Abstract
This paper presents a hybrid fuzzy-PD control scheme for an inverted pendulum pivoted to a wheeled cart. The angular position of the pendulum and displacement of the cart are considered as the outputs of the proposed system that can be controlled by an applied force to the cart. This force would lead to a linear motion of the cart along the X direction of the coordinate system. The nonlinear dynamic model is extracted on the basis of Newton–Euler formulation. After linearization of the obtained model, state-state representation would be obtained. In the next section, a hybrid fuzzy-PD controller is designed for stabilizing the inverted pendulum, in which, the controller parameters are tuned through the genetic algorithm. Hence, a cost function with the aim of minimizing the integral of time-multiplied square of the error (ITSE) over time is considered. The simulation results of the proposed hybrid fuzzy-PD controller for the studied inverted pendulum revealed the acceptable balancing of the system with the application of the force to the cart. Moreover, the system would be stable over time