Abstract

In this work, we use a Mamdani fuzzy controller based on fuzzy rules that represent position and velocity of a particle for a free mechanical vibration model. Here, we focus on three major cases: the harmonic oscillator, the damped vibration, and the negative damping case. This study combines classical numerical methods for ordinary differential equations and fuzzy rule-based systems to describe the dynamical interaction between the position and velocity. In this regard, we propose a p-fuzzy system to study this phenomenon. Computational simulations reveal that the solution of the proposed p-fuzzy system is similar to the corresponding analytic solution of the classical free mechanical vibration problems.