Abstract
Chapter 4 reviews the concepts of static stability, dynamic stability, eigenanalysis, and Lyapunov analysis required for the development of necessary and sufficient conditions for stability of a class of nonlinear systems, Hamiltonian natural systems. The combination of static stability of conservative systems and dynamic stability of adiabatic irreversible work processes in the form of exergy and entropy rate equations will be utilized to develop Hamiltonian Surface Shaping and Power Flow Control (HSSPFC).
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References
Meirovitch, L.: Methods of Analytical Dynamics. McGraw-Hill, New York (1970)
Robinett III, R.D., Wilson, D.G.: Collective systems: physical and information exergies. Sandia National Laboratories, SAND2007 Report (March 2007)
Robinett III, R.D., Wilson, D.G.: Exergy and irreversible entropy production thermodynamic concepts for nonlinear control design. Int. J. Exergy 6(3), 357–387 (2009)
Chetayev, N.G.: The Stability of Motion. Pergamon, Elmsford (1961)
Abramson, H.N.: An Introduction to the Dynamics of Airplanes. Ronald Press, New York (1958)
Ogata, K.: Modern Control Engineering. Prentice-Hall, Englewood Cliffs (1970)
Robinett III, R.D., Wilson, D.G.: What is a limit cycle? Int. J. Control 81(12), 1886–1900 (2008)
Lyapunov, A.M.: Stability of Motion. Academic Press, New York (1966)
LaSalle, J., Lefschetz, S.: Stability by Liapunov’s Direct Method with Applications. Academic Press, San Diego (1961)
Scanlan, R.H., Rosenbaum, R.: Aircraft Vibration and Flutter. Dover, New York (1968)
Anderson, J.D. Jr.: Introduction to Flight. McGraw-Hill, New York (1978)
Robinett III, R.D.: A unified approach to vehicle design, control, and flight path optimization. PhD Dissertation, Texas A&M University (1987)
Robinett III, R.D., Wilson, D.G.: Transient stability and control of renewable generators based on Hamiltonian surface shaping and power flow control: Part I—Theory. In: IEEE MSC Conference, Yokohama, Japan, September 2010
Robinett III, R.D., Peterson, B.J., Fahrenholtz, J.C.: Lag-stabilized force feedback damping. J. Intell. Robot. Syst. 21, 277–285 (1998)
Yechout, T.R., Morris, S.L., Bossert, D.E., Hallgren, W.F.: Introduction to Aircraft Flight Mechanics: Performance, Static Stability, Dynamic Stability, and Classical Feedback Control. AIAA, Washington (2003)
Saaty, T.L., Bram, J.: Nonlinear Mathematics. McGraw-Hill, New York (1964)
Robinett III, R.D., Wilson, D.G.: Exergy and irreversible entropy production thermodynamic concepts for control design: nonlinear systems. In: 14th Mediterranean Conference on Control and Automation, Ancona, Italy, June 28–30, 2006
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Robinett, R.D., Wilson, D.G. (2011). Stability and Control. In: Nonlinear Power Flow Control Design. Understanding Complex Systems. Springer, London. https://doi.org/10.1007/978-0-85729-823-2_4
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DOI: https://doi.org/10.1007/978-0-85729-823-2_4
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