An approach for determining the characteristics of limit cycles in higher order systems with multiple nonlinearities is described. This method utilizes sinusoidal input describing functions to convert the nonlinear problem to an eigenvalue problem. A search procedure employing eigenvalue derivatives finds limit cycle conditions, when they exist. This technique is relatively efficient and reliable and able to treat problems with strong nonlinearities such as Coulomb friction or relays. Two applications are presented, a mechanical servo positioner system and a railway bogie dynamics problem. Comparison of results with simulation is made.
An Equivalent Linearization Algorithm for Nonlinear System Limit Cycle Analysis
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Abel, S. G., and Cooperrider, N. K. (June 1, 1985). "An Equivalent Linearization Algorithm for Nonlinear System Limit Cycle Analysis." ASME. J. Dyn. Sys., Meas., Control. June 1985; 107(2): 117–122. https://doi.org/10.1115/1.3149682
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