Evolutionary Search for Limit Cycle Prediction in Multivariable Nonlinear Systems

A feature of many practical control systems is a Multi-Input Multi-Output (MIMO) interactive structure with one or more gross nonlinearities. A primary design task in such circumstances is to predict and eventually ensure the avoidance of limit cycling conditions. This paper outlines how such a system may be investigated using the Single Sinusoidal Input Describing Function (SIDF) philosophy. A numerical search based on a multi-objective formulation is outlined for the direct solution of the harmonic balance system matrix equation. The search is based on an intelligent Genetic Algorithm (GA) that is capable of predicting specified modes of theoretical limit cycle operation. An advantage of this method is that GA can be directed to search for all possible solutions including sub-harmonic components that are ignored in the derivation of the SIDF. Furthermore the method is capable of quantifying the magnitude, frequency and the phase of the limit cycles as well as the loop interaction effects in the frequency domain which proves useful in any subsequent controller design. A Multi-Objective Genetic Algorithm (MOGA) program is used where the search parameters as well as other GA parameters can be tuned easily and interactively. The program allows user to monitor search progress and implement trade offs between the conflicting objectives when necessary. The search space of GA is the magnitude (for each loop), frequency and the phase between the loops of limit cycle (if any). The dimension of search can be relatively large for systems with more than two inputs, however if the search is directed appropriately and the parameters of GA are fine tuned the MOGA will be globally converge in a reasonable and acceptable computation time

کلیدواژه ها:

Limit cycle ، MOGA ، Describing Function ، MIMO ، Nonlinear Control