as dependent storages
frequently occur in models from many engineering fields. In this paper, we address the explicit
port-Hamiltonian formulation of bond graphs with dependent storages. Our idea is to express the
port-Hamiltonian dynamics and output as functions of only the system inputs and independent
storages. The main result is a rigorous and constructive method to formulate bond graphs
containing dependent storages as explicit PHSs. An acadamic example illustrates and verifies
our method.