Keywords: Hamiltonian mechanics, nonlinear systems, nonequilibrium thermodynamics, Lyapunov functions, exergy generation, exergy dissipation, irreversible entropy, nonlinear control, control design, power flow control
Exergy and irreversible entropy production thermodynamic concepts for nonlinear control design
This paper develops a novel nonlinear control system design methodology that uniquely combines: concepts from exergy and entropy; Hamiltonian systems; Lyapunov's direct method and optimal analysis; and power flow control analysis. Relationships are derived between exergy/entropy and Lyapunov optimal functions for Hamiltonian systems based on the recognition that the Hamiltonian is stored exergy. The control system stability and performance are partitioned and evaluated based on exergy generation and exergy dissipation terms. This control methodology results in both necessary and sufficient conditions for stability of a class of nonlinear systems as a result of the application of the second law of thermodynamics to the time derivative of the Hamiltonian. The methodology is demonstrated with numerical simulation examples.