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Exergy and Entropy Thermodynamic Concepts for Nonlinear Control Design

[+] Author Affiliations
Rush D. Robinett, III, David G. Wilson

Sandia National Laboratories

Paper No. IMECE2006-15205, pp. 119-128; 10 pages
doi:10.1115/IMECE2006-15205
From:
  • ASME 2006 International Mechanical Engineering Congress and Exposition
  • Dynamic Systems and Control, Parts A and B
  • Chicago, Illinois, USA, November 5 – 10, 2006
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 0-7918-4768-3 | eISBN: 0-7918-3790-4
  • Copyright © 2006 by ASME

abstract

This paper develops a novel control system design methodology that uniquely combines: concepts from thermodynamic exergy and entropy; Hamiltonian systems; Lyapunov's direct method and Lyapunov optimal analysis; electric AC power concepts; and power flow analysis. Relationships are derived between exergy/entropy and Lyapunov optimal functions for Hamiltonian systems. The methodology is demonstrated with two fundamental numerical simulation examples: 1) the classic van der Pol nonlinear oscillator system and 2) a Multi-Input-Multi-Output (MIMO) planar 2 Degree-Of-Freedom (DOF) robot that employs PID tracking control. The control system performances and/or appropriately identified terms are partitioned and evaluated based on exergy generation and exergy dissipation terms. Traditionally, almost all modern control design is based on forcing the nonlinear systems to perform and behave like linear systems, thus limiting its maximum potential. These are also known as mainly passive-type control systems. This novel nonlinear control methodology results in both necessary and sufficient conditions for stability of nonlinear systems.

Copyright © 2006 by ASME
Topics: Entropy , Exergy , Design

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