Energy shaping and interconnection and damping assignment control in the bond graph domain

This paper presents an interpretation in the Bond Graph domain of the Energy Shaping and Interconnection and Damping Assignment control methods, developed for the well-known Port-Controlled Hamiltonian Systems with Dissipation. In order to have a stable equilibrium at a prespecified state, the energy function is modified by adding storage elements to the BG such that the closed-loop system energy has a minimum at that state. A new dissipation function is assigned changing the R-field and its interconnection with the rest of the Bond Graph. A desired power conserving interconnection structure is reached through the suitable insertion of power bonds among junctions. Energy shaping, interconnection and damping assignment are performed in a so called Target Bond Graph. The control law is determined by a set of partial differential equations derived from the plant and the Target Bond Graph.