A numerical method is presented for the limit cycle analysis of multiloop nonlinear control systems with multiple nonlinearities. Describing functions are used to model the first harmonic gains of the nonlinearities. Existence of a limit cycle is sought by driving the least damped eigenvalues to the imaginary axis. The evolution of the limit cycle is studied next as a function of a critical system-parameter. It is shown that by defining a suitable error function it is possible to use both eigenvalue as well as the eigenvector sensitivities to formulate a generalized Newton-Raphson method to solve simultaneously for the updates of state variable amplitudes in a minimum norm sense. Several case studies have been presented and the development of a numerical procedure to test the stability of the limit cycle has also been reported.
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September 1988
Research Papers
A New Algorithm for Limit Cycle Analysis of Nonlinear Control Systems
V. K. Pillai,
V. K. Pillai
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, Ariz. 85287
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H. D. Nelson
H. D. Nelson
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, Ariz. 85287
Search for other works by this author on:
V. K. Pillai
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, Ariz. 85287
H. D. Nelson
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, Ariz. 85287
J. Dyn. Sys., Meas., Control. Sep 1988, 110(3): 272-277 (6 pages)
Published Online: September 1, 1988
Article history
Received:
October 15, 1986
Online:
July 21, 2009
Citation
Pillai, V. K., and Nelson, H. D. (September 1, 1988). "A New Algorithm for Limit Cycle Analysis of Nonlinear Control Systems." ASME. J. Dyn. Sys., Meas., Control. September 1988; 110(3): 272–277. https://doi.org/10.1115/1.3152681
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