Convergencia de la trayectoria lingüística en el espacio de estados de un Controlador Difuso aplicado a un Sistema No Lineal

This article presents the design of a fuzzy controller to stability analysis base on the convergence of the linguistic trajectory in the state of space, for an inverted car-pendulum system, the fuzzy controller is of the Mamdani type and, it consists of 25 rules, 3 input variables and each one is composed of five memberships functions. The inverted car-pendulum system is represented by a non-linear model, which is obtained from a linearized equivalent model under the consideration of small oscillations. Results are validated against a PID control base on the trajectory on the phase plane to evaluate the efficiency and effectiveness of the fuzzy controller. The dynamic behavior of the system of both controllers is obtained with a unit impulse input, the simulation of the control system is developed on the MATLAB / SIMULINK software using the FUZZY LOGIC TOOLBOX, which allows to perform test and simulations, and also it shows results of graphic form.