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 element of any general form, the harmonic balance equations are derived. A numerical search based on multiobjective genetic algorithm is addressed for the direct solution of the harmonic balance system matrix equation. The MOGA is employed to solve the multiobjective formulation and obtain the quantitative values for amplitude, frequency and phase difference of possible limit cycle operation. The search space of MOGA is the space of the possible limit cycle parameters, such as amplitudes, frequency and phase difference between the interacting loops. Finally computer simulation is performed to show how the analysis given in the paper is used to predict the existence of the limit cycle of the multivariable nonlinear systems.