Ramírez, Hector Miguel

Irreversible port-Hamiltonian systems (IPHS) are an extension of port-Hamiltonian systems (PHS) for irreversible thermodynamics which encompass a large class of thermodynamic systems that may contain reversible and irreversible phenomena. Energy shaping and damping injection are standard structure preserving passivity based control approaches which have proven to be very successful for the stabilization of PHS. However, in the case of irreversible thermodynamics, the non-linear nature of the systems make it non-trivial to apply these approaches for stabilization. In this paper we propose a systematic procedure to perform, in a first control loop, energy shaping by state modulated interconnection with a controller in IPHS form. Then, a second control loop guarantees asymptotic stability by the feedback of a new closed-loop passive output. The approach allows to stabilize IPHS while preserving the IPHS structure in closed-loop, allowing to interpret the closed-loop system as a desired thermodynamic system. The example of the continuous stirred tank reactor is used to illustrate the approach.

The linear quadratic regulator is a widely used and studied optimal control technique for the control of linear dynamical systems. It consists in minimizing a quadratic cost functional of the states and the control inputs by the means of solving a linear Riccati equation. The effectiveness of the linear quadratic regulator relies on the cost function parameters hence, an appropriate selection of these parameters is of mayor importance in the control design. Port-Hamiltonian system modelling arise from balance equations, interconnection laws and the conservation of energy. These systems encode the physical properties in their structure matrices, energy function and definition of input and output ports. This paper establishes a relation between two classical passivity based control tools for port-Hamiltonian systems, namely control by interconnection and damping injection, with the linear quadratic regulator. These relations allow then to select the weights of the quadratic cost functional on the base of physical considerations. A simple RLC circuit has been used to illustrate the approach.