Port-controled Hamiltonian Systems

Port-controlled Hamiltonian Systems (PCHS) are the natural generalization of Hamiltonian mechanics to describe more general systems as they appear in control engineering. In particular, PCHS theory allows for the presence of control input/output signals of a special nature, the so called power ports, and also extends the Hamiltonian description to arbitrary domains (electrical, hydraulic, thermal) with dissipation, which is present in any real engineering system. PCHS are passive with respect to the port variables, which means that a PCHS evolves to certain kinds of stable orbits (normally stable equilibrium points) when ports are disconnected; this confers PCHS a built-in safety feature which can be very important in critical applications. Interconnecting several PCHS produces again a PCHS. PCHS theory is thus a natural framework for describing complex systems obtained as network interconnections of simpler subsystems. PCHS also yield themselves to a control technique, known as Passivity-Based Control and Injection Damping Assignment (IDA-PBC), which exploits the passive and interconnection properties described above.