Ramírez, Hector Miguel

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.

An irreversible port-Hamiltonian system formulation of a class of piezoelectric actuator with non-negligible entropy increase is proposed. The proposed model encompasses the hysteresis and the irreversible thermodynamic changes due to mechanical friction, electrical resistance and heat exchange between the actuator and the environment. The electromechanical dynamic of the actuator is modeled using a non-linear resistive-capacitive-inductor circuit coupled with a mass-spring-damper system, while the non-linear hysteresis is characterized using hysterons. The thermodynamic behavior of the model is constructed by making the electromechanical coupling temperature dependent, and by characterizing the entropy produced by the irreversible phenomena. By means of numerical simulations it is shown that the proposed model is capable of reproducing the expected behaviors and is in line with reported experimental results.