Dynamic Analysis of Fuzzy Systems

Abstract

In this work, a new methodology for the dynamic analysis of non-linear systems is developed by applying the Mamdani fuzzy model. With this model, parameters such as settling time, peak time and overshoot will be obtained. The dynamic analysis of non-linear fuzzy systems with triangular membership functions is performed, and linguistic variables describing overly complex or ill-defined phenomena are used to fit the model. Scaling factors will simplify the modification of the variables, making them easier to find the system model. The specifications of second-order characteristics in the time domain, such as overshoot and peak time, will be represented graphically. As a case study, the proposed methods are implemented to analyse the dynamics of a tank and a simple pendulum for first-order and second-order systems, respectively, where it is observed that the proposed methodology offers highly positive results.