Modelling the Ball-and-Beam System From Newtonian Mechanics and from Lagrange Methods
Carlos G. Bolívar Vincenty
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Modelling the Ball-and-Beam System From Newtonian Mechanics and from Lagrange Methods | ||
| Published in: | Innovation in Engineering, Technology and Education for Competitiveness and Prosperity: Proceedings of the 12th Latin American and Caribbean Conference for Engineering and Technology | |
| Date of Conference: | July 21-24,2014 | |
| Location of Conference: | Guayaquil,Ecuador | |
| Authors: | Gerson Beauchamp Báez Carlos G. Bolívar Vincenty | |
| Refereed Paper: | #176 | |
Abstract: | ||
| The Ball and Beam is a system commonly used to expose undergraduate students to controller design. One important step of this design process is to develop a mathematical model to describe the behavior of the sytem. There are several possible methods for deriving the equations of motion of a dynamical system. These include Langrangian methods and Newtonian mechanics. Many authors fail to adequately derive the model for the Ball-and-Beam system because they obviate several acceleration terms. Although these terms do not affect the linear model, they are important for nonlinear simulations. When the model is derived from Euler-Lagrange methods, these terms appear naturally. In this paper it is demonstrated that the equations of motion obtained from both methods are identical. From the equation of motion, nonlinear state-space equations are developed. The nonlinear equations are then linearized about the equilibrium point and a transfer function suitable for a linear controller design is obtained. | ||