Control design for thermodynamic systems on contact manifolds

We consider the problem of feedback control design for thermodynamic systems. Following past contributions, we consider the expression of closed-loop control in the Thermo-dynamic Phase Space (TPS) using contact geometry. Some of these past contributions identified restricted classes of admissible controllers by restricting the dynamics to a Legendre submanifold in the TPS. In this paper, we consider the problem of controlling a system through damping feedback control. By allowing this particular class of feedback design technique, we characterize the impact of control on the thermodynamic structure of the closed-loop system in the TPS. An example is considered to illustrate the proposed construction.