Simulação de um sistema barra-bola com compensação em malha direta do peso da bola

Abstract

The ball-beam system consists of a beam and a ball that can roll along the beam according to its inclination, showing a non-linear behavior. The torque acting on the beam due to the weight of the ball accounts for a considerable part of the non-linear components of the ball-beam system. Therefore, this work aims to reduce the influence of the nonlinear terms on the system by designing and simulating a ball-beam system with feedforward compensation of the ball weight. Linearized models were used to design a linear cascade control system tuned by pole placement via prototype Bessel low-pass filter, resulting in a simplified control process and mathematical expressions for the system controller parameters. Simulation of the step responses of the nonlinear ball-beam system showed that the ball weight significantly affected the time response of the system, while the other nonlinear terms had no significant influence. Compensating the weight of the ball with an additional voltage signal in the electric motor resulted in a dynamic behavior nearly identical to the linearized model. It can be concluded that feedforward compensation of the ball weight was sufficient to meet the performance requirements and to increase the reliability of the linear control method in the ball-beam system.