Port-thermodynamic systems and the assignment of their structure by feedback

In this paper we consider the feedback equivalence of homogeneous Hamiltonian control systems. These systems are Hamiltonian control systems which are generated by Hamiltonian drift (autonomous) and control Hamiltonian functions that are homogeneous of degree 1 in the momentum variables, and arise in the Hamiltonian model structure of open thermodynamic systems. It may be shown that the homogeneity conditions can be translated as the invariance of the Liouville 1form. We consider the problem of characterizing classes of state feedbacks for which the closed-loop system is again Hamiltonian and leaves invariant some closed-loop 1-form. In the case when the open- and closed loop 1-forms differ by an added 1-form which is exact, we derive matching equations between the generating function of the added 1-form and the added Hamiltonian function. This approach is applied to the simple example of a non-isothermal mass-spring-damper system.

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