Two-wheeled self-balancing car, modeling, nonlinear system simulation and linearization

Authors

DOI:

https://doi.org/10.5902/2179460X87047

Keywords:

Signals and systems, Control theory, Nonlinear system, Linearization, Simulation

Abstract

Applying the signals and systems theory and control theory studied in electrical engineering and mechanical engineering courses requires sophisticated, expensive and delicate handling devices. The mathematical tools that are taught in the disciplines of signals and systems and control theory in the undergraduate course are often abstract, especially in terms of practical application in an industrial setting, which makes it necessary to use didactic control plants to complement teaching and hands-on experimentation. This paper presents a low-cost two-wheeled self-balancing car system as a teaching tool for engineering. The two-wheeled self-balancing car is a dynamic benchmark system designed to control the car in a vertical position. The car is able to remain balanced through calculations that analyze the angle of the gyroscope and the position of the wheels. DC motor drivers are used to compensate for tilt and balance the car. As the purpose of the article is to serve as support material for undergraduate students who are taking their first steps in the study of signals and systems and control theory, detailed modeling by the laws of physics are presented, together with the simulation of the nonlinear model of the system and a complete linearization of the model.

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Author Biographies

Pedro Henrique Rodrigues da Rosa, Universidade Federal de Santa Maria

Electrical Engineering student, Federal University of Santa Maria - Cachoeira do Sul

Vandrei Rubin Steffanello, Universidade Federal de Santa Maria

Electrical Engineering student, Federal University of Santa Maria - Cachoeira do Sul

André Caldeira, Universidade Federal de Santa Maria

He has a technical degree in Industrial Informatics from E.T. Juscelino Kubitschek (1999) and electromechanics from CFP - Usiminas (minor apprentice) (1999). Degree in Electrical Engineering from Centro Universitário do Leste de Minas Gerais (2007). Master's degree from the CEFET-MG/UFSJ postgraduate program, in which research was carried out in the area of robust control, in particular dealing with stability analysis and the design of H-infinite controllers for systems with a delay in the state vector using convex optimization (LMI's) and non-convex optimization. PhD from the postgraduate program of the Department of Automation and Systems (DAS) at the UFSC teaching institution and the École Doctorale Electronique, Electrotechnique, Automatique, Traitement du Signal - (EEATS), Genoble Images Parole Signal Automatique (Gipsa) laboratory, Université Grenoble Alpes (UGA) in which research was carried out on systems governed by first-order hyperbolic partial differential equations in Riemann Coordinates, contour control of first-order hyperbolic systems, singular systems, systems with delay in the state vector, 2-D singular systems (Roesser, Fornasini-Marchesini and Geral) and local stability analysis (estimation of the region of attraction) and robust control of quadratic nonlinear systems with input delay.

Charles Rech, Universidade Federal de Santa Maria

PhD in Mechanical Engineering, Professor of Mechanical Engineering, Federal University of Santa Maria - Cachoeira do Sul.

Cristiano Frandalozo Maidana, Universidade Federal de Santa Maria

PhD in Mechanical Engineering, Professor of Mechanical Engineering, Federal University of Santa Maria - Cachoeira do Sul.

Simone Ferigolo Venturini, Universidade Federal de Santa Maria

Master in Mechanical Engineering, Professor of Mechanical Engineering, Federal University of Santa Maria - Cachoeira do Sul

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Published

2024-11-08

How to Cite

Rosa, P. H. R. da, Steffanello, V. R., Caldeira, A., Rech, C., Maidana, C. F., & Venturini, S. F. (2024). Two-wheeled self-balancing car, modeling, nonlinear system simulation and linearization. Ciência E Natura, 46(esp. 3), e87047. https://doi.org/10.5902/2179460X87047

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