Análise e projeto de um sistema Ball and Beam

Abstract

This work presents the development, implementation, and analysis of an experimental Ball and Beam platform, a classic control system used for the study of unstable and nonlinear systems. The central objective was to design a didactic bench capable of integrating concepts of mathematical modeling, electronic instrumentation, and digital control, resulting in a highly efficient tool for academic applications. The methodology was based on the phased development of projects, starting with me chanical design via CAD software and manufacturing by precision processes (CNC and 3D printing). In terms of hardware, the architecture was structured around the Arduino Mega 2560 microcontroller, using a VL53L1X laser sensor (ToF) for position feedback and a high-torque servomotor for actuation. The mathematical modeling of the system was deduced from Newton’s Laws, incorporating the experimental determination of the static friction coefficient and the application of second-order IIR digital filters for conditioning the reading signals. The control strategy was based on the digital PID algorithm, whose initial tuning was performed using the analytical and experimental Ziegler-Nichols method During the tests, it was identified that the marginal stabilization of the system occurred with a critical gain of 1.47 and a period of 3.5 s. Although the theoretical parameters served as a basis, fine adjustments were necessary to mitigate the effects of actuator saturation and the nonlinearities of the physical plant. The results demonstrate that the platform achieved satisfactory performance, exhibiting stability, repeatability, and precision in the positioning of the sphere. It is concluded that the developed system is an effective tool for the practical demonstration of control phenomena, successfully fulfilling the established design and performance requirements.