Limit Cycle Identification in Nonlinear Polynomial Systems

Limit Cycle Identification in Nonlinear Polynomial Systems

We present a novel formulation, based on the latest advancement in polynomial system solving via linear algebra, for identifying limit cycles in general n-dimensional autonomous nonlinear polynomial systems. The condition for the existence of an algebraic limit cycle is first set up and cast into a Macaulay matrix format whereby polynomials are regarded as coefficient vectors of monomials. This...

Identification of nonlinear systems using Polynomial Nonlinear State Space models

Limit Cycle Prediction in Multivariable Nonlinear Systems Using Genetic Algorithms

This paper presents an intelligent method based on multiuobjective genetic algorithm (MOGA) for prediction of limit cycle in multivariable nonlinear systems. First we address how such the systems may be investigated using the Single Sinusoidal Input Describing Function (SIDF) philosophy. The extension of the SIDF to multi loop nonlinear systems is presented. For the class of separable nonlinear...

Identification of One Class Nonlinear Systems with Closed Cycle

Structural and parametric identification of the nonlinear systems with a closed cycle on the set of continuous block-oriented models with feedback is considered. The method of the structural identification in the steady state based on the observation of the system's input and output variables at the input periodic influences is proposed. The solution of the parameter identification problems, wh...

Evaluation of the Centre Manifold Method for Limit Cycle Calculations of a Nonlinear Structural Wing

In this study the centre manifold is applied for reduction and limit cycle calculation of a highly nonlinear structural aeroelastic wing. The limit cycle is arisen from structural nonlinearity due to the large deflection of the wing. Results obtained by different orders of centre manifolds are compared with those obtained by time marching method (fourth-order Runge-Kutta method). These comparis...