Automatic computation of polyharmonic balance equations for non-linear differential systems

International Journal of Control

Volumn 76, Issue 4, 2003, Pages 355-365

  Peyton Jones, J C ^a  

^a Villanova University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; HARMONIC ANALYSIS;

NON-LINEAR DIFFERENTIAL SYSTEMS;

NONLINEAR SYSTEMS;

EID: 0142168427     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/0020717031000079436     Document Type: Article

References (13)

1. BARRETT, J. F., 1965, The use of Volterra series to find the region of stability of a nonlinear differential equation. International Journal of Control, 28, 209-216.
2. BILLINGS, S. A., PEYTON JONES, J. C., 1990, Mapping nonlinear integro-differential equations into the frequency domain. International Journal of Control, 52, 863-879.
3. COOK, P. A., 1994, In M. J. Grimble (Ed.) Nonlinear Dynamical Systems Prentice Hall International Series in Systems and Control Engineering.
4. GELB, A., and VANDER VELDE, W. E., 1968, Multiple-input Describing Functions and Nonlinear System Design (New York: McGraw-Hill).
5. GLASS, J. W., and FRANCHEK, M. A., 2000, Frequency-based nonlinear controller design for regulating systems subjected to time-domain constraints. International Journal of Robust Nonlinear Control, 10, 39-57.
6. KAHLIL, H. K., 2001, Nonlinear Systems, 3rd edition (New York: Prentice Hall International).
7. LOZOWICKI, A., 1997, On application of the describing function method for optimization of feedback control systems. International Journal of Robust Nonlinear Control, 7, 911-933.
8. PEYTON JONES, J. C., 1995, Mapping nonlinear integro-differential equations to a generalised describing function form. International Journal of Control, 62, 1145-1160.
9. PEYTON JONES, J. C., and ÇANKAYA, I., 1999, The effect of a constant heeling moment on the main and superharmonic response of a ship in regular beam seas. Int. Shipbuilding Progress, 46, 165-187.
10. PEYTON JONES, J. C., ZHUANG, M., and ÇANKAYA, I., 1997, Symbolic computation of harmonic balance equations. International Journal of Control, 68, 449-460.
11. TAYLOR, J. A., 1998, Robust nonlinear control based on describing functions methods. Proceedings of the ASME Dynamics Systems Measurement and Control Division, Fairfield, NJ, USA, DSC-Vol. 64, pp. 539-546.
12. TOMLINSON, G. R., MANSON, G., LEE, G. M., 1996, A simple criterion for establishing an upper limit to the harmonic excitation level of the duffing oscillator using the Volterra series. Journal of Sound and Vibration, 190, 751-762.
13. WEINER, D. D., and SPINA, J. E., 1980, Sinusoidal Analysis and Modaaeling of Weakly Nonlinear Circuits (New York: Van Nostrand Reinhold Company).