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State feedback control of a car and beam prototype

Camargo Lucas Carvalho, Bispo Victor Hugo Souza, Alves Uiliam Nelson Lendzion Tomaz, Ribeiro Fernando Sabino Fonteque, Breganon Ricardo

International Journal of Applied Mechanics and Engineering

2024

Vol. 29, no. 2

26--38

The Car and Beam prototype is a teaching piece of equipment, inspired by Ball and Beam systems. It consists of a beam supported in its center by means of a rotating axis installed in two rolling bearings, allowing the beam to rotate through the actuation of a servo motor. A car is coupled to this beam, and its displacement is measured using a linear encoder. This paper focuses on two key aspects: firstly, it offers a mathematical model of the Car and Beam system, and secondly, it outlines the development of a state-feedback tracking controller through pole placement to this system. To validate the modeling and control approach, we present simulation and experimental results using three different reference profiles: step, square wave, and sine wave. Our findings demonstrate the effectiveness of the control strategy in tracking predefined trajectories, both in simulation and with the physical prototype. In conclusion, this study highlights the efficacy of the methodology employed for mathematical modeling and the controller's design in the context of this specific application. The results indicate promising potential for further exploration in this domain.