R.D. Robinett III and D.G. Wilson (USA)
Thermodynamics, nonlinear control, exergy, entropy, Lya punov
This paper1 develops a novel control system design methodology that uniquely combines: concepts from ther modynamic exergy and entropy; Hamiltonian systems; Lyapunov’s direct method and Lyapunov optimal analy sis; electric AC power concepts; and power flow analy sis. Relationships are derived between exergy/entropy and Lyapunov optimal functions for Hamiltonian systems. The methodology is demonstrated with two fundamen tal numerical simulation examples: 1) a Duffing oscilla tor/Coulomb friction nonlinear model that employs PID regulator control and 2) a van der Pol nonlinear oscillator system. The control system performances and/or appropri ately identified terms are partitioned and evaluated based on exergy generation and exergy dissipation terms. This novel nonlinear control methodology results in both nec essary and sufficient conditions for stability of nonlinear systems.
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